# Assistant conversation LRABR4 - Canonical URL: - Resource IRI: - Type: assistant conversation - Mode: quick ## Transcript ### 1. User look through these scientific papers paying attention to units, quantities, etc, and gather the ones you find, especially the more interesting domain specific ones ### 2. Assistant tool calls #### Tool call: `list_documents` ```json {} ``` ### 3. Tool result: list_documents FOLDERS - Living Structure, Wholeness & Beauty - Procedural Generation & Co-Creation - Roads, Trails & Movement - Terrain, Hydrology & Erosion - Water Simulation & Rendering Living Structure, Wholeness & Beauty (8) - #MH5J8D Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure - 2025 | Bin Jiang | AI | 12 pp. | doi:10.3390/ai6040074 Micro abstract: Presents Beautimeter, a GPT-based tool that scores buildings and urban scenes against Christopher Alexander’s 15 properties of living structure to assess their coherence and beauty. - #XW22YY Generative Codes: The Path to Building Welcoming, Beautiful, Sustainable Neighborhoods - 2005 | Brian Hanson, Christopher Alexander, Maggie Moore Alexander, Michael Mehaffy, Randall Schmidt | Center for Environmental Structure | 21 pp. Micro abstract: Argues that living neighborhoods arise from generative codes: ordered, participatory steps that let buildings and public spaces unfold from local people, land, and context. - #SKRF4C Geography as a Science of the Earth’s Surface Founded on the Third View of Space - 2022 | Bin Jiang | Annals of GIS | 14 pp. | doi:10.1080/19475683.2021.1966502 Micro abstract: Recasts geography around an organismic view of space, using scaling and spatial dependence to understand—and deliberately create—places with greater living structure. - #PXG56P Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole - 2009 | Christopher Alexander | Unpublished manuscript | 66 pp. Micro abstract: Proposes harmony-seeking computation as a creative process that repeatedly strengthens latent centers in a configuration while preserving and deepening the larger whole. - #MJKTBB Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space - 2023 | Bin Jiang, Chris de Rijke | Annals of the American Association of Geographers | 19 pp. | doi:10.1080/24694452.2023.2178376 Micro abstract: Measures an image’s structural beauty by recursively extracting its nested substructures, revealing a compact hierarchy that also captures visual saliency. - #3XSLTA Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image - 2021 | Bin Jiang, Chris de Rijke | Journal of Imaging | 15 pp. | doi:10.3390/jimaging7050078 Micro abstract: Proposes a quantitative measure of structural beauty based on how many substructures an image contains and how strongly they form a hierarchy across scales. - #ZU8GZV Structure-Preserving Transformations - 2002 | Christopher Alexander | The Nature of Order, Book Two: The Process of Creating Life | 4 pp. | doi:10.2307/j.ctv27ftw6c.5 Micro abstract: Explains structure-preserving transformations: incremental changes that extend the centers and relationships already present in a place rather than weakening its wholeness. - #BYG3BQ Wholeness as a Hierarchical Graph to Capture the Nature of Space - 2015 | Bin Jiang | International Journal of Geographical Information Science | 14 pp. | doi:10.1080/13658816.2015.1038542 Micro abstract: Models spatial wholeness as a hierarchical graph of mutually reinforcing centers, using PageRank and scaling depth to quantify the life of parts and wholes. Procedural Generation & Co-Creation (6) - #4TH488 Explainable AI for Designers: A Human-Centered Perspective on Mixed-Initiative Co-Creation - 2018 | Antonios Liapis, G. Michael Youngblood, Jichen Zhu, Rafael Bidarra, Sebastian Risi | 2018 IEEE Conference on Computational Intelligence and Games (CIG) | 8 pp. | doi:10.1109/CIG.2018.8490433 Micro abstract: Defines explainable AI for game designers, mapping co-creative systems by their explainability, initiative, and domain overlap so explanations serve concrete design tasks. - #9NQ94D Extracting Physics from Blended Platformer Game Levels - 2020 | Adam Summerville, Anurag Sarkar, Joseph C. Osborn, Sam Snodgrass | Joint Proceedings of the AIIDE 2020 Workshops (CEUR Workshop Proceedings, Vol. 2862) | 7 pp. Micro abstract: Infers playable jump physics from generated platformer levels, including hybrid physics models for levels that blend the geometry and style of multiple games. - #7GR3AQ Procedural Content Generation through Quality Diversity - 2019 | Ahmed Khalifa, Antonios Liapis, Daniele Gravina, Georgios N. Yannakakis, Julian Togelius | 2019 IEEE Conference on Games (CoG) | 8 pp. | doi:10.1109/CIG.2019.8848053 Micro abstract: Argues for quality-diversity algorithms in procedural generation, producing broad collections of varied, playable content while exposing the design space for exploration and co-creation. - #CQBDX4 Procedural Content Generation via Machine Learning (PCGML) - 2018 | Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass | IEEE Transactions on Games | 15 pp. | doi:10.1109/TG.2018.2846639 Micro abstract: Defines and surveys PCGML: generating functional game content directly from models trained on existing examples, with uses spanning creation, completion, repair, critique, and compression. - #WZ8DHP Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents - 2026 | Rishabh Kar | arXiv | 25 pp. | doi:10.48550/arXiv.2605.01783 Micro abstract: Integrates procedural generation and validation in an endless runner, using aerial and ground agents to detect blocked or unnavigable content before the player reaches it. - #NRBMD5 Towards Friendly Mixed Initiative Procedural Content Generation: Three Pillars of Industry - 2020 | Frederic Fol Leymarie, Gorm Lai, William Latham | Proceedings of the International Conference on the Foundations of Digital Games (FDG '20) | 4 pp. | doi:10.1145/3402942.3402946 Micro abstract: Distills three requirements for industry-friendly co-creative PCG tools: preserve designer control, keep feedback loops short, and fit into existing production pipelines. Roads, Trails & Movement (7) - #G3TBNG A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories - 2016 | J. Christian Gerdes, John Subosits, Nitin R. Kapania | Journal of Dynamic Systems, Measurement, and Control | 12 pp. | doi:10.1115/1.4033311 Micro abstract: Generates near-optimal racing trajectories quickly by alternating between a minimum-time speed profile and a convex path update that reduces curvature. - #B6P8L4 Active walker model for the formation of human and animal trail systems - 1997 | Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár | Physical Review E | 34 pp. | doi:10.1103/physreve.56.2527 Micro abstract: Models trail systems as self-organization: walkers reinforce attractive routes while unused traces fade, producing dendritic ant trails and low-detour pedestrian networks. - #V4TQYB Interactive procedural street modeling - 2008 | Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka | ACM Transactions on Graphics | 10 pp. | doi:10.1145/1360612.1360702 Micro abstract: Lets designers generate and edit large street networks through tensor fields, combining procedural speed with brush-like global and local control over street patterns. - #UYLTYJ Modelling the Evolution of Human Trail Systems - 1997 | Dirk Helbing, Joachim Keltsch, Péter Molnár | Nature | 11 pp. | doi:10.1038/40353 Micro abstract: Shows how pedestrian trails emerge through feedback between destination-seeking walkers, existing paths, and vegetation recovery, yielding a compromise between directness and shared infrastructure. - #GY93FG Mountain Trail Formation and the Active Walker Model - 2009 | J. P. Hague, S. J. Gilks | International Journal of Modern Physics C | 22 pp. | doi:10.1142/S0129183109014059 Micro abstract: Extends the active-walker model to steep terrain, explaining zigzag mountain trails through slope avoidance, directional persistence, and mutual reinforcement by ascending and descending walkers. - #LXV9AT Principles of Trail Layout and Design - 2019 | California State Parks | California State Parks Trails Handbook | 64 pp. Micro abstract: A field-oriented guide to durable trail design, emphasizing curvilinear alignment, natural drainage, sustainable grades, control points, and close reading of landform and soils. - #XDEFZS Procedural Generation of Roads - 2010 | A. Peytavie, E. Galin, E. Guérin, N. Maréchal | Computer Graphics Forum | 10 pp. | doi:10.1111/j.1467-8659.2009.01612.x Micro abstract: Automatically routes and constructs roads with an anisotropic shortest-path method that weighs slope and obstacles while treating surface segments, bridges, and tunnels consistently. Terrain, Hydrology & Erosion (6) - #NV2YRW FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation - 2024 | Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain | Computer Graphics Forum | 13 pp. | doi:10.1111/cgf.15243 Micro abstract: A GPU framework for routing surface flow through terrain and its depressions fast enough to make erosion, river, lake, and ecosystem simulations interactive. - #96ZMGK Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion - 2016 | Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin | Computer Graphics Forum | 11 pp. | doi:10.1111/cgf.12820 Micro abstract: Generates large, controllable mountain terrains by coupling user-painted tectonic uplift with fluvial erosion, then turning the resulting stream graph into detailed landforms. - #DWXKYQ Physically-based analytical erosion for fast terrain generation - 2024 | Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer | Computer Graphics Forum | 14 pp. | doi:10.1111/cgf.15033 Micro abstract: Turns the stream power law into an interactive terrain tool, replacing thousands of erosion time steps with analytical solutions and a direct control for landscape age. - #MTDKDE Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models - 2014 | Clarence Lehman, David Mulla, Richard Barnes | Computers & Geosciences | 17 pp. | doi:10.1016/j.cageo.2013.04.024 Micro abstract: Introduces Priority-Flood, a simple, optimal algorithm that removes drainage-blocking depressions from elevation models and can also derive watersheds and flow directions. - #AK7NGE Procedural Riverscapes - 2019 | A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial | Computer Graphics Forum | 12 pp. | doi:10.1111/cgf.13814 Micro abstract: Builds editable, animated riverscapes from bare terrain by carving hydrologically plausible channels and blending real-time procedural water primitives instead of simulating fluids. - #DMTA8Y Terrain Generation Using Procedural Models Based on Hydrology - 2013 | Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin | ACM Transactions on Graphics | 10 pp. | doi:10.1145/2461912.2461996 Micro abstract: Generates controllable, multiscale terrain from a sketched drainage network, representing rivers and landforms as an editable hierarchy of continuous procedural primitives. Water Simulation & Rendering (12) - #RBS5K6 A Layered Particle-Based Fluid Model for Real-Time Rendering of Water - 2010 | Daniel Scherzer, Florian Bagar, Michael Wimmer | Computer Graphics Forum | 7 pp. | doi:10.1111/j.1467-8659.2010.01734.x Micro abstract: Renders particle-based water and volumetric foam in real time using perspective-aware surface smoothing, physically guided foam formation, and layered depth compositing. - #C4AY2M A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics - 2011 | B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato | Computer Graphics Forum | 17 pp. | doi:10.1111/j.1467-8659.2010.01828.x Micro abstract: Surveys ocean graphics from spectral deep-water models to near-shore fluid simulation, then covers the foam, spray, and light transport needed for convincing rendering. - #WZMZGY Advected river textures - 2009 | Dirk Arnold, Stephen Brooks, Tim Burrell | Computer Animation and Virtual Worlds | 11 pp. | doi:10.1002/cav.288 Micro abstract: Combines a 2D Navier–Stokes solver, hydrostatic pressure columns, and advected procedural textures to render detailed, terrain-responsive rivers at real-time frame rates. - #92XRH7 Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field - 2011 | Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch | IEEE Transactions on Visualization and Computer Graphics | 13 pp. | doi:10.1109/tvcg.2010.263 Micro abstract: Advects fluid textures with deformable particle grids, preserving both the input texture’s visual spectrum and exact motion along the velocity field without cumulative stretching. - #8SERGP Real-time Breaking Waves for Shallow Water Simulations - 2007 | Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm | 15th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2007) | 8 pp. | doi:10.1109/PG.2007.33 Micro abstract: Adds real-time overturning waves to shallow-water heightfields by detecting steep fronts and spawning connected particle sheets that collapse into splashes and foam. - #CWC7H9 Real-time Rendering of Enhanced Shallow Water Fluid Simulations - 2013 | Antonio Susín, Jesús Ojeda | Computers & Graphics | 9 pp. Micro abstract: Builds a real-time rendering pipeline for shallow-water simulations, adding fine surface detail, advected foam, photon-based caustics, and screen-space reflection and refraction. - #MVUJ8Z Real-time Rendering of River Networks - 2010 | Quintijn Hendrickx, Rafael Bidarra, Ruben M. Smelik | Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games | 1 pp. Micro abstract: Renders branching river networks efficiently with quadratic Bézier curves, GPU distance fields, and streaming normal maps instead of dense geometry or particle simulation. - #5MGCZ5 Real-time River Representation by Dynamic Control of Data on Waves - 2008 | Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato | 4 pp. | doi:10.3169/itej.62.2063 Micro abstract: Dynamically switches river-wave models by viewing distance, preserving nearby reflection and wave detail while retaining wind-driven motion across the full landscape. - #XDESU9 Scalable real‐time animation of rivers - 2009 | Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu | Computer Graphics Forum | 11 pp. | doi:10.1111/j.1467-8659.2009.01363.x Micro abstract: Animates rivers across vast terrains by computing steady flow locally and advecting fine surface detail only where visible, at a screen-space sampling density. - #869NHK Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning - 2011 | Ian Parberry, Jennifer R. Alford, Mary Yingst | Proceedings of the 6th International North American Conference on Intelligent Games and Simulation (GAMEON-NA) | 7 pp. Micro abstract: Uses a spectrally controlled halftone mask to make texture-based ocean foam dissipate as clumped bubbles that pop, rather than merely fading transparently. - #A2QB8L Water Flow in Portal 2 - 2010 | Alex Vlachos | ACM SIGGRAPH 2010 Course: Advances in Real-Time Rendering in 3D Graphics and Games | 54 pp. Micro abstract: Explains Portal 2’s production-friendly water shader: artist-painted flow maps advect layered normal maps, while offsets and noise suppress repetition and pulsing on limited hardware. - #PBM2TC Water surface wavelets - 2018 | Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan | ACM Transactions on Graphics | 13 pp. | doi:10.1145/3197517.3201336 Micro abstract: Represents water waves as spatially varying directional amplitudes, enabling vast interactive simulations with fine detail, moving obstacles, solid coupling, and direct artistic control. Unfiled (2) - #C8FHDZ On implication and negation in partition logic - 2025 | , David Ellerman | Open Journal of Mathematical Sciences | 9 pp. | doi:10.30538/oms2025.0250 Micro abstract: Develops implication as a refinement-sensitive operation on set partitions, showing how relative negation yields local Boolean cores within the non-distributive algebra of partitions. - #ARP5U7 The Topography of Minoan Peak Sanctuaries - 1983 | A. A. D. Peatfield | The Annual of the British School at Athens | 8 pp. | doi:10.1017/s0068245400019729 Micro abstract: Argues that Minoan peak sanctuaries were chosen for visibility and proximity to local settlements, forming a beacon-like sacred network whose contraction tracked settlement abandonment rather than cultic collapse. ### 4. Assistant tool calls #### Tool call: `search_text` ```json { "limit": 50, "query": "meters metres kilometers kilometres km m cm mm" } ``` #### Tool call: `search_text` ```json { "limit": 50, "query": "seconds milliseconds ms fps frames per second real time" } ``` #### Tool call: `search_text` ```json { "limit": 50, "query": "grid resolution cells pixels vertices triangles particles" } ``` #### Tool call: `search_text` ```json { "limit": 50, "query": "slope gradient percent degrees angle" } ``` #### Tool call: `search_text` ```json { "limit": 50, "query": "iterations time steps timestep simulation years age erosion rate" } ``` #### Tool call: `search_text` ```json { "limit": 50, "query": "velocity speed m/s km/h flow discharge depth wavelength frequency Hz" } ``` #### Tool call: `search_text` ```json { "limit": 50, "query": "GPU CPU memory performance minutes hours" } ``` #### Tool call: `search_text` ```json { "limit": 50, "query": "dataset levels samples participants images streets trails rivers" } ``` ### 5. Tool result: search_text Exact matches 1. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 11 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #MHMBEA 5. Implications of the computational approach and future work Matching excerpt #F2DH4H: The measure of structural beauty ( L ), as defined by S (substructures) times H (hierarchy), reminds us of the classic work on aesthetic measure (Birkhoff 1933). The classic work had the same motivation as our computational approach; it was aimed to quantify the degree of beauty by disregarding colors and materials, as well as human aspects such as cultures, education, and ethnicities. The aesthetic measure ( M ) considers the two notions of order ( O ) and complexity ( C ) and combines them together into a single formula: M = O/C . The formula shows an inverse relationship between the degree of beauty and that of complexity, M \propto 1/C , which is against the notion of organized complexity. Eysenck (1942) changed the initial formula to M = O \times C , which makes better sense, at least from the point of organized complexity because the more complex something is, the more beautiful it is. The biggest problem of the classic measure is that it has never been verified by any psychological study (Douchova 2015). On the other hand, the degree of beauty based on living structure is well supported by the mirror-of-the-self experiments mentioned above. 2. Source: Real-time River Representation by Dynamic Control of Data on Waves (#5MGCZ5), Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato, p. 2 Context: #RNRNU8 Real-time River Representation by Dynamic Control of Data on Waves #7TBW6W 4. 水面波の生成 #PN4DGU 4.3 風による波の変化 Matching excerpt #CJYTFT: 図4において、風向きに直交し原点 o を通過する直線 m は次式(6)となるから、任意の点 (x_0, y_0) の直線 m からの距離 e は次式(7)となる。したがって、直線 m からの距離 e を風波の位相と考え、風向きが水面波の進行方向と逆向きであることを考慮すれば、風波は次式(8)となる。 3. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results Matching excerpt #ZHQFZP: In all experiments, unless stated differently, we use a terrain size of 50 \times 50 \text{ km}^2 . We set the maximum tectonic uplift to \mathcal{U} = 5.0 \cdot 10^{-4} \text{ my}^{-1} (meters per year), which is the average uplift among earth mountains. The erosion rate depends on many factors, such as precipitation and rock strength. In order to get a more intuitive setting, we follow the relationship between height, uplift, and erosion detailed in Section 6.4. We set the erosion rate to k = 5.61 \cdot 10^{-7} \text{ y}^{-1} for mountains to culminate at about 2000m. We set the time step at the geological scale \delta t = 2.5 \cdot 10^5 \text{ y} to ensure a fast convergence while avoiding the appearance of high unnatural cliffs. 4. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 4 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #3YZ889 4.3. Lake Overflow Matching excerpt #ZUZCCF: The tree structure is guaranteed to be consistent and coherent under the condition that we cannot add an arc flowing from a previously added node. We remove the unused candidate arcs from G_L and we use a red-black tree for labeling and sorting the set of candidate arcs. Let M denote the number of lakes. A first O(N) pass on the graph is performed. Then our algorithm needs at most M evaluations in a red-black tree of size M , which guarantees a complexity of O(N + M \log(M)) . The number of lakes M is usually much lower than the number of nodes N . The experimental speedup compared to the O(N\sqrt{N}) version is noticeable in the first iterations where the local minima are numerous. 5. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #JT9864 3.1. Geological Background Matching excerpt #MSXUGH: Note that, when applied at the right temporal and spatial scales (typically between 10^5 and 10^7 years and a few tens to hundreds of kilometers), the stream power equation does not only model erosion, but also captures the way a complex relief emerges from a supposedly flat part of the continental crust [How94]. 6. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #JT9864 3.1. Geological Background Matching excerpt #EKXATA: The constants m and n depend on rock strength, climate, and the topology of river networks. While the values of those parameters are poorly understood, the ratio m/n is constrained by the shape of the stream profiles and is thought of being m/n \approx 0.5 [WT99]. As in most geomorphological studies, we use n = 1 and m = 0.5 . Moreover, some geological studies attempt to tune these parameters by example [CB14] and a recent survey [Lag14] studies the limit of geological knowledge regarding the parameters of the stream power equation. 7. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 4 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #3YZ889 4.3. Lake Overflow Matching excerpt #FW262U: The stream trees \mathcal{T} cannot be used directly to simulate water flow over \Omega because these trees are not connected, and the water would stop at internal root nodes that represent lakes. While a solution for connecting lakes to other nodes was proposed as an optional step of the main O(N) algorithm in [BW13], adding this step leads to a complexity of O(N\sqrt{N}) , where N denotes the number of nodes. We describe below a more efficient solution that performs lakes connection in O(N + M \log(M)) where M \ll N is the number of lakes. 8. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 7 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Matching excerpt #L66ZXE: In our approach, we allow only the changes to the drainage area exponent m . Indeed, only the ratio between m and n has a meaning that we can deduce from the equations. Let us suppose we have reached an equilibrium state in a region where u and k are constant over the space. The stream power Equation (1) becomes: 9. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 8 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #FYBSSG 7.1. Performance Matching excerpt #9DU2N2: Table 2 reports timings and statistics for our method for the examples from this paper. Our implementation supports both real-time GPU and high-quality offline photon-traced rendering. The final model has a compact memory footprint: we are able to represent meandering rivers several kilometers in length with complex water effects in less than a few megabytes. Memory consumption is as low as 22 kilobytes for short rivers (of 50m) up to 2.7 megabytes for longer rivers ( \approx 4 km). Even without memory optimization, individual primitives range from 50 bytes to at most 90 bytes. 10. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 7 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results Matching excerpt #ACDG5B: Figures 1 show different views of an extensive river network, spanning a 3 \times 3 km terrain. The scene has the following statistics: an input digital elevation map with a per-pixel resolution of 100m, a river that extends for approximately 4km, more than 40,000 primitives forming the river surface, and a final terrain and water surface resolution of 10cm. 11. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 10 Context: #JJE8HN Procedural Riverscapes #BR5ZZK 8. Conclusion Matching excerpt #L5L326: We have introduced a novel method for generating and interactively animating large-scale river networks up to several kilometers in extent that simultaneously exhibit detail at resolutions as fine as 10cm. Such rivers are a common scene element in many CG applications. Although the framework could be used in films for large-scale scenes with a tight render budget, the main target is real-time applications, such as videogames (including auto-generated worlds), virtual environments, and GIS visualizations (such as Google maps). 12. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 5 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Matching excerpt #LHVW5W: In whatever way a hierarchy exists, it must be assumed that Iouktas stands at the head of it. The magnificence of the architecture and quality of the finds are unparalleled at any other peak sanctuary. 20 The site was in use from MM I, as the earliest finds show. 21 But from MM III the shrine underwent a dramatic change; to that period are dated the first of the monumental structures and from then the votives become noticeably richer. 22 It should be noted that MM III is the suggested date for the shrine buildings on other peak sanctuaries which have them. 23 This date coincides with Knossos' increased control over the island and the setting up of the villa system. Rutkowski has suggested that from MM III the peak sanctuary cult became more institutionalized under Knossian royal authority, perhaps with permanent priests. 24 As the peak sanctuary cult was an apparently unifying factor on Minoan society, centralized control over it could have been used politically. As Knossos was the administrative focus for all Crete, so, perhaps, Iouktas became the focal point for the peak sanctuary cult. 13. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 1 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Matching excerpt #U7KFZC: Faure's arguments from the EM III sherds should be treated with some caution; such pottery continued to be used in east Crete as MM I pottery was introduced and used elsewhere. The large number of peak sanctuaries in Sitias may have less to do with chronology and more 14. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 2 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Matching excerpt #65886B: The altitude of peak sanctuaries varies considerably. Generally, the lowest are around 200 m, e.g. Petsopha at 215 m. At the other end of the scale sanctuaries are also found at over 1000 m, e.g. Karphi at 1148 m, Kastellos at 1160 m, Keria at 1168 m. Despite this huge difference in altitudes Rutkowski has pointed out that all peak sanctuaries fall within certain vegetation zones. 8 Referring to the work of Philippon, 9 Rutkowski has shown that all peak sanctuaries, irrespective of height, are associated with altitude regions that allow for some sort of farming, arable or pastoral, often both. Therefore, today, routes up to the summit pass through vineyards and groves of olive and fruit trees; they climb past mountain meadows of fragrant herb bushes where bees gather nectar, and sheep and goats graze in summer. Indeed, it is striking just how many peak sanctuaries have a gentle slope on one side of the summit, or a high flat area below it, where flocks are still pastured today: e.g. Petsopha, Pyrgos, Vrysinas, Traostalos, Modhi, and Zou. 15. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 6 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Matching excerpt #3W2EH9: Therefore, I suggest an alternative interpretation of the decline of peak sanctuaries: the east Cretans' faith in the peak sanctuary cult was shaken, though not broken, by the natural catastrophes which hit them from MM III to LM I. The causes which led to the abandonment of their homes in LM IB naturally led to a desertion of their shrines. The decline in the numbers of peak sanctuaries did not mean a diminution of the importance of the cult. Where there was continuity of occupation, particularly at Knossos and in west and south Crete, the peak sanctuary cult also continued. 16. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 3 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Matching excerpt #QPEZUU: In some areas, however, it is not the highest point which is chosen. Minoan Palaikastro is sited in a small coastal plain, just north of the mountain Petsopha. This mountain is a ridge, which juts out from the encircling massif. The ridge has three peaks and the sanctuary is sited on the lowest of the three; it is this peak which most directly overlooks the town. From the other summits the view is obscured by lower platforms and cliffs. Faure notes a similar situation with the peak sanctuary at Etia. 12 The shrine is not on the highest peak of the massif, which is Skopeli at 715 m. Rather it is situated on an isolated butte to the north, 100 m lower down. From there, however, one can see the valley plains of Armeni and Chandra. A third example is observable at Zou. 13 The summit is 803 m high, but the peak sanctuary is on the rising edge of a small plateau, north-west of the summit, at an altitude of 725 m. It is only from this high point that the coastal plain of Sitia can be seen; moreover, from the plain this point looks like the summit. 17. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 3 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #96ENPE 2.2. Fourier domain approaches #Z39SP2 2.2.1. General methods Matching excerpt #KWPHGM: with U_{10} the wind speed measured at 10 meters above the surface. 18. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 7 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #SZAWPC 8 Results Matching excerpt #ARNY9X: has native multiresolution support. We can visualize the terrain at multiple scales, and we can use view-dependent clipping algorithms or resource-dependent strategies. The vector-based primitive description of the generated terrain is compact (average of 1 \text{ km}^2 \approx 1.5 \text{ kB} ) and allows the storage of large terrains as shown in Table 3. Even if the construction tree describe the whole domain, the user can evaluate only a portion of the landscape. Hoya Island (Fig 17-B) has an area of 3368 \text{ km}^2 and is composed of 81853 primitives using 8,180 kB. A 30 \text{ km}^2 portion of the terrain represents only 2068 primitives and a 225 kB storage. 19. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 7 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #SZAWPC 8 Results Matching excerpt #Y6MAJM: Performance. Our method generates a vector-based representation of large terrains (several hundreds of square kilometers) in a few seconds (Table 2) and, though it is based on principles from hydrology, it does not rely on complex numerical physics-based simulations. The novel description of the generated terrain 20. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 11 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #V6AZDH 7.3. Applicability of our method Matching excerpt #N9TEH4: Uplift emerges from tectonic activity and is responsible for the formation of mountain ranges. It is therefore used as another tool to control the generation of large-scale landscapes. In Figure 7, we show that the different uplift-based controls developed in previous work [CCB*17, SPF*23] readily extend to our method. These methods use various strategies to fill an uplift map, and provide this map as input to a simulation of the stream power law. We use a user-painted uplift map (Figure 7, left), which could alternatively be generated by one of the aforementioned methods, and show how the map controls the formation of the 4.6\text{My} old mountain at different scales (from left to right a 5\text{km} , 15\text{km} , and 25\text{km} large mountain). We notice in particular that variations in the uplift map mainly dictate the trajectory of the main rivers at smaller scales, and also influence the local ridge-line elevations for larger ranges. 21. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Matching excerpt #2DEC4W: where k , m and n are erosion coefficients. Throughout the paper, we will use some of the common values: m = 0.4 and n = 1 . The choice of n = 1 , also commonly used in geomorphology, makes the equation linear and therefore simplifies the derivation of the analytical solutions. While this choice barely impacts the result as the valley profiles are mostly directed by the ration m/n , we acknowledge that the actual values of m and n remain an open question in geomorphology [Lag14]. 22. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 10 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #66SM5X 7 Discussion and Future Work Matching excerpt #MR4QDN: to run at the same sample time as the vehicle controller. Instead, the planner would operate on a separate CPU and provide a velocity profile and racing line for only the next 1-2 kilometers of the race track every few seconds, or plan a path for the next several hundred meters within a second. 23. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 3 Context: #G4BEE9 Mountain trail formation and the active walker model #A5Y7MA 2. Active walker model for human trails Matching excerpt #J2KKMV: where f(\mathbf{r} - \mathbf{r}_{\mu}) is an arbitrary function that specifies the shape of the damage caused by a footfall. f(\mathbf{r}) is normalized to unity. We take f to be a square with sides l = 10\text{cm} long, i.e. to have similar area to the base of a shoe. With this choice of f , l^2 G_{\max}/I is the approximate number of footfalls that cause G to reach the saturation value G_{\max} . Since the feet of walkers have finite dimensions, we consider equation 2 to be more physical than equation 1. 24. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 9 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #MCXU94 5. Analysis Matching excerpt #4EK97Q: For floating-point DEMs, the improved Priority-Flood above reduces both the time complexity—to O(m \log_2 m) , where m \leq n —and run-time regardless of which underlying algorithm is used for the priority queue. It may also decrease run-times even for integer data by avoiding the overhead associated with maintaining a priority queue. If non-integer keys are used or guarantees regarding the internal structure of the priority queue are absent, prudent design suggests that the improved algorithm be used. 25. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 1 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #8AC6U8 1. Background Matching excerpt #DAJKCD: DEMs have increased in resolution from thirty-plus meters in the recent past to the sub-meter resolutions becoming available today. Increasing resolution has led to increased data sizes: current data sets are on the order of gigabytes and increasing, with billions of data points. While computer processing and memory performance have increased appreciably during this time, legacy equipment and algorithms suited to manipulating smaller DEMs with coarser resolutions make processing these improved data sources costly, if not impossible. Therefore, improved algorithms are needed. 26. Source: Towards Friendly Mixed Initiative Procedural Content Generation: Three Pillars of Industry (#NRBMD5), Frederic Fol Leymarie, Gorm Lai, William Latham, p. 0 Context: #TESG3N Towards Friendly Mixed Initiative Procedural Content Generation: Three Pillars of Industry #8VWJPE ACM Reference Format: Matching excerpt #2WHJXB: © 2020 Association for Computing Machinery. ACM ISBN 978-x-xxxx-xxxx-x/YY/MM...$15.00 https://doi.org/10.1145/nnnnnnn 27. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 10 Context: #RNVWWR Water Surface Wavelets #W3R46F 9 DISCUSSION Matching excerpt #BEDUYL: samples would have a grid cell spacing of 25 cm, even ignoring that it needs to store 2 values per grid cell. Following the Nyquist theorem, the smallest possible wavelength would be 0.5 m. By comparison, we animate wavelengths down to 2 cm. 28. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 10 Context: #RNVWWR Water Surface Wavelets #W3R46F 9 DISCUSSION Matching excerpt #ZB9JR8: Compared to Eulerian height field-based simulations, our method stores 4096^2 (spatial resolution) \times 16 (wave vector resolution) samples for our 4 km by 4 km scene. A height field storing the same number of 29. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #WKY9MT: our results, we show a vast 4\text{km} \times 4\text{km} sea interacting with islands, floating barrels, actively moving boats, and a user-controlled jet-ski. Both the simulation and the heightfield evaluation are computed in parallel on the GPU in each time step. We provide a supplemental document that describes relevant implementation details for both parts. Our laptop with a NVIDIA Geforce GTX 1070 GPU achieves an average frame rate of 60fps with the parameters in Table 1, and this paper includes an interactive demo of our method which recreates this example. Table 2 displays the timing breakdown for an average frame of this animation; note that the timing for the computation of \eta depends on the number of pixels occupied by waves and may vary slightly. 30. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 8 Context: #57PDWB Interactive Procedural Street Modeling #RXG48N References Matching excerpt #T87XNK: BERG, M. D., KREVELD, M. V., OVERMARS, M., AND SCHWARZKOPF, O. 2000. Computational Geometry . Springer-Verlag. 31. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 8 Context: #57PDWB Interactive Procedural Street Modeling #RXG48N References Matching excerpt #ZCBDT2: FISHER, M., SCHRÖDER, P., DESBRUN, M., AND HOPPE, H. 2007. Design of tangent vector fields. ACM, New York, NY, USA , vol. 26, 56. 32. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 5 Context: #57PDWB Interactive Procedural Street Modeling #ZPVYV6 6 Street Graph Generation #JW8A9D 6.2 Minor Street Graph Generation from Tensor Fields Matching excerpt #PUZXXV: Once the major street graph G_M has been constructed, it can be used to generate the minor street graph G_m . The process of generating G_m is similar to that of G_M with the following key difference. The edges in G_M and the boundaries of topographical features divide the domain into regions, inside each of which the user creates a continuous tensor field (see Figure 3 (6)). The tensor field can be discontinuous across region boundaries, i.e., major roads. This implies the tensor field used for minor road tracing is not necessarily the same as we use for major road tracing above. Figure 11 shows the minor road network generated based on the major road network. Note that minor roads do not necessarily follow the same directions as major roads. We point out that the idea of flow tiles proposed by Chenney [2004] for modeling a vector field can also be adopted to achieve the wealth of minor road patterns. 33. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 20 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #D886YY 5 Analysis and Evaluation #CHSR7F 5.5 Quantitative Evaluation #LKK5Z8 5.5.1 Structural results derived from code Matching excerpt #ZHREQJ: F2 — Per-segment scan cost (supports H3). A single call to FlyerCorridorScanner.ScanCorridor performs \lceil L_{\text{seg}}/g_z \rceil + 1 = 21 horizontal probe rows over a segment of length L_{\text{seg}} = 10 m with row gap g_z = 0.5 m. Each row sweeps the corridor with X-step 0.05 m across a width of 2.15 m, giving up to \lceil 2.15/0.05 \rceil + 1 = 44 rays in the worst case (no early-exit on a sufficiently large clear gap). The per-segment ray budget is therefore bounded above by 21 \times 44 = 924 rays, plus a single Physics.OverlapBox call. Because the scanner is gated by tileZ <= _lastScannedTileZAxis , this work is performed at most once per L_{\text{seg}} of forward travel, irrespective of frame rate. The ground tile length is 96 m, so each ground tile incurs \lceil 96/10 \rceil = 10 scanner segments. Note that the scanner segment length (10 m) is not the same as the ground tile length (96 m); the two operate at different granularities, and conflating them overestimates per-tile work by an order of magnitude. 34. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 9 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #QGEMMG 4.3 Player Physics #SGY5B5 4.3.5 Ground Detection Technique Matching excerpt #XJRD8S: Ground detection is handled using ray casting (projecting an invisible line from a point in a chosen direction and reporting the first surface it intersects). A short ray of 0.3 metres is fired from the feet of the player. If this ray hits the groundMask layer, then isGrounded becomes true and the landing state is cleared. This check is required before applying the jump logic, because the player should not be allowed to repeatedly jump while already in the air. 35. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 11 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #5W8C4J 4.4 Procedural Terrain Generation #78P3XF 4.4.4 Navigational Mesh Management Matching excerpt #B9EZ4X: so that its coverage is the interval [z_p - d_{\text{behind}}, z_p + d_{\text{ahead}}] , with d_{\text{ahead}} = 600 m and d_{\text{behind}} = 50 m. 36. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 20 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #D886YY 5 Analysis and Evaluation #CHSR7F 5.5 Quantitative Evaluation #LKK5Z8 5.5.1 Structural results derived from code Matching excerpt #Y2D4BT: F3 — NavMesh coverage relative to look-ahead (supports H4). The aerial agent maintains a forward offset of \Delta z = 200 m, while the ground agent uses a NavMesh look-ahead of D_{\text{lookAhead}} = 300 m, both within the baked region of [z_p - 50, z_p + 600] m (Section 4.4.4). The ground agent therefore evaluates a larger forward window than the aerial agent under default settings, so the two agents do not in general cover the same set of tiles even when both are active. 37. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 5 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Matching excerpt #FD4PEN: where h is the height field, \omega is the angular wave frequency, H(\mathbf{k}) contains amplitude and phase information, \mathbf{k} is a 2D vector such that k_x = 2\pi n / L_x , k_y = 2\pi m / L_y and (n, m) are integers with bounds -N/2 \leq n < N/2 and -M/2 \leq m < M/2 . 38. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 5 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #CSD47K Impulse Driven NS Matching excerpt #JS4LBU: It should also be noted that the flow speed of the river itself should be set in accordance to the grid cell size of the river in order to maintain grid size independent flow rates. For example, if the desired flow rate is 1.3 meters per second and the cell width is 1.0 unit, the flow rate should be set to one half the value of the same flow rate on a grid with a cell width of 2.0 units. 39. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 5 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #LE3TRV 5.2. Curvature Matching excerpt #43XVF5: discretize the angular domain [0, 2\pi] into m intervals. Thus, our approach consists in computing the discrete anisotropic shortest path over a n^2 \times m three-dimensional grid of oriented points, denoted as \mathbf{p}_{ija} , (i, j) \in [0, n]^2 , a \in [0, m-1] . The segments path masks \mathcal{M} generalize to extended masks, denoted as \mathcal{E} , such that \mathcal{E}(\mathbf{p}_{ija}) refers to the set of all the points \mathcal{M}(\mathbf{p}_{ij}) replicated for all a \in [0, m-1] . 40. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 4 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #SR7CUB 5.1. Path segment masks Matching excerpt #CENURU: Table 2 reports timings (in seconds) as well as the cost (in arbitrary unit) and the length (in meters) for computing the anisotropic shortest path with different path segment masks over a 60 \times 60 grid. Timings increase in O(k^2) . 41. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 6 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #N4M5TN 5.4. Stochastic sampling Matching excerpt #WJSTC2: Table 5 reports statistics corresponding to the shortest paths illustrated in Figure 15 and demonstrating the efficiency of the sampling technique. The tunnel and bridge mask areas were set with r_i = 50 m and r_e = 300 m over a 300 \times 300 grid with a sampling grid size of 10 m. The corresponding number of grid points visited at every iteration was equal to \#T = 2728 . In contrast, the number of sample grid points in the stochastic approach was set to \#S = 50 . Timings demonstrate that the speed up is proportional to the ratio \#S/\#T . Approximate matches 1. Source: Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning (#869NHK), Ian Parberry, Jennifer R. Alford, Mary Yingst, p. 2 Context: #5R6DEX Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning #UQWEYD Overview of Our Approach #Z6PB8R The Saturation Function Score: 0.01 Related excerpt #4EFZBU: where \vec{v} = (x, z) is position, \vec{k} is the wave direction, s is the speed of the wave, t is time, K is wave slope, A is wave amplitude, \lambda_{adj} is wavelength adjusted for ocean depth, and \lambda is original wavelength. 2. Source: Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning (#869NHK), Ian Parberry, Jennifer R. Alford, Mary Yingst, p. 2 Context: #5R6DEX Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning #UQWEYD Overview of Our Approach #Z6PB8R The Saturation Function Score: 0.009 Related excerpt #XFF5YH: We use the following formulae from Van Dresek III, Bookout, and Lake [9] for the height y of the wave: 3. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 2 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #PHN7AY 4 Wave Simulation Score: 0.01 Related excerpt #EWBE94: Here, the gradient of the fluid height \nabla H is computed with finite differences from the height field of the shallow wa- 4. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results Score: 0.021 Related excerpt #ZHQFZP: In all experiments, unless stated differently, we use a terrain size of 50 \times 50 \text{ km}^2 . We set the maximum tectonic uplift to \mathcal{U} = 5.0 \cdot 10^{-4} \text{ my}^{-1} (meters per year), which is the average uplift among earth mountains. The erosion rate depends on many factors, such as precipitation and rock strength. In order to get a more intuitive setting, we follow the relationship between height, uplift, and erosion detailed in Section 6.4. We set the erosion rate to k = 5.61 \cdot 10^{-7} \text{ y}^{-1} for mountains to culminate at about 2000m. We set the time step at the geological scale \delta t = 2.5 \cdot 10^5 \text{ y} to ensure a fast convergence while avoiding the appearance of high unnatural cliffs. 5. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 7 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.013 Related excerpt #Z2BRQU: We note x the distance between \mathbf{p} and the corresponding outflow, and d the distance between ep and a ridge. Then we assume that A is proportional to (d-x)^2 . Recall that s = dh/dx , so we obtain: 6. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #JT9864 3.1. Geological Background Score: 0.01 Related excerpt #EKXATA: The constants m and n depend on rock strength, climate, and the topology of river networks. While the values of those parameters are poorly understood, the ratio m/n is constrained by the shape of the stream profiles and is thought of being m/n \approx 0.5 [WT99]. As in most geomorphological studies, we use n = 1 and m = 0.5 . Moreover, some geological studies attempt to tune these parameters by example [CB14] and a recent survey [Lag14] studies the limit of geological knowledge regarding the parameters of the stream power equation. 7. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 7 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.009 Related excerpt #L66ZXE: In our approach, we allow only the changes to the drainage area exponent m . Indeed, only the ratio between m and n has a meaning that we can deduce from the equations. Let us suppose we have reached an equilibrium state in a region where u and k are constant over the space. The stream power Equation (1) becomes: 8. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 7 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.009 Related excerpt #P52B3D: We use the result of these equations to choose the proper ratio m/n to shape the desired river profile. 9. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 6 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.008 Related excerpt #MNZNZU: The erosion parameters in the stream power erosion are not intuitive to set. Even in geology, the impact of these coefficients is not well-understood. The erosion coefficient k and the uplift u are both subject to a multiplication by dt , so only their ratio is relevant. However, its value has a strong influence on the mountain height. We made a series of experiments in order to find a relationship between this ratio and the maximum mountain height. It turned out this relation is linear and the height in kilometers follows the rule h_{max} = 2.244 u/k . 10. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 7 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results Score: 0.022 Related excerpt #ACDG5B: Figures 1 show different views of an extensive river network, spanning a 3 \times 3 km terrain. The scene has the following statistics: an input digital elevation map with a per-pixel resolution of 100m, a river that extends for approximately 4km, more than 40,000 primitives forming the river surface, and a final terrain and water surface resolution of 10cm. 11. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 6 Context: #JJE8HN Procedural Riverscapes #9ZYJP2 6. Animated Procedural River Model #U6BTCY 6.1. Riverflow Primitives Score: 0.017 Related excerpt #MYB6GF: In turn, the function \delta h is defined as an n -fold sum of scaled noise functions n , referred to as fractional Brownian motion m , and characterized by several parameters (persistence p , lacunarity l , and frequency f ): 12. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 12 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #3WQXTG IV. HUMAN TRAIL FORMATION Score: 0.009 Related excerpt #ZBPS6E: For the strength Q_\alpha(\mathbf{r}, t) of the markings produced by footprints at place \mathbf{r} we assume 13. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 2 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #7DFB5R Levels of scale Score: 0.019 Related excerpt #TAB4VD: As the building blocks of a whole, centers are defined at different levels of scale. For example, the snowflake has four scales: 1, 1/3 , 1/9 , and 1/27 (Figures 2a, 2b), while the axial map has five scales based on head/tail breaks (Figure 2f). In general, the levels of scale can be characterized by the ht-index (Jiang and Yin 2014), or the number of times that the scaling pattern of far more small things than large ones recurs. 14. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 4 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #LWK7XQ 2. The 15 properties #ZBHUGU Gradients Score: 0.017 Related excerpt #54527U: The centers gradually strengthen from the smallest to the largest scale, from the shortest to the longest line, from blue to red (Figure 2f), from the smallest to biggest dots (Figure 2b), and from the least-connected to the most-connected lines. This property of gradients can also be referred to as the scaling hierarchy ranging from the smallest to the largest. 15. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 7 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #9FK8U9 3. Wholeness as a hierarchical graph #ATC4YW 3.2 Measuring the degree of life using ht-index for the wholeness Score: 0.017 Related excerpt #WEEX6U: in which m(r) is the number of valid means during the head/tail breaks process for the PR scores. 16. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 2 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work #ESVL3G 119 2. Fluid simulation Score: 0.012 Related excerpt #V5K24C: 120 where \lambda_i = 1 for i = 1..4 and \lambda_i = 1/4 for i = 5..8 . g is 121 the gravity and h and \mathbf{u} are the fluid properties: height level 122 from the underlying terrain and velocity, respectively. They are 123 calculated as 17. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #DBN56J 4.2 River Network Generation #VTGN6K 4.2.2 Node Expansion Score: 0.025 Related excerpt #68SYWN: value \eta (we use \eta = 3/4 e = 1500[\text{m}] in our implementation): 18. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #DBN56J 4.2 River Network Generation #VTGN6K 4.2.2 Node Expansion Score: 0.015 Related excerpt #Q92BYB: We compute the distance between the edge E and the other edges in the geometric graph to avoid collision between the new edge and the existing graph (Fig. 7): this distance should be greater than a user-defined limit denoted as \sigma (we use \sigma = 3/4 e = 1500[\text{m}] in our implementation). The function \sigma \cdot f(s) depends on the Horton-Strahler number to maintain large rivers apart: 19. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 5 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law #S7W7HC 4.2. Recursive algorithm for the 1D analytical solutions Score: 0.009 Related excerpt #H6RTDA: Where S(x, y) represents the difference of elevation between positions x and y and results from the balance uplift and erosion: 20. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 6 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law #5CR379 4.3. Extension to the 2D terrain domain Score: 0.009 Related excerpt #7UDQ47: The choice of a single receiver results in an incorrect evaluation of the slope of the terrain (as \|\nabla z\| requires the spatial derivative from both the x and y directions). We compensate for this approximation by introducing a correction term: for a cell at position x with a receiver at position x_r , we change a(x) to a(x) = kA^m \frac{\delta x \|\nabla z\|}{z(x) - z(x_r)} . Note that we still evaluate the spatial derivatives of \|\nabla z\| downstream, as the difference between the cell elevation and the lowest elevation in the x and y directions, respectively. The inset figure shows the difference between not using (top) and using (bottom) the slope correction, with highlights on the isolines of a terrain constructed by enforcing a constant slope upward a boundary circle. The correction removes the directional artifacts and yields the expected concentric isolines. 21. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Score: 0.009 Related excerpt #2DEC4W: where k , m and n are erosion coefficients. Throughout the paper, we will use some of the common values: m = 0.4 and n = 1 . The choice of n = 1 , also commonly used in geomorphology, makes the equation linear and therefore simplifies the derivation of the analytical solutions. While this choice barely impacts the result as the valley profiles are mostly directed by the ration m/n , we acknowledge that the actual values of m and n remain an open question in geomorphology [Lag14]. 22. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 16 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Score: 0.015 Related excerpt #HWVUS7: To test the effects of discretization, we compute results using smaller \Delta t = 0.5s , \Delta x = 5cm and \Delta y = 5cm in figure 8. In figure 9 we use even smaller steps \Delta t = 0.25s , \Delta x = 2.5cm and \Delta y = 2.5cm . The absence of new features shows our calculations to be stable against finite size scaling. 23. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 11 Context: #G4BEE9 Mountain trail formation and the active walker model #MKLE5Y 4. A model of mountain walkers #KAWSKG 4.2. Discretization scheme Score: 0.013 Related excerpt #L9CKAZ: As humans tend to walk with different step sizes, we varied the speed of the individual walkers. This variation leads to continuous paths. The width of the area studied was chosen as 10m and the length of the observed area (in the direction of the incline) as 25m. This is probably realistic for this type of trail formation, since we suspect that walkers aim for local goals, rather than the final goal of the peak (which is not necessarily visible from all locations). 24. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 36 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance Score: 0.02 Related excerpt #C9JB9Q: An altimeter, topographic map, and compass are used to plot locations on the landform. This data is incorporated into mapping software that produces elevations, average grades, and linear distances between control points. If satellite readings are available, a GPS unit can be used to locate and record specific positions. Elevations are taken with an altimeter at each control point to determine elevation differences between points. 25. Source: Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure (#MH5J8D), Bin Jiang, p. 8 Context: #HAZYNL Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty based on the 15 Properties of Living Structure #63MN28 4. Case Studies for Verification #HW35C5 4.2 Results and Discussion Score: 0.025 Related excerpt #CTR2RC: Beautimeter does not utilize the L = S * H formula directly, but the two approaches are complementary because they address different aspects of architectural and urban evaluation. Beautimeter captures the number of the 15 properties, while the L score offers a quantitative measure and focuses on the structural characteristics that contribute to the sense of life in a built environment. The two methods together offer a comprehensive toolkit that enables architects and urban designers to explore the structural integrity and also the emotional impact of the spaces they create. Such a dual perspective elaborates on what makes some environments feel more alive and beautiful than others, which can lead to more holistic and human-centered architectural and urban designs. 26. Source: Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure (#MH5J8D), Bin Jiang, p. 9 Context: #HAZYNL Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty based on the 15 Properties of Living Structure #P6XUBS 5. Implications of Beautimeter and this Study Score: 0.011 Related excerpt #GDA5RL: Beautimeter is built on universal geometrical properties that capture beauty and coherence in physical spaces, informed by living structure principles that resonate across cultures. While these properties are universal, their interpretation is culturally adaptable, distinguishing them from an international style or so-called Alexander style. Instead, the Alexander style exists in its underlying living structure. The tool allows urban planners to customize the 15 properties to reflect local traditions, cultural symbols, and aesthetic values, ensuring that spaces are not only universally appealing but also culturally meaningful. By integrating geometry with cultural and emotional data, Beautimeter helps create environments that are both visually harmonious and deeply resonant with their users. 27. Source: Real-time Rendering of River Networks (#MVUJ8Z), Quintijn Hendrickx, Rafael Bidarra, Ruben M. Smelik, p. 0 Context: #BTQCB6 Real-time Rendering of River Networks Score: 0.013 Related excerpt #QGGCCR: The distance d to the corresponding projected pixel and the arc length L along the curve are calculated as shown in Figure 1a. The distance from the pixel to the curve is used to discard pixels that are not within the boundaries of the river. This results in an accurate 28. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 10 Context: #RNVWWR Water Surface Wavelets #W3R46F 9 DISCUSSION Score: 0.029 Related excerpt #BEDUYL: samples would have a grid cell spacing of 25 cm, even ignoring that it needs to store 2 values per grid cell. Following the Nyquist theorem, the smallest possible wavelength would be 0.5 m. By comparison, we animate wavelengths down to 2 cm. 29. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 5 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #6AJDFD 4.1 Discretizing \mathcal{A} Score: 0.023 Related excerpt #UG8PZG: in Section 8. As mentioned above, \mathcal{A} varies slowly over space, so we do not require much spatial resolution either. In our implementation we allocate X_{\mathcal{A}} = 4096 grid cells for each spatial dimension, which defines a grid cell spacing of approximately one meter. 30. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 1 Context: #RNVWWR Water Surface Wavelets #ZTWDW3 1 INTRODUCTION Score: 0.015 Related excerpt #EMZ6QE: water height itself, so we can represent them on lower resolution grids. This change of variables allows more efficient computation and larger computational domains (Figure 1). 31. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 6 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #KQNQXW 4.3 Height field evaluation Score: 0.009 Related excerpt #TM83X4: To calculate the actual water height we numerically evaluate the integral in Equation 12. We evaluate the wavenumber in polar coordinates 32. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 55 Context: #8MPFPH X ECOLOGY OF THE ORDINARY #TFM623 Example 20. The Ecology Of The Ordinary Score: 0.012 Related excerpt #T3RSVD: Example 21. Look around you, wherever you are today, in almost any city: Bradford, London, Birmingham, Atlanta, Stockholm, Tokyo, Moscow, Addis Ababa, Cape Town, Singapore, Lyon, Madrid, Santiago, Mumbai. 33. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 29 Context: #EAB6Y7 V EXAMPLES OF HARMONY-SEEKING COMPUTATIONS FROM DIFFERENT FIELDS #5MUWW2 Example 13. Formation Of Giant Voids In The Universe: A Very Large Example of a Generated Wholeness Score: 0.009 Related excerpt #MLT8LP: The actual physical diameter of one of these voids, is unimaginably huge, about 100 million light years. It is in miles, 186,000 * 3600 * 365 * 24 * 100,000,000 = 5865696 * 10^6 * 10^8 \approx 6 * 10^6 * 10^6 * 10^8 = 6 * 10^{20} miles. A jet plane flying at 600 mph, would take a 10^{14} years to cross this void – something like 5000 times the age of the universe itself. I say this only to emphasize the truly huge size of the voids that we are talking about, and in particular to draw attention to the fact that if it is that huge, the ring thickness could be almost anything, and the ratio of ring thickness to ring diameter could have a large range of possible values. 34. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 4 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #Z68DF9 5. Real-Time Foam #P6BSN6 5.2. Layer Creation Score: 0.01 Related excerpt #3BY9UA: where t is the particle thickness function, x_i, y_i are the projected position of the particle, x and y are screen coordinates and \sigma_i is the projected size. In comparison to [vdLS09], we not only calculate the water thickness, but also: 35. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 5 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Score: 0.023 Related excerpt #FH8NYH: A street network is more correctly conceived of as a set of far more short streets than long ones, or a set of far more less connected streets than well connected ones (Figure 2b). The street network has four levels of scale, indicated by the four colors, far more short streets than long ones across the scales, and more or less similar streets on each of the four scales. A coastline is more correctly represented as a set of far more small bends than large ones (Figure 2d). The coastline has three levels of scale, indicated by three sets of bends: [x_1] , [x_2, x_3] , and [x_4, x_5, x_6, x_7] . The notion – or the recurring notion – of far more smalls than larges should be the major criteria for whether things are the right things that enable us to see a living structure, or whether we have the right perspective and scope for seeing a living structure. As another example, within a large enough scope of time or space, there are far more ordinary weather conditions than extraordinary ones, whereas within a limited scope of time (10 days) or space (a city), weather conditions may be more or less similar. 36. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 0 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #GV3UJZ Abstract: Score: 0.019 Related excerpt #MFN8JF: Keywords: Scaling law, Tobler's law, differentiation, adaptation, head/tail breaks, natural streets, the third view of space 37. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 4 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Score: 0.018 Related excerpt #6ERKBH: Let us further clarify the term “things” through two working examples: A street network and a coastline (Figure 2, Jiang and Slocum 2020). Conventionally, in geography or geographic information science, the things often refer to geometric primitives such as pixels, points, lines, and polygons. It is little wonder that Tobler’s law is seen pervasively, as there are more or less similar sized things seen from the perspective of geometric primitives. For example, a street network has more or less similar street segments, or all the street junctions have more or less similar numbers of connections (1–4) (Figure 2a). A coastline consists of a set of more or less similar line segments (Figure 2c). Unfortunately, all these geometric primitives are not the right things for seeing the street network or coastline as a living structure. There is little wonder, constrained by the geometric primitives, that living structure was not a formal concept in geography. 38. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 3 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Score: 0.017 Related excerpt #TDTMQ3: The two laws have a common keyword – “things”: (1) more or less similar things on each scale, and (2) far more small things than large ones across all scales. What are the “things” the two laws refer to? We have provided examples above while introducing these two laws. For example, cities in a country and streets in a city are the things, for they are with far more smalls than larges. Seen from the perspective of cities and streets, the country and the city are living structures. In general terms, the things that collectively constitute a living structure are the right things, whereas the things that collectively do not constitute a living structure are not the right things. For example, if the leaf vein was saved as a gray-scale image with 1024 by 1024 pixels, each of which has a gray scale between 0 and 255, careful examination of these pixel values would show that they do not have far more light (or dark) pixels than dark (or light) ones. This way, we would end up with an absurd conclusion that the leaf vein is not a living structure. In fact, the pixels are not the right things, or the pixel perspective is not the right perspective for seeing the living structure. 39. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 5 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Score: 0.012 Related excerpt #WAL2ZW: (Note: The 10 numbers [1, 1/2, 1/3, \dots, 1/10] are classified into three classes: [1/4, 1/5, \dots, 1/10] , [1/2, 1/3] , and [1] , which can be said to have three inherent hierarchical levels. The dataset, due to its inherent hierarchy, is therefore more living or more structurally beautiful than another dataset [1, 2, 3, \dots, 10] , which lacks any inherent hierarchy, or violates the scaling law.) 40. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 2 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #XRE3JP 2. Two laws together for characterizing living structure Score: 0.009 Related excerpt #P2UTSF: The second evidence is not only statistical, but also geometrical. The leaf vein shown in Figure 1 (Jiang and Huang 2021) apparently has far more small substructures than large ones from the largest square to the smallest white spots. Carefully examining the structure of the leaf vein, it is not difficult to find that there are four different levels of scale according to thickness of their outlines. In contrast, the Sierpinski carpet also has far more smalls than larges; that is, far more small squares than large ones, exactly rather than statistically (Sierpinski 1915). Let us carefully examine the exactitude of the carpet. The largest square in the middle of the carpet is size 1/3 , which is surrounded by eight squares of size 1/9 , each of which is surrounded by eight squares of size 1/27 , each of which is surrounded by eight squares of size 1/81 . Thus, there are two exponential data series, each of which is controlled by some exact number. The size of squares is exponentially decreased by the exact number 1/3 : (1/3, 1/9, 1/27, 1/81) , whereas the number of squares is exponentially increased by the exact number 8: (1, 8, 64, 41. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 5 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Score: 0.009 Related excerpt #WQW77N: For the sake of simplicity, we use the 10 numbers [1, 1/2, 1/3, \dots, 1/10] to show how they are classified through the head/tail breaks (Figure 3, Jiang and Slocum 2020). The dataset is a whole, and its average is about 0.29, which partitions the whole into two subwholes: those greater than the average are called the head [1, 1/2, 1/3] , and those less than the average are called the tail [1/4, \dots, 1/10] . The average of the head subwhole is about 0.61, and it partitions the head subwhole into two subwholes again: those greater than the average are called the head [1] , and those less than the average are called the tail [1/2, 1/3] . Instead of expressing the dataset as a set of numbers, we state the 10 numbers as an iterative system consisting of three subwholes recursively defined: [1] , [1, 1/2, 1/3] , and [1, 1/2, 1/3, \dots, 1/10] . Instead of perceiving these numbers as a set of 10 numbers, we consider them as a coherent whole, consisting of three subwholes including the whole itself. Or alternatively, these numbers as a coherent structure consists of three substructures including the structure itself. The dataset [1, 1/2, 1/3, \dots, 1/10] , because of its inherent hierarchy of 3, is more living than the other dataset [1, 2, 3, \dots, 10] that is without any inherent hierarchy, or violates the notion of far more smalls than larges. 42. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 8 Context: #57PDWB Interactive Procedural Street Modeling #RXG48N References Score: 0.012 Related excerpt #M6VYAD: HILLIER, B., 1998. The common language of space: A way of looking at the social, economic and environmental functioning of cities on a common basis. 43. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 11 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #5W8C4J 4.4 Procedural Terrain Generation #78P3XF 4.4.4 Navigational Mesh Management Score: 0.026 Related excerpt #B9EZ4X: so that its coverage is the interval [z_p - d_{\text{behind}}, z_p + d_{\text{ahead}}] , with d_{\text{ahead}} = 600 m and d_{\text{behind}} = 50 m. 44. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 6 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #SRM4HZ 3 Objectives and Technical Specification #EPG8QB 3.1 Evaluation Questions, Hypotheses, and Metrics Score: 0.014 Related excerpt #U8KTWM: Table 2 maps each research question to the metric and to the implementation source from which the measurement is obtained. 45. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 3 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #KV3Q48 Hydrostatic Pressure Columns Score: 0.023 Related excerpt #C8PJ9C: where d is the length of the pipe (equal to the grid spacing) and the tops and bottoms of the pipes are the min and max of the tops and bottoms of the cells into which the pipe flows: 46. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 3 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #KV3Q48 Hydrostatic Pressure Columns Score: 0.009 Related excerpt #ARDLKR: such that h_{ij} is the height of column at position (i, j) , \rho is the density of the fluid, g is the force of gravity, p_0 is the atmospheric pressure and p_{ij} is an external pressure being exerted on the column at position (i, j) due to rigid body interaction or an impact on the fluid surface. 47. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 5 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #XSQCC8 5.3. Tunnels and bridges Score: 0.021 Related excerpt #3U2T5T: Those path segments have a minimum and a maximum distance, denoted as r_i and r_e , which correspond to the minimum and maximum length a given type of tunnel or bridge can have. Therefore, we define: 48. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 3 Context: #UR2SY7 Procedural Generation of Roads #RNR7U5 4. Cost functions #RUTEZU 4.1. Surface roads Score: 0.01 Related excerpt #A9JRWW: The water height w(\mathbf{p}) is defined as the maximum height of water in a small area \Omega(\mathbf{p}, r) around the projection of \mathbf{p} onto the ground. \Omega(\mathbf{p}, r) denotes a sphere centered at point \mathbf{p} and of radius r . The density of vegetation v(\mathbf{p}) is computed by evaluating the number of trees that lie within \Omega(\mathbf{p}, r) . 49. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 4 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #SR7CUB 5.1. Path segment masks Score: 0.01 Related excerpt #CENURU: Table 2 reports timings (in seconds) as well as the cost (in arbitrary unit) and the length (in meters) for computing the anisotropic shortest path with different path segment masks over a 60 \times 60 grid. Timings increase in O(k^2) . 50. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 4 Context: #UR2SY7 Procedural Generation of Roads #RNR7U5 4. Cost functions #CKBVL8 4.2. Bridges and tunnels Score: 0.009 Related excerpt #QGBJH7: In the case of tunnels, the cost is parameterized by the depth of the tunnel to the surface d(\mathbf{p}) , its slope, and the depth of water bodies that may exist above the tunnel (Figure 6). This latter parameter enables us to simulate expensive tunnels passing under rivers or seas. ### 6. Tool result: search_text Exact matches 1. Source: Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning (#869NHK), Ian Parberry, Jennifer R. Alford, Mary Yingst, p. 5 Context: #5R6DEX Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning #LP9TTY Results Matching excerpt #V5XDSY: We performed some experiments to obtain a preliminary benchmark for the extra computation load required by our new halftoning technique (Figure 7(c)) to the traditional texturing technique (Figure 7(a)). We ran both algorithms for five minutes using NVidia Composer, using FRAPS to measure average frames-per-second. The scene rendered in all experiments is shown in Figure 8. The results are shown in Table 1. We conclude that the extra load on the video appears to be less than 3% higher than traditional texture-fading techniques, which is negligible. 2. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 6 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #CC4RWZ 8 Results Matching excerpt #RTYCL9: The results discussed in this section were calculated on a common PC with an Intel Core 2 Duo CPU (2.13 GHz), and a Nvidia Geforce 7950 GPU. As our implementation is not yet parallelized, it only makes use of one of the cores of the CPU. The actual frame rates of the different cases are given in Table 2. All test cases use between 160k and 200k grid points, and run with 40 to 75 frames per second, including rendering. The distribution of the computational time for the different parts of our algorithm can be found in Table 1. For this measurement a typical wave, as shown in Figure 6, was simulated. Overall, the fluid simulation amounts for 80% of the run time, while the rendering and overhead introduced by the graphics engine require the remaining 20%. Roughly half of the simulation time is spent on the shallow water simulation itself, while the wave simulation algorithm requires circa one fourth of the time. The creation of the surface mesh and the computation of the normals again requires roughly one fourth of the computations. 3. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 6 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #QQ7TWA 9 Conclusions Matching excerpt #XFKY8Q: We have presented a new method to perform real-time simulations of open water scenes with breaking waves. It is based on detecting and tracking the wave front with line segments. The breaking wave itself is represented by a patch of connected particles. Our model for coupling a rigid body simulation with the shallow water simulation moreover makes it possible to create interesting interactive applications, and can handle cases such as submerged bodies. Overall, the algorithm performs with high frame rates, and without causing noticeable slowdowns during the course of the simulation. It furthermore allows the efficient and seamless creation of a textured surface mesh. These properties of the algorithm make it especially interesting and suitable to be used in computer games. Although it is aimed for real-time applications, the algorithm is also interesting for high quality off-line animations. It could, e.g., allow the efficient simulation of large open water shore scenes, while giving animators real-time feedback during their work. 4. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 0 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #XUY95Y Abstract Matching excerpt #KHRCTA: We present a new method for enhancing shallow water simulations by the effect of overturning waves. While full 3D fluid simulations can capture the process of wave breaking, this is beyond the capabilities of a pure height field model. 3D simulations, however, are still too expensive for real-time applications, especially when large bodies of water need to be simulated. The extension we propose overcomes this problem and makes it possible to simulate scenes such as waves near a beach, and surf riding characters in real-time. In a first step, steep wave fronts in the height field are detected and marked by line segments. These segments then spawn sheets of fluid represented by connected particles. When the sheets impinge on the water surface, they are absorbed and result in the creation of particles representing drops and foam. To enable interesting applications, we furthermore present a two-way coupling of rigid bodies with the fluid simulation. The capabilities and efficiency of the method will be demonstrated with several scenes, which run in real-time on today's commodity hardware. 5. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 2 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWE9DD 2 PREVIOUS WORK Matching excerpt #DUQUBK: [17], [18] also share the same input (a texture and an animated flow) and output (an animated texture) as our algorithm. The main difference is that they use a global energy minimization using neighbor-based similarity criteria in the input textures, while we focus on minimizing local distortions. As a consequence, these methods keep the large-scale features, at the expense of conformance to the velocity field, while we keep local features and enforce conformance to the velocity field, at the expense of large-scale features. Our algorithm is better adapted to noise-based textures and to images with only local structure. Our local approach also requires less computations than the global minimization. As a consequence, our algorithm runs in real-time (less than 30 ms per frame) with no pre-computations, compared to several minutes per frame for, e.g. , [15]. 6. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 7 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Matching excerpt #5R6QUN: portional to the overall number of vertices: doubling the number of particles or doubling the number of vertices per grid will both have the effect of doubling the computation time for advection. 7. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Matching excerpt #WP9DC5: One of the strongest advantages of our method is that it runs in real-time, making it useful for interactive applications, such as video-games, exploration of virtual worlds, just-in-time generation of content and virtual modeling. 8. Source: Extracting Physics from Blended Platformer Game Levels (#9NQ94D), Adam Summerville, Anurag Sarkar, Joseph C. Osborn, Sam Snodgrass, p. 2 Context: #3VF3EH Extracting Physics from Blended Platformer Game Levels #KHMPZV Related Work #ATT2UK Physics Extraction Matching excerpt #A6TZBP: per second) – the rest of the games we looked at have speeds of around 5.5 tiles per second. If one wished to take these extracted physics and use them in a playable game, the different x speeds would result in different feeling games, but somewhere in the 4 to 10 tiles per second range would result in games playable by humans. 9. Source: Extracting Physics from Blended Platformer Game Levels (#9NQ94D), Adam Summerville, Anurag Sarkar, Joseph C. Osborn, Sam Snodgrass, p. 1 Context: #3VF3EH Extracting Physics from Blended Platformer Game Levels #KHMPZV Related Work #ATT2UK Physics Extraction Matching excerpt #E3QDD2: To extract the physics, we must first define the “physics” of a static level. In part, this seems ridiculous, as a static level cannot have a conventional physics model, as there is no notion of time. However, while this seems like an intractable problem, we believe that for several platformer games, there is an implicit correlation between horizontal position and time – e.g., a speedrunner of Mario is almost always moving to the right as quickly as they possibly can. In fact, the A* agent that we use to simulate “playing” the levels also operates under this assumption. Thus, we think it is reasonable to relax the physics models from a notion of y position versus time to a relation of y position to x position – with the understanding that the x position is supposed to be constantly progressing in the direction of the goal. It is important to note that the “physics” model we are extracting actually supports an infinite number of different possible physics models – changing the maximal x speed will result in different physics models. Some games have much slower horizontal speeds ( Castlevania has a maximal horizontal speed of \sim 3.7 tiles per second), while others have much faster speeds ( Super Mario Bros. has a maximal horizontal speed of 10 tiles 10. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 4 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #5KSC3E 2.3. Hybrid approaches Matching excerpt #2RHVZB: Hinsinger et al [HNC02] apply a LOD scheme to the method of [TDG00] by reducing both the sampling resolution of the surface mesh and the number of trochoidal components depending on the distance to the viewer. This approach reduces the amount of computations for the ocean simulation and tends towards real-time rates (approximately 20 to 30 frames per sec. on a GeForce 2 GPU), by using only a subset of the components. 11. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 4 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #96ENPE 2.2. Fourier domain approaches #2XBNYQ 2.2.2. Level-Of-Detail and GPU implementations Matching excerpt #KAFWZ7: Hu et al [HVT*06] apply a LOD approach to Tessendorf's method by representing the ocean with two surfaces. The first one, with a high, fixed resolution, is animated using a displacement map stored in a vertex shader, while the second one is sampled adaptively and applied as a bump map stored in a pixel shader. This approach produces a large ocean surface in real-time by animating only visible parts (at approx. 100 frames/sec. on GeForce 3 GPU card). Mitchell [Mit05] implemented Tessendorf's method on GPU by only considering frequencies generating a significant perturbation of the surface. A white noise is first generated using Phillips' spectrum, then frequencies are divided in two sets. Low frequencies accounting for the global motion of waves are stored as a displacement map in a vertex shader. High frequencies, representing fine details, are stored in a normal map used for rendering. Since only a part of the spectrum is animated, a realistic ocean surface is obtained at interactive rates; another implementation by Chiu and Chang [CC06] combine this approach with an adaptive tessellation method [Joh04] (see previous section). 12. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 2 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #B9SCHY 2.1. Spatial domain approaches #W9ZUCV 2.1.2. GPU implementations Matching excerpt #GFZ39R: Series of periodic functions are particularly well suited to GPU computations, and in the last few years research works describing real time implementations have emerged. 13. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 1 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work Matching excerpt #DNQAHN: In the real-time domain, [15] was the first to explore caustics using synthetic texture maps; although inaccurate, they were visually compelling. Nevertheless, to achieve physically realistic results, the more recent techniques are inspired in pathtracing methods and can be generally classified in two groups. In the first group, techniques like, e.g., [16, 17, 3, 18], render from light and create caustic maps, similar to photon maps, but used like shadow maps; reprojected in camera space in order to lit the visible pixels that receive caustics. In the second group, the caustics are traced back from the receiver object to the light through limited areas on the refractive surface as in [19, 20], which usually require the receiver to be planar as a simplification. 14. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 0 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #SDDXFP Abstract Matching excerpt #7CK2EH: Keywords: real-time reflections and refractions, real-time caustics, fluid rendering 15. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Matching excerpt #NYZKTL: which competes with erosion and can lead to a progressive increase in the surface altitude, called surface uplift [EM90]. Rates of rock uplift and erosion vary in space and time and achieve values up to a few millimeters per year in some mountain ranges. 16. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 1 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #CS9FLT 1 Introduction Matching excerpt #ZBUPG9: dictive control (MPC) problem by linearizing the nonlinear vehicle dynamics at every time step and approximating the minimum-time objective by maximizing distance traveled along the path centerline. The resulting racing line for a 90 degree turn was simulated next to an NLP solution. Gerds et al. [7] proposed a similar receding horizon approach, where distance along a reference path was maximized over a series of locally optimal optimization problems that were combined with continuity boundary conditions. One potential drawback of the model predictive control approach is that an optimization problem must be reformulated and solved at every time step, which can still be computationally expensive. For example, Timings and Cole reported a computation time of 900 milliseconds per 20 millisecond simulation step with the CPLEX quadratic program solver on a desktop PC. 17. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 10 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #66SM5X 7 Discussion and Future Work Matching excerpt #MR4QDN: to run at the same sample time as the vehicle controller. Instead, the planner would operate on a separate CPU and provide a velocity profile and racing line for only the next 1-2 kilometers of the race track every few seconds, or plan a path for the next several hundred meters within a second. 18. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 0 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories Matching excerpt #BPF8Q6: The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward-backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this fixed speed profile, the algorithm updates the vehicle's path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs very well when validated on the Thunderhill Raceway course in Willows, CA. The predicted lap time converges after four to five iterations, with each iteration over the full 4.5 km race course requiring only thirty seconds of computation time on a laptop computer. The resulting trajectory is experimentally driven at the race circuit with an autonomous Audi TTS test vehicle, and the resulting lap time and racing line is comparable to both a nonlinear gradient descent solution and a trajectory recorded from a professional racecar driver. The experimental results indicate that the proposed method is a viable option for online trajectory planning in the near future. 19. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 9 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #LGLUMA 6 Experimental Validation Matching excerpt #8AQDAB: The resulting experimental lap time for the iterative two-step algorithm was 138.6 seconds, about 0.6 seconds faster than the experimental lap time for the gradient descent algorithm (139.2 seconds). For safety reasons, the trajectories were generated using a conservative peak road friction value of \mu = 0.90 , resulting in peak lateral and longitudinal accelerations of 0.9g . In reality, the true friction value of the road varies slightly, but is closer to \mu = 0.95 on average. As a result, both of these lap times are slightly slower than the fastest lap time recorded by a professional race car driver (137.7 seconds) and the predicted lap times from Section 5. A summary of all lap times is provided in Table 2. 20. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 8 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #W352NS 5 Algorithm Implementation and Simulated Results #MQ2VEA 5.4 Lap Time Convergence and Predicted Lap Time Matching excerpt #UCVJLC: Fig. 11 shows that the predicted lap time converges monotonically over four or five iterations, with significant improvements over the centerline trajectory occurring over the first two iterations. The predicted minimum lap time of 136.4 seconds is similar to the predicted lap time of 136.7 seconds from the nonlinear gradient descent approach, although in reality, the experimental lap time will depend significantly on unmodelled effects such as powertrain dynamics. 21. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 10 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #LGLUMA 6 Experimental Validation Matching excerpt #FQB2Z9: trajectory from the iterative two-step algorithm would be 0.3 seconds quicker than that of the nonlinear algorithm, compared to the 0.6 second speed advantage observed experimentally. The simulation also predicted a relative time advantage for the two-step algorithm from sections (a) to (c) and from (e) to (h), a trend seen in the experimental data as well. The two-step algorithm has relatively poor performance from section (c) to (d). This portion of the track corresponds to the sharp right-handed turn shown in Fig. 9, where the two-step solution differs significantly from the human driver data and the gradient descent solution. This turn also occurs on a steep downhill segment of the track, which was not accounted for by the fast generation algorithm. The experimental results indicate the minimum curvature heuristic is relatively poor for this particular turn when compared to a nonlinear algorithm that explicitly minimizes lap time. Accounting for three-dimensional topography effects in the curvature minimization or adding a term in the cost function to minimize distance traveled may improve the performance in the future. 22. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 10 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #66SM5X 7 Discussion and Future Work Matching excerpt #A5S6ML: The possibility of real-time trajectory planning for race vehicles creates several fascinating areas of future research. An automobile’s surroundings are subject to both rapid and gradual changes over time, and adapting to unpredictable events requires a real-time trajectory planning algorithm. On a short time scale, the real-time trajectory planner could find a fast but stable recovery trajectory in the event of the race vehicle entering an understeer or oversteer situation. On an intermediate time scale, the fast executing two-step algorithm could continuously plan a racing line in the presence of other moving race vehicles by constraining the permissible driving areas to be collision-free convex “tubes” [16]. Finally, the algorithm could update the racing trajectory given estimates of the friction coefficient and other vehicle parameters learned gradually over several laps of racing. 23. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 10 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #66SM5X 7 Discussion and Future Work Matching excerpt #CK2TWF: The primary benefit of the proposed algorithm is not improved lap time performance over the nonlinear algorithm but rather a radical improvement in computational simplicity and speed. Each two-step iteration of the full course takes only 26 seconds on an Intel i7 processor, whereas the nonlinear algorithm from [5] typically runs over the course of several hours on the same machine. The most significant computational expense for the proposed algorithm is solving the convex curvature minimization problem for all 1843 discrete time steps T over the 4.5 km racing circuit. 24. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 1 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #CS9FLT 1 Introduction Matching excerpt #XZG9K9: in an autonomous Audi TTS testbed via a previously published closed-loop path following controller [10]. The resulting lap time compares well with the lap time recorded for the nonlinear optimization trajectory. Section 7 concludes by discussing future implementation of the algorithm in a real-time path planner. 25. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 1 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #CS9FLT 1 Introduction Matching excerpt #E9YJ7A: While experimental validation was reported only by [5] and [7], all of the aforementioned methods are feasible for experimental implementation, as an autonomous vehicle can apply a closed-loop controller to follow a time-optimal vehicle trajectory computed offline. However, there are significant benefits to developing a fast trajectory generation algorithm that can approximate the globally optimal trajectory in real-time. If the algorithm runtime is small compared to the actual lap time, the algorithm can run as a real-time trajectory planner and find a fast racing line for the next several turns of the racing circuit. This would allow the trajectory planner to modify the desired path based on the motion of competing race vehicles and estimates of road friction, tire wear, engine/brake dynamics and other parameters learned over several laps of racing. Additionally, the fast trajectory algorithm can be used to provide a very good initial trajectory for a nonlinear optimization method. 26. Source: Real-time Rendering of River Networks (#MVUJ8Z), Quintijn Hendrickx, Rafael Bidarra, Ruben M. Smelik, p. 0 Context: #BTQCB6 Real-time Rendering of River Networks Matching excerpt #MSQQ8G: A commonly used method to visualize Bézier curves is to sample along the curve at a fixed rate, and then tessellate these samples into a geometric structure. However, to achieve smooth results, many samples are needed, resulting in a high vertex count. Because this is often not desirable in real-time rendering, we render the Bézier curves with bounding quads using only four vertices per curve. An implicitly defined distance field is used to project each pixel in the quad onto the nearest point on the curve. Using only quadratic order Bézier curves allows us to define the distance field as a function of the Bézier control points, which does not require any iterative algorithms. As a result this function is, due to its parallel nature, particularly suited for being evaluated on the GPU. Because of the low vertex count, no LOD techniques are necessary for large scale river networks, and rendering performance depends mostly on the total surface of visible water in screen-space. 27. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Matching excerpt #CWJDCB: As a starting point, Figure 1 shows a real digitized terrain, subsequently altered by fluvial erosion and sediment deposition, and overlaid with flow-dependent vegetation, lakes, and rivers, in under 1.5 seconds. 28. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 7 Context: #RNVWWR Water Surface Wavelets #MEQNZV 6 EXTENSIONS #5W242X 6.2 Pre-computing wave motions Matching excerpt #23W9S2: wave motion until the amplitudes reach a steady state, and then storing the \mathcal{A} functions as static textures. We can then interpolate these \mathcal{A} textures at any point in space and use them to efficiently compute wave heights at run-time. This pre-computation of \mathcal{A} leads to a considerable speed-up over running the full simulation ( 4.7\times speedup from \approx 60\text{fps} to \approx 280\text{fps} in this example). Our method is arguably more efficient than Lagrangian wavefront tracking (though the methods have very different numerical parameters and the errors behave differently), and the run-time behavior is more convenient and load-balanced for graphics hardware than an adaptive triangle mesh. 29. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 1 Context: #RNVWWR Water Surface Wavelets Matching excerpt #Z9BPVH: Additional Key Words and Phrases: Water animation, real-time animation, natural phenomena 30. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 0 Context: #RNVWWR Water Surface Wavelets Matching excerpt #D2FPFW: obstacles in real time while simultaneously preserving minute details and accommodating very large simulation domains. 31. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 5 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #6AJDFD 4.1 Discretizing \mathcal{A} Matching excerpt #4APXZ6: Lastly, the simulations in this paper use real-valued \mathcal{A} functions as initial conditions. This function then stays real for all time according to Equation 10, so our implementation does not bother to store complex \mathcal{A}_{abc} coefficients. 32. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 0 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #9QMYPL 1. Introduction Matching excerpt #HU5QE8: the undesirable spherical particle structure. Second, there exists as yet no realistic real-time method to create foam, which is an important visual element in most situations where real-time fluids are used (see Figure 1). 33. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 5 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #JEPXQL 7. Conclusions and Future Work Matching excerpt #YJNSYU: We presented a new method for rendering particle-based fluids with foam in real time. The first contribution is an adaptive curvature flow smoothing method that avoids over- or under-smoothing as present in previous methods. Our second contribution is a fast physically guided foam rendering algorithm based on Weber number thresholding and a layered compositing algorithm. Our approach provides more realistic fluid rendering at comparable cost to previous methods, and is simple to implement and integrate into existing engines. In future work, we plan to use the volumetric information available in the layers to generate soft shadows. We will also investigate whether situations that require more than 3 layers are likely to appear. 34. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 0 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #9QMYPL 1. Introduction Matching excerpt #FJR986: This paper presents a real-time fluid simulation and rendering system that overcomes these drawbacks: 35. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 5 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #T8YYAV 6. Results Matching excerpt #754PPX: Table 1 compares the computational cost of [vdLGS09] with our method (SPH simulation time not included). The indicated running times are an average for a default camera movement. Our method has comparable performance with the benefit of improved image quality especially at near or far viewpoints. Even foam does not significantly increase running time for our method. Figure 6 presents the computational cost of [vdLGS09] and our method using the example of a camera zoom movement in the waterfall scene (like the one of the filter comparison shown in the accompanying video). It takes on average 23.12% of the computation time to render the water and foam depth, 24.4% for the thickness passes, 27.43% for the adaptive curvature flow filtering and 25.05% for the composition (including update of data structures). This measurement represents the mean breakdown of 6k frames used different viewpoints. Figure 1 36. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 10 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #TH9KVK 6. The new geography, its implications, and future works Matching excerpt #NWEHXV: Geographic information gathered through geographic information technologies has provided rich data sources for studying living structures on the Earth's surface from the perspectives of space, time, and human activities. This is particularly true for big data emerging from social media or the Internet. The big data are better than government owned or defined data for revealing the underlying living structure for two main reasons. First, big data have high resolution (like GPS locations of a couple of meters), and finer time scales (down to minutes and seconds for social media location data). Thus, they are better than government data for seeing living structure at different levels of scale. Second, government-defined spatial units, such as census tracts, are too rough or too arbitrary for seeing living structure. Instead, we should use naturally defined spatial units such as natural cities and auto-generated substructures (Jiang 2018, Jiang and Huang 2021), which are all defined from the bottom up, rather than imposed from the top down, thus making it easy to see living structures. While working with big data, we should try to avoid using grid-like approaches such as the digital elevation model. Although the digital elevation model has far more low elevations than high ones, the grid approach is not the right perspective for seeing living structures. Instead, we should use watersheds or water streams which are naturally or structurally defined. All these topics will be studied in the future for the new geography. 37. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 5 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #SRM4HZ 3 Objectives and Technical Specification #EPG8QB 3.1 Evaluation Questions, Hypotheses, and Metrics Matching excerpt #EDMX8Z: RQ3 (Performance). Can both agents perform their per-tile inspection within the 16.66 ms frame budget associated with 60 FPS, or at least within the 33.33 ms budget associated with 30 FPS, as defined by Unity’s profiling guidance [12, 13]? Hypothesis H3: the per-segment cost is bounded by a small constant independent of run length, because the scanner is gated by an integer tile index and amortises the OverlapBox sweep across many ray probes. 38. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 0 Context: #JCB5RE Advected river textures #DQ7LJZ Introduction Matching excerpt #8KBMFE: of our method is to approximate as much detail as possible while remaining efficient enough for interactive applications. We have also adopted the additional requirement that the method should be suitable for coupling with a rigid-body physics engine allowing 3D objects in the scene to interact with the river's surface. Specifically, we achieve the following: detailed fluid surface construction that responds appropriately to the underlying 3D terrain, simulation of the surface detail of real rivers, above real-time frame rates on commodity hardware, and an algorithm designed with rigid-body coupling in mind. To realize these goals we incorporate a 2D Navier–Stokes solver for its stability, efficiency, and accuracy, that is informed by 3D information gleaned from a series of Hydrostatic Pressure (HSP) columns. We do not use HSP columns alone since it is not a suitable approach for large-scale river representations as it cannot capture detailed effects 2 . We then couple the results of our pseudo-3D Navier–Stokes–HSP fluid solver with a texture advection method in order to derive highly detailed river surfaces. Example renderings running at 60–120 frames per second (85 on average) can be found in Figure 1. 39. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 2 Context: #JCB5RE Advected river textures #G2SPEY Previous Work Matching excerpt #MNRCLS: Texture advection 12,37 transports colour based on a simulation or function. For our purposes we recast texture advection moving surface waves along a river as dictated by our fluid simulation. Kwatra et al. 38 recently tied texture synthesis to a full 3D NS solver. However, as they were not concerned with real-time performance, their technique is not immediately applicable to our problem domain. Their system required up to 200 seconds per frame in order to render a small volume of fluid and it can be argued that they remain somewhat artificial and procedural in appearance. 40. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 8 Context: #JCB5RE Advected river textures #HMVN46 Results Matching excerpt #PRVSL6: Level of Detail provides notable performance improvements as can be seen in Table 1. Even the modest LOD optimizations we have implemented make a significant difference to the frame rate and to the number of polygons rasterized per second. All screenshots and timings were produced on an off-the-shelf dual-core Athlon XP 3800+ computer with an nVidia 8600GT graphics card and 4GB RAM. However, the code has not been parallelized or GPU optimized, meaning that only one of the two cores on the CPU has been directly used. Most of example river beds used in this paper have been imported from DEM files of real rivers. 41. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 1 Context: #JCB5RE Advected river textures #G2SPEY Previous Work Matching excerpt #2HFBD6: methods retain conservation of mass and can represent free-form surfaces and splashing 19 . However, such methods are limited by the number of particles that can be used in real-time. In 2003, Müller et al. 20 achieve interactive rates with 5000 particles. Clavet et al. 21 simulate 1000 particles at 10 fps while offering two-way arbitrary object to fluid coupling. Kipfer and Westermann 22 simulate rivers using SPH at interactive rates with 3000 particles, though we argue that the fluid does not achieve a truly realistic river surface. In recent years commercial GPU based solutions have appeared that can handle roughly 100,000 particles but even this is insufficient to simulate a river with fine grained detail. Realistic rivers would require perhaps tens to hundreds of millions of particles which is simply not feasible at this time. Though we note SPH has successfully been used offline to create stunning simulations 23,24 . 42. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 1 Context: #JCB5RE Advected river textures #G2SPEY Previous Work Matching excerpt #EAV5V5: Hydrostatic Pressure (HSP) columns presented by Kass and Miller 27 and extended to 3D by Mould and Yang 28 form a system of columns and pipes that move water based on the laws of hydrostatics. Several simulators incorporate HSP solvers as it is one of the few techniques that is efficient enough to produce a large-scale fluid simulation in real-time. Holmberg and Wunsch 2 use an HSP based system to represent a very small river section. Their aim was more to generate splashing based on interactions between fluid and terrain than large-scale rivers or a detailed surface representation. Maes et al. 1 later used HSPs and a particle system to model both a river fluid surface and splashing effects. But the method is unstable if time deltas become too large, and does not achieve real-time frame rates even with extensive GPU optimization. HSPs are also “not capable of simulating certain situations such as vortices. A second problem arises from the fact that turbulence is a feature of flow and not of the fluid at rest. This means that . . . the equations generated for flow are incomplete and ignore many of the visible characteristics of water such as viscous shear stresses.” 2 We therefore do not use HSP columns directly, but use them to inform our NS solver and method of texture advection. 43. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 0 Context: #JCB5RE Advected river textures Matching excerpt #VPL9P5: We present a new method for the realistic real-time simulation of rivers. Our solution includes a 2D fluid solver that simulates the flow of a river's surface, an efficient method for adaptively computing 3D flow information and an animated 3D procedural wave texture that is advected through the fluid via advection particles in order to mimic the highly detailed fluid surfaces that are characteristic of rivers. Our technique that couples animated texture advection with a pseudo-3D fluid simulation produces stable results that are representative of large-scale real-world rivers and suitable for use in real-time applications. Our system surpasses prior work on real-time river rendering both with regards to efficiency and visual quality, which we establish through the rendering of rivers tens of kilometers long. Copyright © 2009 John Wiley & Sons, Ltd. 44. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 0 Context: #JCB5RE Advected river textures #DQ7LJZ Introduction Matching excerpt #EWXZK3: Real-time fluid simulation is a challenging problem in which “no single method (exists) that can capture all the subtle effects of water” 1 . Our work specifically focuses on real-time river rendering which is problematic for several reasons: the arbitrary 3D terrain geometry of the riverbed must be taken into account, rivers often include situations with both shallow and deep water, even slow moving rivers have highly detailed dynamic geometries, and rivers are generally very large, stretching many kilometers. Rendering large scale river flows for real-time applications is therefore difficult because of the complexity involved in generating a fluid surface that is both detailed enough to be visually realistic and efficient enough to be interactive. 45. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 8 Context: #JCB5RE Advected river textures #AZAUNZ Conclusion Matching excerpt #T9Y2PR: We have developed an efficient approach to rendering large-scale fluid flows over arbitrary terrains with a relatively high level of realism. By combining an impulse driven 2D Navier–Stokes simulation with multi-tier hydrostatic pressure columns we have created a low computational-cost fluid solver that provides sufficient 3D information to simulate a river in real-time. We then employ procedural wave generation to produce an animated texture which is advected through the fluid simulation. This produces a highly detailed fluid surface representation that exhibits many of the visual elements that are characteristic of rivers. Our technique is applicable to real-time and interactive simulation scenarios and has been designed with rigid-body physics objects in mind. We feel that this work is therefore a major step forward in the area of real-time river rendering for interactive applications. 46. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 1 Context: #JCB5RE Advected river textures #G2SPEY Previous Work Matching excerpt #EF396K: The most common approach for real-time simulation are Navier–Stokes based solvers. Early work by Chen et al. 11 proposed a method for real-time Navier–Stokes; however, the system suffers from instability issues and only operates on limited size volumes of water. Stam's 12 groundbreaking work later outlined techniques for stable advection. Thon and Ghazanfarpour 13 simplify the problem for rivers by using a 2D Navier–Stokes solver to drive Perlin Noise functions 14 along streaklines. However, their system does not incorporate 3D flow information and produces animations with a procedural appearance lacking key visual features found in rivers. Neyret and Praizelin 15 proposed a simpler model for streams using a two-dimensional Laplace equation, but only produce schematic 2D animations. In recent work, Lee and Sullivan 16 present a method for efficiently computing shallow water equations but only at the expense of stability and they are unable to simulate volumes of fluid at the river scale. To date, real-time free-surface 3D solvers remain unfeasible for large volumes of fluid. 47. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 5 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #CSD47K Impulse Driven NS Matching excerpt #JS4LBU: It should also be noted that the flow speed of the river itself should be set in accordance to the grid cell size of the river in order to maintain grid size independent flow rates. For example, if the desired flow rate is 1.3 meters per second and the cell width is 1.0 unit, the flow rate should be set to one half the value of the same flow rate on a grid with a cell width of 2.0 units. 48. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 4 Context: #B9LYTR Scalable real-time animation of rivers #S3P9T2 4. Computing flow velocities #R6ERAY 4.2. Interpolation of stream function Matching excerpt #5K5CS4: where p is a positive real number and f is a function that ensures C^2 continuity: f(0) = 0 , f(1) = 1 , with null first and second derivatives at 0 and 1. We used: 49. Source: Generative Codes: The Path to Building Welcoming, Beautiful, Sustainable Neighborhoods (#XW22YY), Brian Hanson, Christopher Alexander, Maggie Moore Alexander, Michael Mehaffy, Randall Schmidt, p. 4 Context: #CU9CAT Generative Codes #5RWPGZ Historical Background Matching excerpt #QXR2S9: The result of this is more like a carefully-plotted piece of fiction than real life: for a time you might be fooled into thinking this is real, but sooner or later the hand of the author can be glimpsed. 50. Source: Generative Codes: The Path to Building Welcoming, Beautiful, Sustainable Neighborhoods (#XW22YY), Brian Hanson, Christopher Alexander, Maggie Moore Alexander, Michael Mehaffy, Randall Schmidt, p. 15 Context: #CU9CAT Generative Codes #MU7M8B The Process of Procurement #9DEDCQ Independent, Community-Oriented Project Management: The Operational Underpinning of a Generative Code Matching excerpt #ZU3GVM: Second , it is the specialized field of project management which trains people to thread their way through such complexity, while holding fast to cost and time targets. Approximate matches 1. Source: Real-time River Representation by Dynamic Control of Data on Waves (#5MGCZ5), Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato, p. 2 Context: #RNRNU8 Real-time River Representation by Dynamic Control of Data on Waves #M8MFLM 5. シミュレーション結果 Score: 0.016 Related excerpt #6PE2J2: 上記手法を適用して、河川のリアルタイム表現を試みた。分割された各領域と適用したモデルの関係を表1に示す。近距離景は最も詳細なモデル、遠距離景は最も粗なモデル、中距離景は中間のモデルとなるが、流速の変化に基づく川の流れ変化は視認性が良いため、中距離景は遠距離景に流速計算を加えたモデルとする。ただし、風の影響は遠方でも視認できるため、全モデルに適用する。また、中および遠距離景では波の高さを計算せず、余弦波で描れる法線ベクトルを擬似的に与えるバンパマッピング法を用いる。風の影響も同様で、水面波の変化を法線ベクトルに反映する。さらに、可視化前の法線ベクトルに 1/f ノイズを加えて自然な流れを表現する。表2に本シミュレーションで使したPCの性能を示す。なお、本手法では波の波形計算後、風の影響やノイズの付加を考慮しており、高速化のためのテーブルが必要がある。また、CPUとGPUとの負荷分散を考慮して、波の形状計算までをCPU、レンダリング以降をGPUで行っている。 2. Source: Real-time River Representation by Dynamic Control of Data on Waves (#5MGCZ5), Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato, p. 3 Context: #RNRNU8 Real-time River Representation by Dynamic Control of Data on Waves #M8MFLM 5. シミュレーション結果 Score: 0.015 Related excerpt #26QLGQ: 図6に示す。近距離景では水面波の様子だけでなく、川岸での反射も表現できている。図6で使用したポリゴン数は、近距離景1,840、中距離景8,820、遠距離景9,340であり、川以外の表示物として92,000ポリゴンを使用している。表示時間を測定したところ、総合計112,000ポリゴンの表示物に対して、表示速度は37fpsであった。なお本結果では、遠距離ほどポリゴン数が多くなっている。これは、領域分割を行った結果、遠距離ほど川の領域が長くなったためである。しかしながら、視点からの距離に応じてメッシュの精度を制御するLOD手法 9) の適用によりさらなる高速化は可能である。ただし、メッシュサイズを大きくし過ぎると、波の形状を再現できない可能性があり、LOD手法の適用には注意が必要である。また、ポリゴン数を変えて性能測定した結果、モデル切換えによる性能向上は1Kポリゴンの川で約8%、12Kポリゴンの川で約96%（ほぼ倍の性能）となった。 3. Source: Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning (#869NHK), Ian Parberry, Jennifer R. Alford, Mary Yingst, p. 5 Context: #5R6DEX Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning #LP9TTY Results Score: 0.027 Related excerpt #V5XDSY: We performed some experiments to obtain a preliminary benchmark for the extra computation load required by our new halftoning technique (Figure 7(c)) to the traditional texturing technique (Figure 7(a)). We ran both algorithms for five minutes using NVidia Composer, using FRAPS to measure average frames-per-second. The scene rendered in all experiments is shown in Figure 8. The results are shown in Table 1. We conclude that the extra load on the video appears to be less than 3% higher than traditional texture-fading techniques, which is negligible. 4. Source: Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning (#869NHK), Ian Parberry, Jennifer R. Alford, Mary Yingst, p. 5 Context: #5R6DEX Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning #LP9TTY Results Score: 0.019 Related excerpt #RMEZSJ: Still pictures such as shown in Figure 7 and Figure 8 do not adequately capture the full effect of our algorithm. Figure 9 shows how foam bubbles fade and pop over time in the wake of each wave. This can be seen to best advantage in an animation such as the one we have placed online at [10]. 5. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 6 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #CC4RWZ 8 Results Score: 0.027 Related excerpt #RTYCL9: The results discussed in this section were calculated on a common PC with an Intel Core 2 Duo CPU (2.13 GHz), and a Nvidia Geforce 7950 GPU. As our implementation is not yet parallelized, it only makes use of one of the cores of the CPU. The actual frame rates of the different cases are given in Table 2. All test cases use between 160k and 200k grid points, and run with 40 to 75 frames per second, including rendering. The distribution of the computational time for the different parts of our algorithm can be found in Table 1. For this measurement a typical wave, as shown in Figure 6, was simulated. Overall, the fluid simulation amounts for 80% of the run time, while the rendering and overhead introduced by the graphics engine require the remaining 20%. Roughly half of the simulation time is spent on the shallow water simulation itself, while the wave simulation algorithm requires circa one fourth of the time. The creation of the surface mesh and the computation of the normals again requires roughly one fourth of the computations. 6. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 6 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #QQ7TWA 9 Conclusions Score: 0.012 Related excerpt #XFKY8Q: We have presented a new method to perform real-time simulations of open water scenes with breaking waves. It is based on detecting and tracking the wave front with line segments. The breaking wave itself is represented by a patch of connected particles. Our model for coupling a rigid body simulation with the shallow water simulation moreover makes it possible to create interesting interactive applications, and can handle cases such as submerged bodies. Overall, the algorithm performs with high frame rates, and without causing noticeable slowdowns during the course of the simulation. It furthermore allows the efficient and seamless creation of a textured surface mesh. These properties of the algorithm make it especially interesting and suitable to be used in computer games. Although it is aimed for real-time applications, the algorithm is also interesting for high quality off-line animations. It could, e.g., allow the efficient simulation of large open water shore scenes, while giving animators real-time feedback during their work. 7. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 7 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Score: 0.026 Related excerpt #FCMCYQ: Timing results for a zoom in the fire example, using a fixed-size viewport ( 256 \times 256 ). 8. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON Score: 0.021 Related excerpt #B3QB7D: All pictures and timings in this paper and in the companion video 2 were computed on an Intel Core i7, running at 2.67 GHz, with an Nvidia GeForce GTX 275. 9. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Score: 0.02 Related excerpt #FB5X95: For Fig. 4, 6, 7, 8 and most of the video sequences, we used a fluid covering the entire picture, an output texture size of 512 \times 512 , and 300 grids of 8 \times 8 vertices (including grids being faded in or faded out). The timings correspond to the fire example (Fig. 4). 10. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Score: 0.018 Related excerpt #WP9DC5: One of the strongest advantages of our method is that it runs in real-time, making it useful for interactive applications, such as video-games, exploration of virtual worlds, just-in-time generation of content and virtual modeling. 11. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 8 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #K4JT29 4.3 Evaluation and comparison #8TM3YZ 4.3.3 Comparison with Eulerian Texture Advection Score: 0.011 Related excerpt #DT4Z7F: Max and Becker [11] used a single latency for the entire domain. Their method preserves the optical flow at the cost of stretching the texture in fast areas. Adjusting the latency for these fast areas breaks the illusion of motion (and thus the optical flow) in slow areas. See Fig. 7 and the companion video. 12. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 6 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #2RYGP7 6.3. Performance Score: 0.019 Related excerpt #D6XHTB: Table 1 reports the performance of our method as a function of the number of sampling points. Although we did not fully optimize the implementation, our method provides interactive feedback at every time step which enables us to visualize a simulation at interactive rates and to tune parameters. 13. Source: Extracting Physics from Blended Platformer Game Levels (#9NQ94D), Adam Summerville, Anurag Sarkar, Joseph C. Osborn, Sam Snodgrass, p. 2 Context: #3VF3EH Extracting Physics from Blended Platformer Game Levels #KHMPZV Related Work #ATT2UK Physics Extraction Score: 0.013 Related excerpt #A6TZBP: per second) – the rest of the games we looked at have speeds of around 5.5 tiles per second. If one wished to take these extracted physics and use them in a playable game, the different x speeds would result in different feeling games, but somewhere in the 4 to 10 tiles per second range would result in games playable by humans. 14. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 8 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #FYBSSG 7.1. Performance Score: 0.016 Related excerpt #9DU2N2: Table 2 reports timings and statistics for our method for the examples from this paper. Our implementation supports both real-time GPU and high-quality offline photon-traced rendering. The final model has a compact memory footprint: we are able to represent meandering rivers several kilometers in length with complex water effects in less than a few megabytes. Memory consumption is as low as 22 kilobytes for short rivers (of 50m) up to 2.7 megabytes for longer rivers ( \approx 4 km). Even without memory optimization, individual primitives range from 50 bytes to at most 90 bytes. 15. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 5 Context: #JJE8HN Procedural Riverscapes #TFD8TX 5. River Network Amplification #AZ7MGY 5.4. Rosgen Scene Statistics Score: 0.013 Related excerpt #YCESD5: Table 1 reports the parameters and primitives statistics for Figures 14. The generation time of the two construction trees (riverbed and water) is negligible for these scenes (around 15ms). The number of primitives is related to the average density, which has been set in these examples to a sample every 50cm. It is possible to optimize the construction trees by grouping equivalent parameter primitives into a larger one. 16. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 2 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #B9SCHY 2.1. Spatial domain approaches #W9ZUCV 2.1.2. GPU implementations Score: 0.018 Related excerpt #GFZ39R: Series of periodic functions are particularly well suited to GPU computations, and in the last few years research works describing real time implementations have emerged. 17. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 6 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #GKHL8Q 6. Results and Discussion Score: 0.03 Related excerpt #68CY35: were captured with the fluid covering the whole viewport, and even in this case, the whole algorithm does not cost more than 10ms for a reasonably sized viewport. In perspective, [23] made total internal refraction available although without surface reflection which, in the best case, reported 138fps, i.e., 7.24ms per frame on a Nvidia 8800 GTX, using only one bounce for internal refraction on a viewport of 512 2 . Although our GPU is newer than theirs, in a similar scenario, we achieve less than half their time with both refraction and reflection. 18. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 6 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #GKHL8Q 6. Results and Discussion Score: 0.029 Related excerpt #P6Z6YL: Nevertheless, the timing results for both these techniques combined, the lower scale detail and the foam advection, never exceed the 2ms mark. 19. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 6 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #GKHL8Q 6. Results and Discussion Score: 0.021 Related excerpt #CLEMXK: For the caustics, as shown in Table 1 and concluded in [3], the performance of the caustics algorithm depends primarily on the size of the grid of photons, but in our case also on the direction of the light, which can cause more photons to miss the light space raycast and use the second camera space one, thus increasing the number of computations and texture fetches needed to try to find a final position for them. Also, as the raycasting is done in the vertex shader it is further slowed down because of the increased penalty of texture fetches in that shader stage. Although a direct comparison with [3] is difficult because of the different hardware used, they reported to achieve about 200fps with a 128 2 photon grid, which is the same that saying that each frame costs 5ms to compute. With newer hardware but the dual light and camera space raycasts we propose, the cost of computing caustics is, in our case, below 2ms for the same configuration. 20. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 3 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work #XEPFKX 179 3.2. Surface Foam Score: 0.021 Related excerpt #GRWR54: Overall, as seen in Figure 5, the results are convincing and the computations are faster due to the limited requirements, which make it ideal in real-time applications. 21. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 0 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #SDDXFP Abstract Score: 0.018 Related excerpt #BVUXWL: The visualization of simulated fluids is critical to understand their motion, with certain light effects restricted or with added computational complexity in the implementation if real-time simulation is required. We propose some techniques that improve the rendering quality of an enhanced shallow waters simulation. To improve the overall appeal of the fluid representation, lower scale details are added to the fluid, coupling external non-physical simulations, and advecting generated surface foam. We simulate caustics by raytracing photons in light and screen-space, and apply refraction and reflections also in screen-space, through a number of render passes. Finally, it is shown how a reasonably sized fluid simulation is executed and rendered at interactive framerates with consumer-level hardware. 22. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 0 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction Score: 0.016 Related excerpt #DHJP5S: With present fluid simulations being performed in GPUs at interactive framerates, we also need realistic visualizations which reproduce these effects of the light. In our case, we start from a heightfield fluid simulation enhanced with particles for the simulation of splashes in breaking wave conditions, like the ones proposed in [1] or [2], which are also fully coupled with dynamic objects. From there, we aim to provide these expected, light-based effects, namely refractions, reflections and caustics. 23. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 5 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #GKHL8Q 6. Results and Discussion Score: 0.014 Related excerpt #A3VUS3: We have tested the previous algorithms on an Intel Core2Duo E8400 with 4GB of RAM and a Nvidia GTX280 running Ubuntu 11.10. The resulting averaged timings of the caustics and refraction/reflection algorithms are shown in Table 1, as these are the ones that tax more on the GPU by the use of raycasting. 24. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 0 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction Score: 0.014 Related excerpt #NGMSBP: In the real-time field, however, GPUs are used which implement rasterization algorithms. These algorithms rely on high coherency for the operations executed, which impose some constraints to simulate light as a raytracer could do, by simulating each separate light beam. For this reason, photorealistic rendering is achieved at interactive framerates by simplifying the algorithms used or even using tricks that are perceptually feasible. 25. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 6 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #GKHL8Q 6. Results and Discussion Score: 0.013 Related excerpt #HHS3QR: The performance of the refraction/reflection algorithm is quite variable, it depends on the size of the viewport as well as the coverage of the fluid in screen: the more visible pixels, the more rays are cast. For fair comparison, the results in Table 1 26. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 2 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work #XEPFKX 179 3.2. Surface Foam Score: 0.013 Related excerpt #3X8RZ9: 183 In contrast to [2], where diffuse disks are generated and ad- 184 vected with the fluid when particles fall into the surface fluid 185 again, we simplify the idea. Using a floating-point single com- 186 ponent texture mapped to the surface fluid, we detect where a particle has fallen and initialize that texel to a certain maximum time-to-live (TTL) for the foam. This texture is then advected using the fluid's velocity field, tracing back as in [29]. Each frame, the values of the texture are decreased \Delta t until they become 0. These values are then multiplied with the desired foam color and mapped to the fluid mesh, resulting in the blended foam. 27. Source: Real-time Rendering of River Networks (#MVUJ8Z), Quintijn Hendrickx, Rafael Bidarra, Ruben M. Smelik, p. 0 Context: #BTQCB6 Real-time Rendering of River Networks Score: 0.014 Related excerpt #BLMDAJ: Different solutions have already been proposed that vary widely in level of realism versus applicability in real-time systems. Recent work includes several different kinds of particle systems, such as a screen-space particle system [Yu et al. 2009] and an optimized three dimensional particle system [Kipfer and Westermann 2006]. Particle systems are an intuitive approach for simulating water flow but often require large amounts of memory and computation power. 28. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #B5KJYH 8. Conclusion Score: 0.016 Related excerpt #BDZQP4: In terms of raw performance, our GPU implementation executes in under 55ms on terrains up to 4096^2 sample resolution. This opens up new opportunities and research avenues for the future use of flow and depression routing in an interactive context. Further work on our algorithm is also required to reach more general applications, for instance by allowing for multiple recipients (Multiple Flow Directions). 29. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Score: 0.011 Related excerpt #CWJDCB: As a starting point, Figure 1 shows a real digitized terrain, subsequently altered by fluvial erosion and sediment deposition, and overlaid with flow-dependent vegetation, lakes, and rivers, in under 1.5 seconds. 30. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Score: 0.026 Related excerpt #WKY9MT: our results, we show a vast 4\text{km} \times 4\text{km} sea interacting with islands, floating barrels, actively moving boats, and a user-controlled jet-ski. Both the simulation and the heightfield evaluation are computed in parallel on the GPU in each time step. We provide a supplemental document that describes relevant implementation details for both parts. Our laptop with a NVIDIA Geforce GTX 1070 GPU achieves an average frame rate of 60fps with the parameters in Table 1, and this paper includes an interactive demo of our method which recreates this example. Table 2 displays the timing breakdown for an average frame of this animation; note that the timing for the computation of \eta depends on the number of pixels occupied by waves and may vary slightly. 31. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Score: 0.018 Related excerpt #9AHGRG: Varying these parameters has different effects on the visual results and performance of our method, and we explore each of them in our supplementary video. The number of \mathcal{A} samples in our simulation depends linearly on the resolution of our 4\text{D } X_{\mathcal{A}} \times X_{\mathcal{A}} \times \Theta_{\mathcal{A}} \times K_{\mathcal{A}} simulation grid, so doubling the resolution of any dimension will roughly increase the memory and the runtime by a factor of 2. Increasing the spatial resolution X_{\mathcal{A}} will allow the wavefronts to exhibit a higher curvature, allowing more detailed interactions with highly curved boundaries. Figure 8 shows the effect of X_{\mathcal{A}} on the simulation quality. Increasing the angular resolution \Theta_{\mathcal{A}} allows a more precise behavior in each direction. Increasing the wavenumber resolution K_{\mathcal{A}} allows more detailed dispersion of wave groups (different amplitude groups travel at different speeds). We show an example with K_{\mathcal{A}} = 4 simulated wave groups in Figure 9 and in our video, which shows more accurate wave group dispersion but roughly quadruples the run time (drops the frame rate from 70fps to 20fps). 32. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 7 Context: #RNVWWR Water Surface Wavelets #MEQNZV 6 EXTENSIONS #5W242X 6.2 Pre-computing wave motions Score: 0.018 Related excerpt #23W9S2: wave motion until the amplitudes reach a steady state, and then storing the \mathcal{A} functions as static textures. We can then interpolate these \mathcal{A} textures at any point in space and use them to efficiently compute wave heights at run-time. This pre-computation of \mathcal{A} leads to a considerable speed-up over running the full simulation ( 4.7\times speedup from \approx 60\text{fps} to \approx 280\text{fps} in this example). Our method is arguably more efficient than Lagrangian wavefront tracking (though the methods have very different numerical parameters and the errors behave differently), and the run-time behavior is more convenient and load-balanced for graphics hardware than an adaptive triangle mesh. 33. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 5 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #T8YYAV 6. Results Score: 0.024 Related excerpt #LUVPJR: We have used an Intel Q9450 CPU with a GeForce GTX 280 graphics card. The SPH simulation was done with NVIDIA PhysX. Particle counts range from 20k to 64k, depending on the scene. All images were taken at 1280 \times 720 resolution. The curvature flow filtering step was done at half resolution. We use off-screen buffers to store our various intermediate results: 32 bit float for the water depth, 16 bit float for the foam depth, and 16 bit each for T_{wb} , T_{wf} , T_f and T_{ff} . This results in a total of 112 bit per pixel. 34. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 5 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #T8YYAV 6. Results Score: 0.021 Related excerpt #754PPX: Table 1 compares the computational cost of [vdLGS09] with our method (SPH simulation time not included). The indicated running times are an average for a default camera movement. Our method has comparable performance with the benefit of improved image quality especially at near or far viewpoints. Even foam does not significantly increase running time for our method. Figure 6 presents the computational cost of [vdLGS09] and our method using the example of a camera zoom movement in the waterfall scene (like the one of the filter comparison shown in the accompanying video). It takes on average 23.12% of the computation time to render the water and foam depth, 24.4% for the thickness passes, 27.43% for the adaptive curvature flow filtering and 25.05% for the composition (including update of data structures). This measurement represents the mean breakdown of 6k frames used different viewpoints. Figure 1 35. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 1 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #JZMDNB 2. Previous Work Score: 0.013 Related excerpt #R4ZPDC: Current real-time approaches are usually limited in the number of particles they can handle, and do not include realistic foam [MCG03]. One way to render the water surface from the results of the particle simulation are Müller et al.'s [MSD07] screen space meshes , created using a marching squares technique on the particle depth map. Although the algorithm provides view-dependent level of detail and filtering in screen space, rendering foam with this approach is prohibitive, because of the large amount of geometry that needs to be generated. Thürey et al. [TSS*07] present a shallow water-based particle model that is coupled with a SPH simulation to simulate bubbles and foam effects, but the method simulates individual foam particles, which is expensive. 36. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 3 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #34V9L7 4. Adaptive Curvature Flow Score: 0.012 Related excerpt #M4AQMB: Each iteration of the Euler integration simply renders a full-screen pass with z_{i+1} = z_i + \Delta t H_s . As proposed by [vdLGS09], the number of iterations are chosen depending on the smoothness that is desired. 37. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 0 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #9QMYPL 1. Introduction Score: 0.011 Related excerpt #HU5QE8: the undesirable spherical particle structure. Second, there exists as yet no realistic real-time method to create foam, which is an important visual element in most situations where real-time fluids are used (see Figure 1). 38. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 4 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #Z68DF9 5. Real-Time Foam #T4PBCD 5.1. Foam Formation Score: 0.011 Related excerpt #ADKHXF: Similar to [MMS09], we assume that the surface tension and the characteristic length are fixed for the SPH simulation. We also assume that the characteristic length l is the particle diameter, which is a simplification for our real-time purposes, and that the surrounding air is not moving, and therefore the relative velocity v is the velocity of the particles. The velocity v and the density \rho are obtained from the physics simulation package. 39. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 8 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #QGEMMG 4.3 Player Physics #7CDRPL 4.3.3 Frame Loop Score: 0.015 Related excerpt #Q7VNXL: The frame loop is separated according to Unity's execution model. The Update() function (called once per rendered frame) is used for input, animation and ground checks, while FixedUpdate() (called at a fixed physics interval, independent of frame rate) is used for the physics update where the linear velocity is overwritten and the model tilt is corrected. 40. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 9 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #QGEMMG 4.3 Player Physics #ACMUGX 4.3.6 Dynamics Update Score: 0.013 Related excerpt #UF5N8K: so the controller accelerates and decelerates with a time constant of approximately 0.1 s. Here, runSpeed is the configured running speed, v_z the current forward velocity, \Delta t the physics timestep, and the factor 10 controls the rate at which the velocity approaches its target. 41. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 15 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #ANC93R 4.7 Runtime User Interface Score: 0.012 Related excerpt #BFFHXU: Here, z_p(t) is the player position on the Z-axis at time t , and \Delta_{\text{offset}} = 45 . The offset is used because the player starts from -45 m on the Z-axis during initialisation. The score is updated every frame and displayed through the TextMeshPro UI element. 42. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 11 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #5W8C4J 4.4 Procedural Terrain Generation #FMTB7D 4.4.2 Tile Spawning Score: 0.011 Related excerpt #NWMNKQ: so that the system does not extend the world beyond the range that any agent or the player will reach in the near term. The parameters above denote: t the current time; t_{\text{lastSpawn}} the time of the previous spawn; \Delta t_{\text{spawn}} the active spawn interval; v_p(t) the player's instantaneous speed; z_p(t) the player's forward position; z_g the forward position of the most recent tile; \gamma the speed-to-interval coupling constant; and \delta t the sampling step used to estimate v_p . 43. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 5 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #SRM4HZ 3 Objectives and Technical Specification #EPG8QB 3.1 Evaluation Questions, Hypotheses, and Metrics Score: 0.011 Related excerpt #EDMX8Z: RQ3 (Performance). Can both agents perform their per-tile inspection within the 16.66 ms frame budget associated with 60 FPS, or at least within the 33.33 ms budget associated with 30 FPS, as defined by Unity’s profiling guidance [12, 13]? Hypothesis H3: the per-segment cost is bounded by a small constant independent of run length, because the scanner is gated by an integer tile index and amortises the OverlapBox sweep across many ray probes. 44. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 6 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Score: 0.014 Related excerpt #WTCDC3: The average lifespan, A , of the particles can be adjusted depending on how turbulent and quickly the river is moving. Our system provides a graphical particle display that assists in the adjustment of this value, as seen in Figure 5. By representing each particle as a color determined by its birth location it is easy to see how far the particles remain traveling in groups of similar color. We note that there is significant leeway in choosing good settings for these parameters; finding a single optimum setting for these constants is not required since the system is not overly sensitive to the tuning of this parameter. Moreover, we use a pseudo-random function with values in the range of (0.5, 2.0) to scale each particle's life span with respect to the average, A . The aim being to avoid situations in which many particles are dying or spawning simultaneously. 45. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 7 Context: #JCB5RE Advected river textures #HMVN46 Results Score: 0.012 Related excerpt #G3SJ82: Our real-time method for simulating and rendering rivers is visually more convincing than existing methods and runs at far higher frame rates. Minute details in the river flow can be seen as a result of complex interactions between fluid and terrain and the fluid with itself. These complex interactions are a direct result of combining HSP columns with a 2D Navier-Stokes solver. 46. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 7 Context: #B9LYTR Scalable real-time animation of rivers #LQXUW2 6. Implementation and results Score: 0.023 Related excerpt #R825Y2: pend on the complexity of the scene. In the test, we achieved real-time performance even in the worst case where the projected surfaces occupy the whole window. Certainly, the performance will decrease if we decrease the Poisson-disk radius. However, a moderate value as we used in this test is sufficient due to the adaptivity of the particles and the sprite-based rendering scheme. 47. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 7 Context: #B9LYTR Scalable real-time animation of rivers #LQXUW2 6. Implementation and results Score: 0.021 Related excerpt #EUX776: In order to demonstrate the benefits of our method in real applications we tested it in a 25 \times 25 \text{ km}^2 scene with a river network, branchings and obstacles. We used a 800 \times 600 window with r = d = 20 pixels. We used two kinds of waves: noise perturbations and wind ripples. For the former, we used a precomputed Perlin noise reference texture. For the latter, we used Fourier generation using analytical time evolution [Tes04] for wind waves. Both reference textures contain height fields, that are used by the water shader for bump mapping and environment mapping. The test was done on an AMD Athlon 3200 processor at 1.8 GHz with a GeForce 8800 GTS graphics board. The particles and the final rendering results are shown in Figure 11. 48. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 8 Context: #B9LYTR Scalable real-time animation of rivers #LQXUW2 6. Implementation and results Score: 0.012 Related excerpt #34BVNC: channels without interrupting the animation, which is due to our procedural velocity generation. In addition, the river appearance can be easily modified using the reference wave textures. 49. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 3 Context: #B9LYTR Scalable real-time animation of rivers #XF2N2Y 3. Overview #LFKVYW Algorithm 1 Scalable real-time animation of rivers Score: 0.011 Related excerpt #B6RXPQ: 1: loop 2: for all new visible terrain quads do 3: Compute the quad's channels network. 4: Compute the stream function boundary values. 5: Build a structure for fast distance evaluations. 6: end for 7: Advect particles with the flow in world space. 8: Resample particles to keep uniform screen density. 9: Render wave sprites associated with particles. 10: end loop 50. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 2 Context: #B9LYTR Scalable real-time animation of rivers #JW4T3Z 2. Previous work #HEUBG3 2.2. Fluid surface Score: 0.011 Related excerpt #9S8VXN: All these methods are Eulerian: they update a fixed texture grid at each frame. There are also Lagrangian methods that combine a particle system with sprites to reconstruct the fluid appearance. They are mainly used for splashing water [Won, IC00, BSHK04]. This sprite-based texturing has also been used to simulate running drops on a surface [NHS02], and GPU adaptive structures have been proposed to efficiently render such textures, even with overlapping sprites [LHN05]. Our second contribution extends the Lagrangian advection methods with a method to advect particles in world space, while maintaining a constant density in screen space. ### 7. Tool result: search_text Exact matches 1. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 4 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #8ES8PA 6 Rendering the Waves Matching excerpt #RELDNA: For the rendering of a wave patch, its particles with their connectivity can be directly reused as vertices. The wave patches already represent a close surface, which, however, does not have a thickness. Thus, we create two instances of this surface for rendering, and displace the second one downward along the normal direction. To get a closed mesh, the sides of these two meshes are connected with quads. As mentioned above, the initial position of the particles of the wave patch ensures an overlap with the shallow water surface. It correctly represents the top of the wave, while the displacement of the lower side is chosen to represent the mass of the fluid according to the parameter p_m . Given a particle \mathbf{x} on the wave patch that is used as a vertex for the upper mesh, the position of the corresponding second vertex \mathbf{x}' is given by \mathbf{x}' = \mathbf{x} + p_m \mathbf{n} . 2. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 0 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #J39ZBT 1 Introduction Matching excerpt #AX5MHW: An effective way to increase the performance of the simulation of large bodies of liquids is the reduction of the problem from three to two dimensions. Instead of using 3D grid cells, the liquid is represented by a two dimensional height field. For calm situations, e.g., with smooth waves, this representation can still capture the main visual properties of the free surface fluid. Other situations, like overturn- 3. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 5 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #B8YMKE 7 Two-Way Rigid Body Coupling Matching excerpt #WQKL7W: rigid bodies. The difference \Delta b(\mathbf{x}) = b(\mathbf{x}, t) - b(\mathbf{x}, t - 1) indicates the change in volume covered by bodies between the current and the last time step. This change is distributed to the four direct neighbor cells, similar to algorithms for changing ground depth. Hence, for a grid cell at position \mathbf{x} with a neighbor cell at \mathbf{x}' 4. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 7 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Matching excerpt #5R6QUN: portional to the overall number of vertices: doubling the number of particles or doubling the number of vertices per grid will both have the effect of doubling the computation time for advection. 5. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 1 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #W73RWJ 1 INTRODUCTION Matching excerpt #DZCPD6: and this grid is advected and deformed by the flow. Each grid is mapped to a fixed area of the input texture. To maintain texture properties, particles are eliminated when the distortion of their grid becomes too large. We maintain a constant particle density over the flow, killing or generating new particles when needed. In a final step, we reconstruct the texture by blending together these textured grids. Due to its Lagrangian nature, the complexity of our algorithm only depends on the pixels that are actually generated. Thus it works on very large scenes, potentially unbounded, in real-time. 6. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 4 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #EMCT8G 3.3 Particle Sampling and Distortion #GY3LGQ 3.3.2 Grid Advection and Particle Deletion Matching excerpt #B5BH49: At their creation, grids are slightly larger than kernel size, to avoid triggering condition 1 too early. We create grids of width (2 + \beta)d , with a small \beta (in our implementation, \beta = 0.6 ). The size of the grid is a compromise between particle lifetime and the number of vertices it will require to ensure a given resolution. 7. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 3 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #SJ444N 3.1 Overview Matching excerpt #JFX5K6: Fig. 2 provides the overview of our algorithm. In the next section, we define precisely what is our input data. The remainder of this section details each step of the algorithm: placing the particles and advecting the grid vertices (Section 3.3), blending between neighboring grids (Section 3.4) and rendering the advected texture (Section 3.5). 8. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 4 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #EMCT8G 3.3 Particle Sampling and Distortion #GY3LGQ 3.3.2 Grid Advection and Particle Deletion Matching excerpt #QY44AD: At each time step, we advect all the vertices of the grid with the velocity field of the flow. We use the new positions of the vertices to compute the new position of the particle as the center of mass of the grid vertices. 9. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 4 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #EMCT8G 3.3 Particle Sampling and Distortion #867R3P 3.3.3 Estimating the Grid Distortion Matching excerpt #WWDF42: Q_t is equal to 1 for an un-distorted triangle, and is equal to 0 for a triangle where the distortion is larger than \delta_{\max} . For each grid vertex V , we then compute its quality, Q_V as the mean of the quality of its incident triangles. We kill a particle if, for any vertex in the grid, we have Q_V < \frac{1}{2} (i.e., we keep a margin of quality for the fading-out). 10. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 1 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #W73RWJ 1 INTRODUCTION Matching excerpt #GJ7THM: Our algorithm works as follows: we start by placing sample particles along the flow. These particles are advected by the flow. A grid is attached to each particle, 11. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #W6ZWF7 3.5 Reconstruction and Rendering #9GCRR9 3.5.3 Discussion Matching excerpt #5EKFRP: The indirect method is more efficient, both in memory and computation time: the tile grid is much smaller than the size of the texture itself, the images computed for each grid can be very low resolution, do not depend on the channels of the input texture, and only the sampled texels are evaluated. 12. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 4 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #EMCT8G 3.3 Particle Sampling and Distortion #G6FS45 3.3.4 Dealing with Boundaries Matching excerpt #QZA5DQ: If the flow has boundaries, when a grid straddles one of these boundaries, the vertices outside of the boundary are not used for practical computations, but they are still advected to avoid unnecessary distortions. We extrapolate the velocity field outside of the boundary of the flow with a push-pull algorithm [23]. 13. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 7 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Matching excerpt #W9NQ77: If we zoom on the object, more texture resolution is needed. The direct method requires to allocate and compute the full size texture even if only a part is visible on screen, while the rendering time of the indirect method remains constant since only visible pixels are rendered (see Table 1). The same behavior would occur for a rotation from facing view to grazing view angle. 14. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 2 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #SJ444N 3.1 Overview Matching excerpt #J7E6R3: We generate a set of deformable textured grids that are advected with the flow. We start with a random Poisson disk distribution of particles and create regular grids centered on these particles. Each grid is mapped to a random area of the input texture. At each time step we: 15. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 6 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #2RYGP7 6.3. Performance Matching excerpt #W7JZEK: The number of iterations needed to obtain a fully-formed mountain chain is difficult to estimate because it depends on a number of input parameters (see the discussion below). Yet, thanks to the implicit resolution, it does not depend on the resolution of the terrain. In our experiments, the mountains were fully shaped after 50 iterations and the geometry stops evolving after 100 – 300 iterations, as shown in Figure 12. A solution to accelerate convergence could be to progressively refine the sampling grid. Note that this refinement needs to be uniform, in order to preserve the possible emergence of local stream and the details in the shape of rivers. 16. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 8 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #FYBSSG 7.1. Performance Matching excerpt #GZJUCV: grid cells (typically, 10 \times 10 grid cells per patch). At run-time our tessellation shader performs frustum patch culling, adaptive tessellation of patches based on view distance, and final vertex height calculation using grid lookups. This implementation allows for interactive rendering in excess of 70fps at 1,920 \times 1,080 resolution for scenes with tens of thousands of primitives. 17. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 2 Context: #JJE8HN Procedural Riverscapes #Z6DVCN 4. River Network Graph Matching excerpt #V4N668: The analysis proceeds as follows: given a terrain \mathcal{T} composed of regular grid cells C_{ij} , we first generate a discretized river network \mathcal{D} , and then convert it into a river network graph \mathcal{G} with nodes and edges labelled with flow data, as a precursor to river network amplification (as described in Section 5). 18. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 9 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #XKG89F 3. Ocean dynamics simulation in shallow water #7ZY9G2 3.4. Discussion Matching excerpt #ZYU7YU: On the other hand, Lagrangian approaches can be used to simulate a wide range of phenomena. Their main advantage is their ability to represent fine-scale details and to flow anywhere in a virtual environment, but a large number of particles is usually needed to obtain realistic results. This problem can be alleviated using adaptive split-and-merge schemes to reduce computation costs. However it is worth noticing that most of the computation time for one particle is spent in testing neighboring particles or other objects for collision. Therefore a broad-phase collision detection is usually implemented by storing particles in a virtual grid, meaning that Eulerian or Lagrangian approaches share common problems such as defining an appropriate size for the grid's cells. This is also illustrated by hybrid methods which produce realistic results by adding details to Eulerian approaches using particle systems. The literature presented in section 3 is summarized on Table 2. 19. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 5 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #XKG89F 3. Ocean dynamics simulation in shallow water #7C4MCW 3.1. Eulerian approaches Matching excerpt #877SAX: A full 3D resolution of NSE was introduced in the Computer Graphics community by Foster and Metaxas [FM96, FM97], inspired from a physical approach proposed by Harlow and Welch [HW65] based on a uniform voxel decomposition of the 3D space. Velocity of the fluid is defined at the centers of each face of voxels; gradient and Laplacian are computed using finite differences between faces of adjacent voxels. Divergence at a given voxel is obtained from the updated velocities at its faces. In order to guarantee fluid incompressibility, the pressure field at a given voxel is modified according to the divergence. Virtual particles are placed in the voxel grid to extract the fluid surface, i.e. to discover its location, however the resulting surface does not look visually convincing. This problem was later addressed by Foster and Fedkiw [FF01] who represent it as an implicit, level-set surface evolving according to the fluid's velocity. Nevertheless, visual results show compressibility artifacts since a noticeable volume of fluid disappears during the animation. 20. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 2 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #B9SCHY 2.1. Spatial domain approaches #32XXKC 2.1.3. Adaptive schemes Matching excerpt #CF2HYZ: Finch [Fin04] and Lee et al [LGL06a, LGL06b] propose a Level of Details (LOD) tessellation by adapting the resolution of the surface to the distance between the viewer and the horizontal plane; using the angle between the camera and the surface, vertices outside the pyramid of vision are also discarded before rendering stage. The implementation by Lee et al provides a 40% gain in computation time compared to a fixed-resolution approach, and outperforms the implementation of Johanson [Joh04] (tests were conducted on a Pentium 4 at 3.0GHz and a GeForce 6600 GPU). 21. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 2 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #B9SCHY 2.1. Spatial domain approaches #32XXKC 2.1.3. Adaptive schemes Matching excerpt #D2EFZZ: In order to limit computation time, adaptive schemes have been proposed to limit computations only in visible areas and/or to reduce the number of periodic functions used to represent the surface dynamically, depending on the distance to the viewer. This approach consists in discarding high frequencies in distant areas, also limiting aliasing effects such as moiré patterns visible on the horizon. The "grid project" concept proposed by Johanson [Joh04] consists in projecting the pyramid of vision onto the height map representing the water surface. Distant areas are automatically sampled at low resolution, whereas high resolution is used near the viewer. 22. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 8 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #XKG89F 3. Ocean dynamics simulation in shallow water #ZEVP5C 3.3. Hybrid approaches Matching excerpt #69YFQM: The main idea in hybrid approaches is to simulate the main body of fluid using an Eulerian method, and fine-scale details such as foam, spray or bubbles with a Lagrangian method. By adding small details, very realistic results are obtained, and interest for this approach is growing more and more with the development of efficient simulations. O'Brien and Hodgins [OH95] couple an Eulerian method with a particle system to represent sprays. Navier-Stokes equations are solved in 2D, and sprays are generated depending on the magnitude of the vertical velocity at each cell; these particles are then advected using the velocity in the grid. The Eulerian simulation of Takahashi et al [TFK + 03] is coupled with particles generated in high curvature regions, then advected independently. Greenwood and House [GH04] use a level-set approach [EMF02] coupled with particles generated in high curvature regions, advected using the velocity of their corresponding cell. The friction of the fluid is also taken into account to generate bubbles. This method was later extended by Zheng et al [ZYP06] by deforming each bubble based on surface tension, thus avoiding non-realistic spherical bubbles. 23. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 3 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #5GWRQA 4. Photon-based Caustics Matching excerpt #UM3N89: This grid of points has the same resolution as the orthographic projection used previously in Step 2. In a vertex shader, the vertices will be raycast first in light space using the depth map from Step 2. If there is no intersection found, i.e., the photon exited through a wall of the frustum, the raycasting will be repeated in camera space. If there is not an intersection yet, the point is discarded (rendered out of frustum). Otherwise, if an intersection is found at light space, it is transformed to camera space and checked for correctness: 24. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 1 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work Matching excerpt #UWQ7FS: As these grid-based approaches have a fixed resolution, in order to increase the perceived level of detail, other techniques have been applied as the advection of additional textures to simulate flow [9], coupled with normal mapping as in [2]. 25. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 3 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work #XEPFKX 179 3.2. Surface Foam Matching excerpt #PWC4XJ: Using a texture for the foam introduces a constraint, however: its resolution should be dictated by the size of the particles as, it could happen that more than one texel should be initialized, depending on the particle to texel size ratio or, conversely, that the texels are too big for the particle size. 26. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 2 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #C5TMDU 3. The Priority-Flood Algorithm #CUHFR9 3.1. History Matching excerpt #KKQVW4: Vincent and Soille [1991] describe an O(n) algorithm for labeling watersheds in integer digital images by sorting all the pixels into an ascending order. The image is then flooded upwards from its lowest pixels. A distance function is used to determine which cells form the boundaries between two watersheds. 27. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 2 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #SD69QC 3. Overview Matching excerpt #S8B4Q9: There are three layers of terrain input to our algorithms. The first is the elevation grid. We refer to each element of the grid as a terrain cell c , with n being the total number of cells. We prefer to use the term “cell” as opposed to the more familiar “vertex” or “node” in this context because we want to make clear that this represents a rectangular area on the terrain surrounding the sample. The neighbors of c , denoted by N_c , are the 4 cells directly adjacent to c in the x and y directions (Figure 2 (b)). The second input layer is the amount of water (or any loose material) initially deposited on the terrain and subject to flow. This can be interpreted as rainfall or precipitation and is denoted as p_c . The final layer is a user-defined boolean mask b_c \mapsto \{0, 1\} indicating the presence (1) or absence (0) of outflow cells. These serve as boundary conditions and act to trap water flow. Typically, outflow cells would line the edges of the grid, but there are cases, such as groundwater sinks, estuaries, and sea shores where they would be placed within the domain. 28. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 5 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #6AJDFD 4.1 Discretizing \mathcal{A} Matching excerpt #UG8PZG: in Section 8. As mentioned above, \mathcal{A} varies slowly over space, so we do not require much spatial resolution either. In our implementation we allocate X_{\mathcal{A}} = 4096 grid cells for each spatial dimension, which defines a grid cell spacing of approximately one meter. 29. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #WV3FXP: For discretizing \mathcal{A} we chose a spatial resolution of X_{\mathcal{A}} = 4096 for each dimension because it maps well to the GPU and allows an exceptionally large simulation domain. Many of the up-close interactions in our video have an effective resolution of approximately 10^2 grid cells on the screen at a time. We chose \Theta_{\mathcal{A}} = 16 wave directions for the simulation because it maps well to the GPU, and because fewer samples showed some directional bias artifacts when visualizing the \mathcal{A} function directly. We could not tell much difference if we increase the angular resolution to 32. We chose only K_{\mathcal{A}} = 1 - 4 wavenumber samples because we did not think the 30. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 4 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #UL9HZ6 3.3 Discussion Matching excerpt #GU6CNX: Low-frequency \mathcal{A} . We prove in Appendix B that the Fourier transform of \mathcal{A} is essentially a low-pass-filtered version of the Fourier transform of \eta . In other words, we can reconstruct the wave height function \eta using only low-frequency variables. This frequency shift has important consequences in the eventual discretization of the method, because the Nyquist limit prevents us from discretizing the high-frequency \eta function directly without aliasing, while the discretization of \mathcal{A} is possible even with coarse grid resolutions. Instead of the grid resolution imposing limits on the resolution of visible water waves, our algorithm will impose limits on the resolution of the wave amplitudes, which are not visualized directly and arguably more difficult to discriminate perceptually. 31. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #9AHGRG: Varying these parameters has different effects on the visual results and performance of our method, and we explore each of them in our supplementary video. The number of \mathcal{A} samples in our simulation depends linearly on the resolution of our 4\text{D } X_{\mathcal{A}} \times X_{\mathcal{A}} \times \Theta_{\mathcal{A}} \times K_{\mathcal{A}} simulation grid, so doubling the resolution of any dimension will roughly increase the memory and the runtime by a factor of 2. Increasing the spatial resolution X_{\mathcal{A}} will allow the wavefronts to exhibit a higher curvature, allowing more detailed interactions with highly curved boundaries. Figure 8 shows the effect of X_{\mathcal{A}} on the simulation quality. Increasing the angular resolution \Theta_{\mathcal{A}} allows a more precise behavior in each direction. Increasing the wavenumber resolution K_{\mathcal{A}} allows more detailed dispersion of wave groups (different amplitude groups travel at different speeds). We show an example with K_{\mathcal{A}} = 4 simulated wave groups in Figure 9 and in our video, which shows more accurate wave group dispersion but roughly quadruples the run time (drops the frame rate from 70fps to 20fps). 32. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 2 Context: #RNVWWR Water Surface Wavelets #MGX8HM 2 RELATED WORK #SJKC5Z 2.2 Numerical solutions to Partial Differential Equations Matching excerpt #YT5868: Each of these methods tend to be much more flexible than spectrum-based methods, because they make minimal assumptions about the environment. For example, spectrum-based methods have difficulties with simulating obstacle interactions because their derivation assumes periodic boundaries, while direct simulation approaches have no such limitation. On the other hand, these methods must simulate wave propagation by iterating local kernel operations instead of simply plugging a time parameter into a cosine function. All of these methods discretize wave heights and momentum directly on an Eulerian grid or mesh, and, as a consequence, the resolution of the grid is directly tied to the amount of visible detail in the waves. Nyquist’s theorem requires that the grid must be fine enough to resolve the highest frequency in the heightfield; otherwise aliasing and instability may occur. Similarly, the stability of an explicitly integrated wave simulation is also intimately related to the grid spacing by the CFL condition. This stability problem can be overcome by implicit integration, at the expense of additional computation and a more complex and less GPU-friendly implementation. 33. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #DWR9FU: The performance of our method comes from a few sources. First, the fact that \mathcal{A} is low resolution allows us to discretize it on a coarse grid, so we don't need an expensive simulation of \mathcal{A} to get detailed visual results. We can exploit this coarse grid by either using a huge simulation domain (as in the above example), or by using very few degrees of freedom to make the simulation faster. Next, the pre-computed profile buffer \Psi saves us two orders of magnitude in computation by reducing a 2D integral to a 1D integral with a texture lookup. Lastly, both the simulation and the wave height evaluation are embarrassingly parallel operations spread out among many points in space, so they greatly benefit from GPU acceleration. 34. Source: Partition lens across the corpus (#TUCFMG) Matching note #TUCFMG: Ellerman’s partition logic suggests a useful cross-corpus lens, but only where blocks are mutually exclusive and jointly exhaustive (#ZBQE96). The clearest exact case is hydrological catchments: terrain cells are equivalent when they drain to the same outlet, and watershed labeling assigns one common label to every such equivalence class (#NNC37P, #477DMT). FastFlow similarly defines a basin as cells sharing a stream tree/root (#A6G5PJ) and propagates basin identifiers upstream (#C9XNSJ); saddle crossings then connect or merge basin blocks (#L94DMG), suggesting dynamic coarsening of a catchment partition. Hydrological terrain generation also constructs Voronoi cells and hierarchical watersheds/subwatersheds (#KAMGFF, #WL3SCW), giving nested partitions at multiple scales. Other exact or near-exact corpus examples include planar regions cut by major streets/topographic boundaries (#PUZXXV); recursive figure/ground and connected-pixel segmentation (#FXLSNG); head/tail classes (#WQW77N); MAP-Elites bins that partition behavior/search space (#DJQRBX, #964T2S); fluid particles classified into rendering layers (#48RCD2); and walker populations grouped by entry–destination pair (#RRJ2BJ). Alexanderian centers should not be treated as a partition without qualification because their local symmetries and centers overlap across scales (#LNKPPL). Conceptually, a deterministic map from each terrain cell to its terminal outlet realizes Ellerman’s function-to-partition idea (#BLF82B): catchments are the inverse-image fibers of the outlet map. 35. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 1 Context: #57PDWB Interactive Procedural Street Modeling #P35TFV 3 Pipeline Overview Matching excerpt #P7VVVZ: Stage One allows the user to produce a tensor field using a range of design operations, such as combining individual basis fields, computing tensor fields from boundaries, using a brush stroke interface, and rotating the field with noise. These tools allow the user to iteratively refine the design (Section 5). During editing, the user can manipulate a tensor field T and three rotation fields R_1 , R_2 , and R_3 which we use to rotate the eigenvector directions. The computational domain is a regular 2D grid D with the values of the aforementioned field stored at the vertices. Bilinear interpolation is used to obtain values inside the cells of D . These data structures are also the input to the next stage. 36. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 3 Context: #57PDWB Interactive Procedural Street Modeling #QNKCB5 5 Tensor Field Generation #A8XR5R 5.2 Combination and Editing of Basis Fields Matching excerpt #HJQFYZ: To implement the brush interface, we first extract the cell strip \{S_1, \dots, S_n\} ( S_i \in D ) that contains the polyline representing the brush curve. We then assign tensor values to the vertices of the cells in the strip according to the orientations of the brush stroke. For example, if a line segment \overline{AB} is inside a cell S_i , we assign the tensor whose major eigenvector is E_v = \overline{AB} to the four vertices of S_i . If a vertex is shared by more than one cell in the strip, the average of the tensor values is used. A similar approach has been used to create periodic orbits in vector field design [Chen et al. 2007]. 37. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 13 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #SS95BH 4.5 Wave Function Collapse-Inspired Object Spawning #9QFS2V 4.5.2 Placement Matching excerpt #37JYJN: The placement stage starts after the grid cells and the number of spawning attempts have already been calculated. The cells are randomly chosen, but the selection is not completely left open. Once a cell is selected, its neighbouring cells ( i - 1, i + 1 ) are marked as occupied. This prevents objects from clustering too closely on the same ground tile and keeps the placement more distributed across the available width. 38. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 13 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #SS95BH 4.5 Wave Function Collapse-Inspired Object Spawning #7UQS7L 4.5.1 Grid Construction Matching excerpt #HX2644: For every tile, the number of spawning attempts is calculated from the spawn-density percentage. This makes the amount of generated objects dependent on the configured spawn rate, while still keeping it bounded by the number of available grid cells: 39. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 3 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #E3MLLW 2 Background and Related Work #44QQN5 2.3 Wave Function Collapse Matching excerpt #NTPV9Z: In Momentum , WFC is not used as a complete terrain-generation method, nor is it implemented through a neural network or trained machine learning model. The implementation is a simpler one-dimensional, WFC-inspired object placement mechanism. For each generated ground tile, the lateral axis is divided into grid cells. Cells are selected for object placement, neighbouring cells are marked as occupied to reduce clustering, and the traversable lane is preserved through a dedicated clearance parameter. A ray cast then confirms that valid ground exists before an object is instantiated. Object spawning is handled by a dedicated spawn manager that controls the lifecycle of obstacle prefabs already present in the project assets. These prefabs are grouped according to skybox variants, allowing the spawned objects to remain visually consistent with the active environment theme. WFC is therefore used as a controlled object-placement strategy rather than as a complete map-generation algorithm. 40. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 6 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Matching excerpt #MWUXDB: where f(p_i) is a function that returns the value of the particle's combined input textures. We use a texture resolution equal to the grid resolution at its highest level of detail setting so that the resulting surface is no more or less detailed than the geometry itself. The number of advection particles varies over time as they spawn, however, the initial state matches the number of advection particles with the grid resolution of the advection texture. 41. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 2 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #4FM3ZS 2D Navier–Stokes Simulation Matching excerpt #FKVHJ9: The NS solver itself is based on the work of Stam 39 which uses a grid of cells where each cell has a velocity and pressure value associated with it. The initial state of the grid is a zero state where all grid cells have zero for both velocity and density. By solving the Navier–Stokes equations the solver modifies the velocities and densities of all cells in the system with the output of one step becoming input of the next. 42. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 6 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Matching excerpt #5FN7U3: where, \mathbf{u}(\mathbf{x}, t) is the particle's current position, and -\mathbf{u}(\mathbf{x}, t)\Delta t is the vector that we use to translate the particle back through time by the amount specified in \Delta t . Note that, as with the NS advection, this step will likely place the particle somewhere in between four grid cells, so we perform bilinear interpolation from the four neighboring grid cells to compute the end result. 43. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 3 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #KV3Q48 Hydrostatic Pressure Columns Matching excerpt #U432ME: An HSP grid is constructed and used to compute pressure values at each grid cell in the fluid volume, using the laws of hydrostatics. The fluid volume is discretized into small columns which are further split vertically into cells (see Figure 2). Each cell's pressure is computed based on the pressure of neighboring cells. The laws of hydrostatics dictate that fluid will attempt to equalize its pressure which is used to determine the rate that fluid flows from one cell to another. 44. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 3 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #KV3Q48 Hydrostatic Pressure Columns Matching excerpt #C8PJ9C: where d is the length of the pipe (equal to the grid spacing) and the tops and bottoms of the pipes are the min and max of the tops and bottoms of the cells into which the pipe flows: 45. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 7 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Matching excerpt #33BTWQ: In the initial bootstrapping phase, we first assign an advection particle to every cell in the grid. We then run the simulation until all initial advection particles have died and respawned at least once, thereby reaching a stable state. In practice this requires a few seconds of 46. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 4 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #PVQNK6 Bootstrapping the Hydrostatic Pressure Columns Matching excerpt #5XHFSS: After the initial Navier-Stokes system is solved, and the results have been provided as input to the HSP solver, the resultant pressure grid is used, in turn, to influence the augmented 2D Navier-Stokes solver with the 3D pressure data. And since rivers are basically static with regards to their flow path we can simply pre-compute and store the HSP grid prior to simulation. The algorithm completes a single HSP update in approximately 3–5 seconds with a column depth of three cells. 47. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 4 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #CSD47K Impulse Driven NS Matching excerpt #JDXE4W: Before applying the impulses an initial state must be computed so that we know which direction and with what magnitude the impulses should be applied. We refer to this process as priming the flow which is depicted in Figure 3. First, an impulse field is propagated across the simulation grid over a number of steps starting with an initial impulse hint from the user at one edge of the river which dictates the basic direction of the river. The first time step causes the impulses to be applied as the fluid is solved. At any cell where the velocity is not zero, that velocity vector is normalized and saved as the flow hint for that cell. In the next time step impulses are applied to the initial cells given by the user and those cells already affected by the simulation. The algorithm sweeps across the river in successive time-steps from the user specified source location. This is repeated until all cells have a flow hint associated with them. In the second phase of the flow priming procedure the simulation is run with flow hinting enabled until one “advection particle” is able to travel the length of the river. 48. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 9 Context: #UR2SY7 Procedural Generation of Roads #SBCAWF 7. Results Matching excerpt #JLGV3R: Efficiency The performance of our algorithm depends on the resolution of the underlying sampling grid. Our experiments show that our optimized algorithm can generate realistic trajectories in less than 1 second when using a 100 \times 100 grid with both curvature control and tunnel and bridge detection activated. 49. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 4 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks Matching excerpt #Q847GQ: Recall that the discrete path is a rectilinear path composed of straight segments connecting sample points. Existing techniques only consider 4 or 8 connectivity between sample points. Therefore, the segments of the discrete path can only have 4 or 8 directions, with a maximal angle resolution of 45 degrees. Shift paths [JV04] can partially overcome this problem by allowing paths to shift away from the grid points, but require a computationally demanding relaxation step to shift path segments. 50. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 5 Context: #B9LYTR Scalable real-time animation of rivers #NRD5JU 5. Adaptive texture advection #7RRTRY 5.1. Dynamic particle distribution Matching excerpt #HFR87U: New particles are generated in screen space, but we need their world position to advect them in the next frames. In order to get them we render the fluid surfaces to a buffer, using the vertices world positions as vertex color. We then read back on CPU the pixels of this buffer that correspond to the new particles. Note that we also fade in the sprites of new particles in order to avoid popping (see Equation 6). Approximate matches 1. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 0 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #J39ZBT 1 Introduction Score: 0.013 Related excerpt #AX5MHW: An effective way to increase the performance of the simulation of large bodies of liquids is the reduction of the problem from three to two dimensions. Instead of using 3D grid cells, the liquid is represented by a two dimensional height field. For calm situations, e.g., with smooth waves, this representation can still capture the main visual properties of the free surface fluid. Other situations, like overturn- 2. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 4 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #8ES8PA 6 Rendering the Waves Score: 0.011 Related excerpt #RELDNA: For the rendering of a wave patch, its particles with their connectivity can be directly reused as vertices. The wave patches already represent a close surface, which, however, does not have a thickness. Thus, we create two instances of this surface for rendering, and displace the second one downward along the normal direction. To get a closed mesh, the sides of these two meshes are connected with quads. As mentioned above, the initial position of the particles of the wave patch ensures an overlap with the shallow water surface. It correctly represents the top of the wave, while the displacement of the lower side is chosen to represent the mass of the fluid according to the parameter p_m . Given a particle \mathbf{x} on the wave patch that is used as a vertex for the upper mesh, the position of the corresponding second vertex \mathbf{x}' is given by \mathbf{x}' = \mathbf{x} + p_m \mathbf{n} . 3. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 3 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #JL4FVP 5 Wave Patch Generation: Score: 0.011 Related excerpt #ESTKYQ: The fluid sheet of an overturning wave is represented with a wave patch that is built from connected particles generated at the wave line. In time intervals t_g a set of particles along the wave line is spawned for each point of the line, adding another layer of quads to the patch. Amongst each other, the particles have the same connectivity as the wave line. If a previous set of particles exists, the new set is connected to the previous one. If the same point on the line existed at the generation time of both particle sets, this is trivial. From these one-to-one connections, quads can be easily generated to form a closed surface of the wave patch. If points were added or removed from the wave line, these are marked, and corresponding connection shapes are inserted to guarantee a closed surface, as shown in Figure 5. To ensure that these three cases are sufficient, we only allow a single merging or insertion for a point within the time interval t_g . 4. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 4 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #EMCT8G 3.3 Particle Sampling and Distortion #WBB3XW 3.3.1 Particle Distribution Score: 0.028 Related excerpt #HLAFUC: For each particle, we create a regular grid (see Fig. 2, left), centered on it, of width larger than 2d . Combined with the properties of the boundary sampling algorithm, this guarantees a gap-less coverage of the fluid. 5. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 4 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #EMCT8G 3.3 Particle Sampling and Distortion #GY3LGQ 3.3.2 Grid Advection and Particle Deletion Score: 0.028 Related excerpt #B5BH49: At their creation, grids are slightly larger than kernel size, to avoid triggering condition 1 too early. We create grids of width (2 + \beta)d , with a small \beta (in our implementation, \beta = 0.6 ). The size of the grid is a compromise between particle lifetime and the number of vertices it will require to ensure a given resolution. 6. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 7 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Score: 0.028 Related excerpt #5R6QUN: portional to the overall number of vertices: doubling the number of particles or doubling the number of vertices per grid will both have the effect of doubling the computation time for advection. 7. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 4 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #EMCT8G 3.3 Particle Sampling and Distortion #867R3P 3.3.3 Estimating the Grid Distortion Score: 0.023 Related excerpt #WWDF42: Q_t is equal to 1 for an un-distorted triangle, and is equal to 0 for a triangle where the distortion is larger than \delta_{\max} . For each grid vertex V , we then compute its quality, Q_V as the mean of the quality of its incident triangles. We kill a particle if, for any vertex in the grid, we have Q_V < \frac{1}{2} (i.e., we keep a margin of quality for the fading-out). 8. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Score: 0.02 Related excerpt #FB5X95: For Fig. 4, 6, 7, 8 and most of the video sequences, we used a fluid covering the entire picture, an output texture size of 512 \times 512 , and 300 grids of 8 \times 8 vertices (including grids being faded in or faded out). The timings correspond to the fire example (Fig. 4). 9. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 2 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #SJ444N 3.1 Overview Score: 0.02 Related excerpt #J7E6R3: We generate a set of deformable textured grids that are advected with the flow. We start with a random Poisson disk distribution of particles and create regular grids centered on these particles. Each grid is mapped to a random area of the input texture. At each time step we: 10. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 1 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #W73RWJ 1 INTRODUCTION Score: 0.019 Related excerpt #DZCPD6: and this grid is advected and deformed by the flow. Each grid is mapped to a fixed area of the input texture. To maintain texture properties, particles are eliminated when the distortion of their grid becomes too large. We maintain a constant particle density over the flow, killing or generating new particles when needed. In a final step, we reconstruct the texture by blending together these textured grids. Due to its Lagrangian nature, the complexity of our algorithm only depends on the pixels that are actually generated. Thus it works on very large scenes, potentially unbounded, in real-time. 11. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 3 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #SJ444N 3.1 Overview Score: 0.016 Related excerpt #JFX5K6: Fig. 2 provides the overview of our algorithm. In the next section, we define precisely what is our input data. The remainder of this section details each step of the algorithm: placing the particles and advecting the grid vertices (Section 3.3), blending between neighboring grids (Section 3.4) and rendering the advected texture (Section 3.5). 12. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 5 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #4UR6QN 3.4 Blending and Continuity #NQC7ZJ 3.4.1 Vertex Weights Score: 0.013 Related excerpt #GQTAMB: The spatial component merges three factors: the quality around each grid vertex ( Q_V , defined in section 3.3.3), a fall-off with the distance to the particle (in our implementation we take it linear), and a continuity factor ensuring a weight 0 on the boundary of the grid (to avoid spatial discontinuities during blending): 13. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 4 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #EMCT8G 3.3 Particle Sampling and Distortion #GY3LGQ 3.3.2 Grid Advection and Particle Deletion Score: 0.012 Related excerpt #QY44AD: At each time step, we advect all the vertices of the grid with the velocity field of the flow. We use the new positions of the vertices to compute the new position of the particle as the center of mass of the grid vertices. 14. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 1 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #W73RWJ 1 INTRODUCTION Score: 0.011 Related excerpt #GJ7THM: Our algorithm works as follows: we start by placing sample particles along the flow. These particles are advected by the flow. A grid is attached to each particle, 15. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 8 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #FYBSSG 7.1. Performance Score: 0.029 Related excerpt #GZJUCV: grid cells (typically, 10 \times 10 grid cells per patch). At run-time our tessellation shader performs frustum patch culling, adaptive tessellation of patches based on view distance, and final vertex height calculation using grid lookups. This implementation allows for interactive rendering in excess of 70fps at 1,920 \times 1,080 resolution for scenes with tens of thousands of primitives. 16. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 8 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #FYBSSG 7.1. Performance Score: 0.02 Related excerpt #KNSGXF: We have developed a GPU implementation that utilizes a regular grid acceleration structure and tessellation shader. A single flow primitive is centered in each grid cell, with a consistent radius that overlaps with its immediate neighbors. At most four flow primitives impinge on a given point and these are combined with the blend operator. Next, a terrain patch is defined to cover a square region of 17. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 7 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results Score: 0.012 Related excerpt #ACDG5B: Figures 1 show different views of an extensive river network, spanning a 3 \times 3 km terrain. The scene has the following statistics: an input digital elevation map with a per-pixel resolution of 100m, a river that extends for approximately 4km, more than 40,000 primitives forming the river surface, and a final terrain and water surface resolution of 10cm. 18. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 7 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #XKG89F 3. Ocean dynamics simulation in shallow water #WB9J3L 3.2. Lagrangian approaches Score: 0.014 Related excerpt #Y7LSHT: where N_p is the total number of particles, m_j (resp. S_j ) is the mass (resp. the scalar value) of particle j , r is the distance between particles i and j , R is the maximal interaction radius, and W is a symmetric interpolation function. The gradient \nabla S_i and Laplacian \nabla^2 S_i are given by: 19. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 9 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #XKG89F 3. Ocean dynamics simulation in shallow water #7ZY9G2 3.4. Discussion Score: 0.013 Related excerpt #ZYU7YU: On the other hand, Lagrangian approaches can be used to simulate a wide range of phenomena. Their main advantage is their ability to represent fine-scale details and to flow anywhere in a virtual environment, but a large number of particles is usually needed to obtain realistic results. This problem can be alleviated using adaptive split-and-merge schemes to reduce computation costs. However it is worth noticing that most of the computation time for one particle is spent in testing neighboring particles or other objects for collision. Therefore a broad-phase collision detection is usually implemented by storing particles in a virtual grid, meaning that Eulerian or Lagrangian approaches share common problems such as defining an appropriate size for the grid's cells. This is also illustrated by hybrid methods which produce realistic results by adding details to Eulerian approaches using particle systems. The literature presented in section 3 is summarized on Table 2. 20. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 3 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #5GWRQA 4. Photon-based Caustics Score: 0.021 Related excerpt #UM3N89: This grid of points has the same resolution as the orthographic projection used previously in Step 2. In a vertex shader, the vertices will be raycast first in light space using the depth map from Step 2. If there is no intersection found, i.e., the photon exited through a wall of the frustum, the raycasting will be repeated in camera space. If there is not an intersection yet, the point is discarded (rendered out of frustum). Otherwise, if an intersection is found at light space, it is transformed to camera space and checked for correctness: 21. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 2 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work #ESVL3G 119 2. Fluid simulation Score: 0.018 Related excerpt #YV6WWR: 131 As the fluid is provided as a heightfield, its basic visual- 132 ization can be a triangle mesh representing the whole domain, 133 being the vertices equally displaced in the xz plane and their 134 y coordinate the value of the heightfield at that point. We use 135 this representation, and apply some techniques that enable more 136 complex visual effects as caustics and refraction, which aren't 137 restricted to this Shallow Waters simulation and may be applied 138 to other refractive/reflective surfaces. These techniques are ex- 139 plained in the next sections. 22. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 2 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work #ESVL3G 119 2. Fluid simulation Score: 0.014 Related excerpt #MRZNT4: 140 For the particles, we render them as points, expanded to 141 quadrilaterals and use depth and normal replacement, similarly 142 to [26]. For refraction, methods like [21, 27] can be used. In 143 our case we use the first one, where an arbitrary offset is ap- 144 plied to the refracted vector from the particle surface normal 145 and used to look up at the framebuffer; although the results of 146 this arbitrary offset on the refracted vectors are not physically 147 correct, they are perceptually feasible and simpler to implement 148 than the latter one, for example. 23. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 0 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work Score: 0.011 Related excerpt #5WQTQA: In the specific case of eulerian fluid simulation, the fluid is usually represented as a scalar field and its visualization is done by raycasting the volume or by using mesh-extracting techniques like marching cubes for further use. Nevertheless, 3D full simulation can be still quite costly, so other solutions as 24. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 5 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #C5TMDU 3. The Priority-Flood Algorithm #BLBXVK 3.2. The Algorithm Score: 0.012 Related excerpt #DETKUR: Because the algorithm does not rely on the structure or connectedness of the underlying DEM, it can be applied to 4-, 6-, 8-, or, indeed, n -connected grids. The underlying grid need not even be rectangular—for instance, it may be a mesh based on a Delaunay triangulation. 25. Source: Real-time Rendering of River Networks (#MVUJ8Z), Quintijn Hendrickx, Rafael Bidarra, Ruben M. Smelik, p. 0 Context: #BTQCB6 Real-time Rendering of River Networks Score: 0.015 Related excerpt #MSQQ8G: A commonly used method to visualize Bézier curves is to sample along the curve at a fixed rate, and then tessellate these samples into a geometric structure. However, to achieve smooth results, many samples are needed, resulting in a high vertex count. Because this is often not desirable in real-time rendering, we render the Bézier curves with bounding quads using only four vertices per curve. An implicitly defined distance field is used to project each pixel in the quad onto the nearest point on the curve. Using only quadratic order Bézier curves allows us to define the distance field as a function of the Bézier control points, which does not require any iterative algorithms. As a result this function is, due to its parallel nature, particularly suited for being evaluated on the GPU. Because of the low vertex count, no LOD techniques are necessary for large scale river networks, and rendering performance depends mostly on the total surface of visible water in screen-space. 26. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 2 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #SD69QC 3. Overview Score: 0.023 Related excerpt #S8B4Q9: There are three layers of terrain input to our algorithms. The first is the elevation grid. We refer to each element of the grid as a terrain cell c , with n being the total number of cells. We prefer to use the term “cell” as opposed to the more familiar “vertex” or “node” in this context because we want to make clear that this represents a rectangular area on the terrain surrounding the sample. The neighbors of c , denoted by N_c , are the 4 cells directly adjacent to c in the x and y directions (Figure 2 (b)). The second input layer is the amount of water (or any loose material) initially deposited on the terrain and subject to flow. This can be interpreted as rainfall or precipitation and is denoted as p_c . The final layer is a user-defined boolean mask b_c \mapsto \{0, 1\} indicating the presence (1) or absence (0) of outflow cells. These serve as boundary conditions and act to trap water flow. Typically, outflow cells would line the edges of the grid, but there are cases, such as groundwater sinks, estuaries, and sea shores where they would be placed within the domain. 27. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 2 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #SD69QC 3. Overview Score: 0.02 Related excerpt #GUKBY3: grid of elevations z , often referred to as a Digital Elevation Model (DEM). This is an implementation decision and adaptation of our algorithms to other heightfield structures, such as Triangular Irregular Networks [Ban07], is straightforward. Note, however, that z is a unique mapping h(x, y) = z over the x, y plane and so we do not support true 3D terrains with caves and overhangs [GGP + 19]. 28. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance #SKBWC5 7.3.1. Spatial scaling Score: 0.012 Related excerpt #22P7V2: We show in Figure 16 the relationship between performance and terrain size, for resolutions ranging (logarithmically) from 64 \times 64 to 8192 \times 8192 . We observe that parallelism is limited by the maximum simultaneous threads in our GPU model at around 8192 \times 8192 , where performance follows a near-linear trend. 29. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance Score: 0.01 Related excerpt #8VZYXE: For our test dataset, we incorporated a mix of real and synthetic terrains. We began by extracting a set of 10 real terrains from the IGN RGE ALTI Digital Elevation 1m dataset [IGN22] chosen on the basis of topographic variety. These 10 terrains were sampled at cell resolutions of 512 \times 512 , 1024 \times 1024 , 2048 \times 2048 and 4196 \times 4196 to support scaling experiments. 30. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 10 Context: #RNVWWR Water Surface Wavelets #W3R46F 9 DISCUSSION Score: 0.018 Related excerpt #ZB9JR8: Compared to Eulerian height field-based simulations, our method stores 4096^2 (spatial resolution) \times 16 (wave vector resolution) samples for our 4 km by 4 km scene. A height field storing the same number of 31. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 10 Context: #RNVWWR Water Surface Wavelets #W3R46F 9 DISCUSSION Score: 0.016 Related excerpt #BEDUYL: samples would have a grid cell spacing of 25 cm, even ignoring that it needs to store 2 values per grid cell. Following the Nyquist theorem, the smallest possible wavelength would be 0.5 m. By comparison, we animate wavelengths down to 2 cm. 32. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Score: 0.016 Related excerpt #WV3FXP: For discretizing \mathcal{A} we chose a spatial resolution of X_{\mathcal{A}} = 4096 for each dimension because it maps well to the GPU and allows an exceptionally large simulation domain. Many of the up-close interactions in our video have an effective resolution of approximately 10^2 grid cells on the screen at a time. We chose \Theta_{\mathcal{A}} = 16 wave directions for the simulation because it maps well to the GPU, and because fewer samples showed some directional bias artifacts when visualizing the \mathcal{A} function directly. We could not tell much difference if we increase the angular resolution to 32. We chose only K_{\mathcal{A}} = 1 - 4 wavenumber samples because we did not think the 33. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 2 Context: #RNVWWR Water Surface Wavelets #MGX8HM 2 RELATED WORK #C6S3T5 2.3 Hybrid approaches Score: 0.013 Related excerpt #69Z8HX: not vary with a number of particles, and it trivially interfaces with texture maps for easy artistic control. 34. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 5 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #T8YYAV 6. Results Score: 0.019 Related excerpt #LUVPJR: We have used an Intel Q9450 CPU with a GeForce GTX 280 graphics card. The SPH simulation was done with NVIDIA PhysX. Particle counts range from 20k to 64k, depending on the scene. All images were taken at 1280 \times 720 resolution. The curvature flow filtering step was done at half resolution. We use off-screen buffers to store our various intermediate results: 32 bit float for the water depth, 16 bit float for the foam depth, and 16 bit each for T_{wb} , T_{wf} , T_f and T_{ff} . This results in a total of 112 bit per pixel. 35. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 4 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #Z68DF9 5. Real-Time Foam #P6BSN6 5.2. Layer Creation Score: 0.016 Related excerpt #3BY9UA: where t is the particle thickness function, x_i, y_i are the projected position of the particle, x and y are screen coordinates and \sigma_i is the projected size. In comparison to [vdLS09], we not only calculate the water thickness, but also: 36. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 3 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #34V9L7 4. Adaptive Curvature Flow Score: 0.013 Related excerpt #6HBEL2: However, close inspection of the screen-space curvature formulation reveals that the reference coordinate system for calculating the curvature is the window coordinate system. This means that, given equal iteration sizes, a particle that appears larger on screen (because it is closer due to perspective) will have a significantly larger radius in this coordinate system and therefore significantly lower curvature than a particle that is farther away. The resulting artifact is that smoothing will have a lower effect on closer particles, which therefore retain the unwanted spherical appearance, whereas particles far from the viewer will be overly smoothed, so that the fluid surface loses its defining characteristics such as highlights. This can be observed in Figure 4, left. 37. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 3 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #34V9L7 4. Adaptive Curvature Flow Score: 0.011 Related excerpt #QUJBJA: One possible solution would be to remap the curvatures into a common reference coordinate system, for example by dividing H_s by z for each evaluation of H_s . However, our experiments have shown that this makes the integration very unstable, because the screen-space evaluation for larger particles is very noisy due to depth quantization. On the other hand, depth correction would make the resulting curvatures large in magnitude, leading to oscillation. 38. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 2 Context: #57PDWB Interactive Procedural Street Modeling #QNKCB5 5 Tensor Field Generation #FCEMBJ 5.1 Generation of Basis Fields Score: 0.021 Related excerpt #885URQ: Grid: An important building block for most cities is the grid pattern. Parcels are generated by two orthogonal sets of parallel roads. A grid pattern can be defined by a regular element indicating the direction of the major eigenvector field. See Figure 4 for a tensor field guiding streets in a regular grid pattern. Given the direction (u_x, u_y) defined at a point \mathbf{p}_0 we can compute l = \sqrt{u_x^2 + u_y^2} and \theta = \arctan(\frac{u_y}{u_x}) and define the following basis field (the constant direction field) [Zhang et al. 2007]: 39. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 5 Context: #57PDWB Interactive Procedural Street Modeling #ZPVYV6 6 Street Graph Generation #4SLJV9 6.1 Major Street Graph Generation from Tensor Fields Score: 0.015 Related excerpt #HMKV6C: G can be turned into a polygonal mesh by identifying the polygons in the graph. This is highly desirable when the user wishes to add buildings or other structures in between roads. 40. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 3 Context: #57PDWB Interactive Procedural Street Modeling #QNKCB5 5 Tensor Field Generation #A8XR5R 5.2 Combination and Editing of Basis Fields Score: 0.013 Related excerpt #HJQFYZ: To implement the brush interface, we first extract the cell strip \{S_1, \dots, S_n\} ( S_i \in D ) that contains the polyline representing the brush curve. We then assign tensor values to the vertices of the cells in the strip according to the orientations of the brush stroke. For example, if a line segment \overline{AB} is inside a cell S_i , we assign the tensor whose major eigenvector is E_v = \overline{AB} to the four vertices of S_i . If a vertex is shared by more than one cell in the strip, the average of the tensor values is used. A similar approach has been used to create periodic orbits in vector field design [Chen et al. 2007]. 41. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 13 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #SS95BH 4.5 Wave Function Collapse-Inspired Object Spawning #9QFS2V 4.5.2 Placement Score: 0.012 Related excerpt #9NP2NZ: The X-coordinate of the object is fixed from the selected grid cell. The Z-axis position is given a small jitter so that objects are not spawned in a perfectly straight line: 42. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 6 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Score: 0.021 Related excerpt #MWUXDB: where f(p_i) is a function that returns the value of the particle's combined input textures. We use a texture resolution equal to the grid resolution at its highest level of detail setting so that the resulting surface is no more or less detailed than the geometry itself. The number of advection particles varies over time as they spawn, however, the initial state matches the number of advection particles with the grid resolution of the advection texture. 43. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 5 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #LE3TRV 5.2. Curvature Score: 0.012 Related excerpt #VT22AA: ing a two-dimensional discretization of the domain \Omega \subset \mathbb{R}^2 , we perform a three-dimensional discretization of the continuous domain \Omega \times [0, 2\pi] which represents all the positions in \Omega with all the possible orientations (Figure 10). We 44. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 2 Context: #UR2SY7 Procedural Generation of Roads #RKKRAC 3. Discrete anisotropic shortest path algorithm Score: 0.011 Related excerpt #Q22N4N: Grid sampling and graph definition Let \mathbf{p}_{ij} , (i, j) \in [0, n-1]^2 denote the grid points uniformly sampling the search domain. Those points correspond to the nodes of the graph \mathcal{G} . Because the cost function c is anisotropic, the segments connecting a point \mathbf{p}_{ij} to adjacent grid points may not give a good approximation of the optimal path [JV04]. The originality of our approach is to consider that every grid point \mathbf{p}_{ij} is implicitly connected to a large set of neighboring grid points within distance r . We define this subset as: 45. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 6 Context: #B9LYTR Scalable real-time animation of rivers #NRD5JU 5. Adaptive texture advection #7RRTRY 5.1. Dynamic particle distribution Score: 0.019 Related excerpt #BEMANJ: Particle sampling domain. We can either use particles to sample the whole screen, or only the projected area of moving fluids. The latter makes insertion of new particles more complicated, especially if the apparent width of the channel is very small; the former is simple and more robust. It generates more particles, but particles outside the fluid are not advected nor rendered, and thus their cost is very small. We have elected to generate particles over the whole screen area. 46. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 3 Context: #B9LYTR Scalable real-time animation of rivers #XF2N2Y 3. Overview #LFKVYW Algorithm 1 Scalable real-time animation of rivers Score: 0.016 Related excerpt #B6RXPQ: 1: loop 2: for all new visible terrain quads do 3: Compute the quad's channels network. 4: Compute the stream function boundary values. 5: Build a structure for fast distance evaluations. 6: end for 7: Advect particles with the flow in world space. 8: Resample particles to keep uniform screen density. 9: Render wave sprites associated with particles. 10: end loop 47. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 7 Context: #B9LYTR Scalable real-time animation of rivers #LQXUW2 6. Implementation and results Score: 0.015 Related excerpt #EUX776: In order to demonstrate the benefits of our method in real applications we tested it in a 25 \times 25 \text{ km}^2 scene with a river network, branchings and obstacles. We used a 800 \times 600 window with r = d = 20 pixels. We used two kinds of waves: noise perturbations and wind ripples. For the former, we used a precomputed Perlin noise reference texture. For the latter, we used Fourier generation using analytical time evolution [Tes04] for wind waves. Both reference textures contain height fields, that are used by the water shader for bump mapping and environment mapping. The test was done on an AMD Athlon 3200 processor at 1.8 GHz with a GeForce 8800 GTS graphics board. The particles and the final rendering results are shown in Figure 11. 48. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 5 Context: #B9LYTR Scalable real-time animation of rivers #NRD5JU 5. Adaptive texture advection #7RRTRY 5.1. Dynamic particle distribution Score: 0.015 Related excerpt #HFR87U: New particles are generated in screen space, but we need their world position to advect them in the next frames. In order to get them we render the fluid surfaces to a buffer, using the vertices world positions as vertex color. We then read back on CPU the pixels of this buffer that correspond to the new particles. Note that we also fade in the sprites of new particles in order to avoid popping (see Equation 6). 49. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 6 Context: #B9LYTR Scalable real-time animation of rivers #NRD5JU 5. Adaptive texture advection #KWALBE 5.2. Sprite-based texturing Score: 0.014 Related excerpt #NBX6SY: In order to find the sprites that overlap a given pixel we use an indirection grid (as in [LHN05], but in screen space). Each cell of the grid stores the precise location and parameters of the sprites that cover it. The grid is encoded into a texture, called indirection texture . This scheme allows us to treat our system of dynamic sprites as an ordinary material described by a fragment shader and applied to a mesh rendered as a simple geometry. 50. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 2 Context: #B9LYTR Scalable real-time animation of rivers #XF2N2Y 3. Overview Score: 0.012 Related excerpt #J9JNDY: Runtime data. At run-time the terrain data is subdivided in a dynamic quadtree, based on the viewer position and distance. Each quad contains raster data and clipped vector data for its corresponding terrain part (see Figure 2a). This quadtree is computed as described in [BN08]. When a new quad becomes visible we compute on the fly the stream function values at channel boundaries (see Section 4.1). We also create an acceleration structure to quickly compute distances to channel boundaries (see Section 4.4). This data remains in memory as long as the quad is visible. ### 8. Tool result: search_text Exact matches 1. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 3 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #PHN7AY 4 Wave Simulation Matching excerpt #7B2E9D: As the wave crest might have passed \mathbf{p} , we first perform a projection along \mathbf{u}_p onto the maximum of the fluid height field. Once this maximum is found, we perform another forward projection onto the point of the steepest gradient on the wave slope at position \mathbf{p}' . We now ensure that this new point is valid with respect to the original wave speed c . If |\mathbf{p}' - \mathbf{p}| > 2c we remove the point from the line. Likewise, we ensure that this region of the wave is still steep enough to produce a wave. Thus, if |\mathbf{u}_p| < t_H/2 , the point is also discarded. 2. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 2 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #PHN7AY 4 Wave Simulation Matching excerpt #EWBE94: Here, the gradient of the fluid height \nabla H is computed with finite differences from the height field of the shallow wa- 3. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #JT9864 3.1. Geological Background Matching excerpt #PGNGMP: The stream power equation states that the rate of change of surface topography h(\mathbf{p}) at a position \mathbf{p} is controlled by the balance between the surface uplift u(\mathbf{p}) and the fluvial erosion, which is a function of the local slope s(\mathbf{p}) and the drainage area A(\mathbf{p}) . The local slope s(\mathbf{p}) is defined as the surface topographic gradient: 4. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 8 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Matching excerpt #JCR3MQ: Figure 15 shows that this method can model a large variety of landscape: starting from a simple height map formed with two strokes and a gradient, we obtain a plausible canyon. We chose a height dependent maximal slope for thermal erosion to obtain the succession of cliffs and slopes in the result. 5. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 8 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Matching excerpt #9VNYCT: The thermal erosion has an important influence on the shape of the valleys. It affects their regularity as shown by Figure 17. If the maximum slope given for the mountain is 30^\circ , which is the usual talus angle for thermal erosion [MKM89], our erosion model results in a layout of very regular geometric valleys. 6. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 7 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Matching excerpt #4MKD3J: The uplift has a strong influence on the resulting terrain and it is the main way the user affects the final shape. As shown in Figure 13, the main impact is in the gradient of the uplift values. The actual shape of the uplift does not have a strong influence, except on the boundaries. Having the same uplift shape, a slowly decreasing gradient leads to a very straight erosion in the gradient direction, whereas a set of steps of constant values gives more random valleys with sudden jumps on the gradient in the mountain heights. We can also observe that lower values of uplift lead to smaller valleys, and that the thermal erosion is important with regular slopes for high uplift values. 7. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 8 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #P3AR99 III. TRUNK TRAIL FORMATION BY ANTS Matching excerpt #2L5Q8L: For the detection of chemical markings, insects like ants use specific receptors which are located at their so-called antennae. Their perception is mainly determined by the angle 2\varphi of perception, which is given by the angle between the antennae (cf. Fig. 2). Therefore, we make the assumption 8. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 9 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #P3AR99 III. TRUNK TRAIL FORMATION BY ANTS Matching excerpt #J42VPY: where the angle \omega_\alpha is given by the current walking direction 9. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 6 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #9FK8U9 3. Wholeness as a hierarchical graph #JH73PK 3.1 Measuring the degrees of life using the PageRank scores for the centers Matching excerpt #5G7BZM: The PR scores capture the spirit of wholeness, or the degree of life. We suggest a directed graph, in which surrounding centers point to a central one for computing the PR scores. The degrees of life in the snowflake’s centers look the same as their sizes (Figure 4). However the degrees of life of axial lines differ from their length shown previously because PR is recursively defined. To this point, all centers are assigned degrees of life measured by PR scores. Based on degrees of life of centers, we can derive the ht-index as an indicator for the degree of life of the wholeness. 10. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 6 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #9FK8U9 3. Wholeness as a hierarchical graph #JH73PK 3.1 Measuring the degrees of life using the PageRank scores for the centers Matching excerpt #PWRUHE: Note: The degrees of life are visualized by dot sizes and the spectral colors, with red as the highest degree, blue as the lowest degree, and other colors as degrees between the highest and lowest. 11. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 11 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #GM64DB 6. Conclusion Matching excerpt #YFGBKT: To quantify the living structure, this paper developed a model of wholeness based on Alexander’s mathematical view of space. This model is a hierarchical graph in which numerous centers are represented by the nodes and their interactions are the directed links. Based on the initial definition of wholeness, particularly its recursive nature of centers, we suggested PR scores and ht-index as good proxies for the degrees of life because of their recursive nature. The three case studies presented some strong results. For example, the centers with the highest degrees of life in the Alhambra plan capture fairly well human intuitions on a living structure. More importantly, the degrees of life for both Manhattan’s and Sweden’s street networks demonstrate very striking power laws. These results are encouraging in terms of recognizing and appreciating the living structure. However, we are still far away from creating the kind of living structure known as the field of harmony-seeking computations (Alexander 2005). In this regard, we believe that the mathematical model of wholeness and related measures shed light on the wholeness-extending transformations. Our future work points in this direction. 12. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 1 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #3KT2GU 1. Introduction Matching excerpt #VGSLCH: The remainder of this paper is structured as follows. Section 2 illustrates the 15 structural properties using the Koch snowflake and a French town layout. Section 3 defines the wholeness as a hierarchical graph and suggests how to quantitatively measure degrees of life for individual centers and the whole. Section 4 presents three case studies applied to an architectural plan and street networks of a city and country for measuring degrees of life or beauty in geographic spaces. Section 5 further discusses the mathematical model of wholeness related to beauty, creation/design, big data, and complexity science. Finally, Section 6 draws conclusions and points to future work. 13. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 8 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #TXBKLJ 4. Case studies: Computing the degrees of life #B54GRW 4.1 The plan of Alhambra Matching excerpt #6EPSE6: The process of identifying the convex spaces and their relationships is time-consuming and tedious. The set of convex spaces must be the least number of fattest convex spaces; otherwise, the set would not be unique. The process starts with the first fattest convex space, the second fattest, and so on, until all spaces are covered (Hillier and Hanson 1984). As to their relationships, we must determine through visual inspection, i.e., which centers tend to support other ones? For example, peripheral centers support central ones. There is usually little ambiguity in terms of the relationships. We deliberately did not use any automatic process in order to make the relationships as accurate as possible for such small data. In this regard, this case study complements the following two cases involving big data, in which some automatic processes were adopted. Figure 6 shows the computed degrees of life, in which dots indicate the degree of life for the centers. The results are highly instructive. For example, the three centers with the highest degrees of life are rather obvious because of the recurring structural properties such as local symmetries, levels of scale, strong centers, thick boundaries, and positive space among the 15 properties. The ht-index of the wholeness is 6, derived from the degrees of life for all the centers, using equation [2]. 14. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 5 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #9FK8U9 3. Wholeness as a hierarchical graph Matching excerpt #25Z8H8: The idea of wholeness has been discussed in a variety of sciences such as physics, biology, neurophysiology, medicine, cosmology, and ecology (e.g., Bohm 1980), but no one prior to Alexander (2002-2005) has ever formulated and defined it in precise mathematical language. Following Alexander's definition of wholeness, some previous efforts have been made (e.g., Salinas 1997) to quantify the degree of life of architecture. The proposed measure L does indicate approximately the degrees of life, but it lacks of the recursive property. We represent a whole as a graph, in which the nodes and links represent identified centers and their relationships within the whole (Figure 3). With the graph, we can compute the degrees of life for the individual centers and the whole. What is unique for our model is that it captures fairly well the recursive nature of wholeness as defined by Alexander. This section presents the two measures, the PR scores and ht-index, and argues why they can be a good proxy of degrees of life or beauty. In the next section, we further illustrate through case studies that a living structure demonstrates a scaling hierarchy of far more low-degree-of-life centers than high-degree-of-life centers; and the degree of the scaling hierarchy can be characterized by the ht-index: the higher the ht-index, the higher degree of life or wholeness. 15. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 3 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #DBN56J 4.2 River Network Generation #VTGN6K 4.2.2 Node Expansion Matching excerpt #BMNJ7A: River Slope map. During the expansion step, the elevation of each new node should be higher than its ancestors to guarantee a consistent water flow. This elevation is computed according to a local river slope-magnitude value that is provided either by the user (Fig. 1 and 17) or generated procedurally (Fig. 18). Either way, the river slope-magnitude (a scalar value) defines only the height variation and provides no information on the direction of the expansion. Mapped on the whole terrain, this river slope map provides an intuitive way to describe how the drainage network will expand. 16. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Matching excerpt #CLXYG3: where \lambda \in [0; 0.25] is another slope-magnitude function that describes if the terrain is mountainous. This terrain slope map can also be either generated 17. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 2 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #3G9YBV 3 Algorithm Overview Matching excerpt #WJMLJ9: The output is controlled by two user-defined maps. The river slope map drives the dendritic shape of the river and directs the Rosgen type of each river. The terrain slope map controls the location of mountains and flatlands. The crest and ridge elevations are obtained by combining the river elevation and the terrain slope information. Both maps are either user-defined (Fig. 1, Fig. 17) or generated procedurally (Fig. 18, Fig. 20). 18. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #UAYDMD 6 Terrain Model Generation #ASA4YQ 6.1 River Primitives Generation Matching excerpt #W9URWJ: tally forming n - 1 confluences inside the cell V (denoted k in Fig. 12). The process starts with two neighboring water entries on the contour of V . We denote the first confluence k_0 . Each water entry is then connected incrementally to the last created confluence. The connection angle is computed for each junction, depending on the position and water flow of the input rivers. When the junction involves two rivers having significantly different water flows (and thus two different Horton-Strahler numbers), the connection angle is set to be nearly perpendicular. Similarly, junction of two rivers of the same size will cause a small angle. Once the junctions are built, 19. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 7 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #4VW4H2 5. Combining river network and elevations #USAEE8 5.3. Optimization-based altitude correction Matching excerpt #3DA84K: A key insight of our algorithm is that we work on the space of elevation differences d_c = z(c) - z(c_r) , which has two advantages. First, it simplifies the treatment of the non-negativity of the slope: to preserve the river network, we force d_c \geq 0 . Second, the elevation is reconstructed by accumulating the elevation differences, this propagates the influence of each constraint along the entirety of the tree at each step of gradient descent, while an approach based on the elevations would only propagate the information by one cell at each step. 20. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 9 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Matching excerpt #UQAJXY: Hydrology-based and physically-based. Many procedural methods targeted the instant generation of terrains, often through the use of noise functions [EMP*02]. Closer to us, Gnevaux et al. [GGG*13] proposed a procedural approach based on hydrology. They generate a river network whose formation and elevation is guided by a slope map. The elevation of areas between rivers is computed using a second slope map. Since our method, similarly, computes the elevations progressively in the order defined by the river network, we alter the a(s) term of Eqn. 3 so as to enforce a small slope for main rivers ( \|\nabla z\| = 0.06 if the drainage is above 2500m^3y^{-1} ), and a stronger slope for the sides of the mountain ( \|\nabla z\| = 0.6 ), corresponding to the two slope maps of [GGG*13]. In Figure 6, we compare our method (right) with this hydrology-based approach. While the latter convincingly arranges rivers and surrounding mountains, our physically-based solutions yield more diverse patterns at all scales, self-emerging from the combination of uplift, stream power law, and hillslope [CMA*16]. 21. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 7 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #4VW4H2 5. Combining river network and elevations #USAEE8 5.3. Optimization-based altitude correction Matching excerpt #57GHRE: We remap z to [0, 1] and use gradient descent to solve Eqn. 22. The sequential nature of the computation of z_c from \mathbf{d} is not readily compatible with existing automatic differentiation solver, therefore we show in Appendix A how we accumulate the gradients with respect to \mathbf{d} throughout the river network. To prevent exploding gradients, we weigh each gradient of the discontinuity term \partial L_d / \partial d_c by the number of nodes N_c upstream of c - which can be computed from the drainage area as N_c = A_c / 8_c^2 . We use the step size for the gradient descent l_r = 0.01 , which we modulate locally to enforce the inequality d_c \geq 0 . 22. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 8 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #W352NS 5 Algorithm Implementation and Simulated Results #MQ2VEA 5.4 Lap Time Convergence and Predicted Lap Time Matching excerpt #4SXSQS: The final curvature and velocity profile for the two-step fast generation method is compared with the equivalent profiles for the gradient descent algorithm in Fig. 12. Notice that the piecewise linear nature of the nonlinear gradient descent method is due to the clothoid constraint imposed by 23. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 5 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #W352NS 5 Algorithm Implementation and Simulated Results #L9NZJM 5.3 Comparison with Other Methods Matching excerpt #8Q264A: The generated racing path after five iterations is shown in Fig. 7. To validate the proposed algorithm, the racing line is compared with results from a nonlinear gradient descent algorithm implemented by Theodosis and Gerdes [5] and an experimental trajectory recorded from a professional racecar driver in the testbed vehicle (Fig. 6). While time-intensive to compute, the gradient descent approach generates racing lines with autonomously driven lap times within one second of lap times measured from professional racecar drivers. 24. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 9 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #LGLUMA 6 Experimental Validation Matching excerpt #QGKPRG: for an autonomous lap of driving is shown in Fig. 13 for both the two-step trajectory and the trajectory from the gradient descent. 25. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 1 Context: #G4BEE9 Mountain trail formation and the active walker model #2F9V87 1. Introduction Matching excerpt #JWYPGD: On inclines, there is a third influence. Walkers may ascend slopes diagonally if the gradient of the incline becomes too steep to ascend directly. Walking at an angle to the line of fastest ascent has the effect of decreasing the effective gradient of the incline, permitting travel up steeper slopes. On descent, it may not be possible to walk directly down a very steep slope without becoming unbalanced, again leading walkers to take a diagonal path. Our aim in this article is to determine if the walkers' desire to avoid steep gradients, in combination with the rules of the active walker model, can be used to simulate the zigzag paths that can be observed in mountainous regions. 26. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 13 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Matching excerpt #AJSDD6: We complete our simulations using algorithm one, by examining walkers that travel consecutively up and down the incline. Results of the simulations can be seen in figure 7. A slightly different weathering time of T = 1500s was used. There is no requirement that the forbidden angles are the same for hikers moving up and down the incline. In general, we expect that the different mechanisms for walking up and down inclines lead to different forbidden angles. In this set of simulations, we choose a forbidden angle of \theta_1 = 25^\circ for walkers moving up the diagram (down the gradient). Those moving down the diagram (up the gradient) have a minimum safe angle of \theta_2 = 10^\circ . We run simulations for a range of \alpha . Some zig-zag patterns can be seen for low alpha, but patterns of decent size do not appear until \alpha \gtrsim 0.45 (panel d). Again, the sizes of the bends in the path increase in size with \alpha . The 27. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 6 Context: #G4BEE9 Mountain trail formation and the active walker model #MKLE5Y 4. A model of mountain walkers #U98348 4.1. New rules for mountain walking Matching excerpt #ZHYXRP: It is our aim extend the active walker model to construct a “mountain walker model”. As we have discussed in section 3, our model should take account of the inability of walkers on steep inclines to walk directly up or down a slope if the gradient becomes too great, and avoid sudden changes of direction that can cause instability. 28. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 8 Context: #G4BEE9 Mountain trail formation and the active walker model #MKLE5Y 4. A model of mountain walkers #U98348 4.1. New rules for mountain walking Matching excerpt #EVCYWF: Rule IIa (To be used with rule Ia) If the angle \gamma , chosen from equation 6, falls within a forbidden zone ( |\gamma| < \theta ), the angle along which the walker moves is mapped to the nearest minimum angle of safety (either \theta or -\theta ). We assume that the larger the incline of the slope, the larger the region of angles that are not permitted. This is equivalent to having an infinite effective potential barrier in certain directions. In the event that \gamma = 0 our walker has a preference to move left. If there is a mapping, we reconstruct \mathbf{e} from \gamma as \mathbf{e} = \cos(\gamma)\mathbf{i} + \sin(\gamma)\mathbf{j} , noting that the sense of \mathbf{i} is up the plane. The new \mathbf{e} is then used to update the position of the walker via eqn. 5. 29. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 5 Context: #G4BEE9 Mountain trail formation and the active walker model #43C2RF 3. The biomechanics of walking on inclines Matching excerpt #54E5UT: Experiments have shown that the requirements on joints increase dramatically on moderate slopes 11,12 : walking on a 10^\circ incline requires hip flexibility of 60^\circ , compared with 30^\circ on the flat. Demands on ankle flexibility increase in a similar way. Joints in the leg such as the ankle, knee and hip are also subjected to significantly increased forces 12 . As determined in Ref. 11, the ankle becomes fully bent for more of the walking cycle as the gradient increases from 0^\circ to 10^\circ . The physiological constraints on the angles through which joints can bend indicate that hills eventually become too steep to walk up directly. To compensate for the limits of joint flexibility, the walker can choose to change the angle of ascent, to avoid walking directly uphill. This leads to a smaller effective gradient. The inability to walk directly uphill can 30. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 4 Context: #G4BEE9 Mountain trail formation and the active walker model #43C2RF 3. The biomechanics of walking on inclines Matching excerpt #BKC6DS: In this section, we aim to give a brief summary of the physiological factors that must be considered when modeling walkers on inclined planes. Some insight into the manner of walking that is adopted on an incline can be gained from attempts to develop bipedal robots that can climb sloping surfaces 16 . If exactly the same method is used to climb a slope as to walk on flat paths, the center of gravity is positioned further back than usual, which may lead to a fall 16 (a good introduction to the biomechanics of walking on flat surfaces can be found in Ref. 15). Humans (and robots developed to climb slopes) compensate for the effects of the slope by leaning forward, which can be achieved by flexing the ankle. This is satisfactory for very shallow slopes. However, if a slope is too steep, it becomes physiologically impossible to turn the ankle joint through the angle necessary to hold the center of gravity over the feet (for example, the person investigated in Ref. 11 could not bend his/her ankle by more than 24^\circ a ). Thus good foot contact cannot be maintained with the ground when walking directly up very steep inclines. 31. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 1 Context: #G4BEE9 Mountain trail formation and the active walker model #2F9V87 1. Introduction Matching excerpt #364B8H: The energetics of walking on an incline have been discussed by Alexander in a simple model of bipedal locomotion 1 . From energy considerations, walkers aim to change the angle of ascent from the vertical if a hill reaches a steep enough gradient. In Ref. 1, human walkers are omniscient, and are able to assess the energetic outlay for an entire route. In this way, they can assess if more energy would be expended taking a shallower and longer route, or if a quick hike up a steep route would be more favorable. We consider that it is unlikely that the information about all possible routes is available for global decisions to influence route and planning, and expect that decisions are more likely to be local. Moreover, modeling has concluded that humans choose well trodden paths in a more local manner 8 . We therefore consider that insight into mountain trail formation could be gained from active walker simulations of inclined planes. 32. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 6 Context: #G4BEE9 Mountain trail formation and the active walker model #MKLE5Y 4. A model of mountain walkers #U98348 4.1. New rules for mountain walking Matching excerpt #ASTVR4: Rule 1a The new direction of the walker is taken as the weighted average of the recent angle of motion \phi and the angle of motion that would be favored on a flat surface. 33. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 10 Context: #G4BEE9 Mountain trail formation and the active walker model #MKLE5Y 4. A model of mountain walkers #KAWSKG 4.2. Discretization scheme Matching excerpt #FSSBCW: The average angle (equation 8) is approximately, 34. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 4 Context: #G4BEE9 Mountain trail formation and the active walker model #A5Y7MA 2. Active walker model for human trails Matching excerpt #ESH66K: \nabla_{\mathbf{r}_\mu} V(\mathbf{r}_\mu, t) is the direction of favorable ground. The symbol \nabla_{\mathbf{r}_\mu} represents the gradient of V taken with respect to the position vector of the walker \mathbf{r}_\mu (the subscript acts as a reminder that the gradient is not taken with respect to \mathbf{r} ). \mathbf{e} is a dimensionless unit vector. 35. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 8 Context: #G4BEE9 Mountain trail formation and the active walker model #MKLE5Y 4. A model of mountain walkers #U98348 4.1. New rules for mountain walking Matching excerpt #ZGTQAD: Rule IIb (To be used with rule Ib) If the angle, \beta = \tan^{-1}(e_y/e_x) , lies within a forbidden zone ( |\beta| < \theta ), then the vector \mathbf{e} is mapped to the closest angle outside the forbidden region. If \beta = 0 the walker moves left. Since \beta = 0 on the first iteration, our paths show a bias in that direction. 36. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 39 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #XG25M6 5.7.5.2. Designed Control Points #XDF6ZN 5.7.5.2.1. Watercourse Crossings Matching excerpt #GXVNNF: Watercourse crossings include wet crossings (such as armored stream crossings) and fords or dry crossings (such as bridges). Some wet trail crossings in low volume watercourses can be crossed even during peak flows. These streams are usually ephemeral. Appropriate crossing locations have a mild stream gradient that is controlled by a feature such as bedrock, boulders, or large trees, often referred to as “nick points”, in or near the channel. These features stabilize the channel gradient and make it easier to construct and maintain the crossing. The channel must be straight and not subject to lateral scour, undercutting, or deposition. Streambanks must be stable with moderate slopes for successful construction of the trail in and out of the channel. Photo 5.22 depicts a wet crossing with a low gradient, straight channel with bedrock at the base of the crossing to control the stream gradient and stabilize moderately sloped approaching banks. 37. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 61 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Matching excerpt #3D6F5A: 50% SIDE SLOPE 38. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 61 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Matching excerpt #RNV97G: 30% SIDE SLOPE 39. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 61 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Matching excerpt #V93SPV: 40% SIDE SLOPE 40. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 9 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #BUKYGV 5.5. Mechanical Wear #V5SGUS 5.5.1. Identification of Mechanical Wear by Use Type #PEUZYA 5.5.1.4. Acceleration, Braking, and Turning/Curving #YE7XWW 5.5.1.4.1. Pedestrians Matching excerpt #R2B6SZ: When hikers and trail runners brake they lower their center of gravity, lean backward, transfer their weight to the heels of their feet, and push backward with their leg muscles. These actions transfer the weight of the user to the heel of the foot, which increases the pounds per square inch applied to the trail tread. Similarly, the angle of the foot also becomes more acute increasing the angle of impingement. 41. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 9 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #BUKYGV 5.5. Mechanical Wear #V5SGUS 5.5.1. Identification of Mechanical Wear by Use Type #PEUZYA 5.5.1.4. Acceleration, Braking, and Turning/Curving #YE7XWW 5.5.1.4.1. Pedestrians Matching excerpt #HZ2LVE: When hikers or trail runners accelerate, they lower their center of gravity, lean forward, rise up on the balls of their feet, and push downward with their leg muscles. These actions transfer the weight of the user to the balls of their feet, which increases the pounds per square inch applied to the trail tread. The angle of the foot also becomes more acute increasing the impingement angle. (See Photo 5.4.) 42. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 61 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Matching excerpt #P679US: 20% - 5% SIDE SLOPE 43. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 9 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #BUKYGV 5.5. Mechanical Wear #V5SGUS 5.5.1. Identification of Mechanical Wear by Use Type #PEUZYA 5.5.1.4. Acceleration, Braking, and Turning/Curving #YE7XWW 5.5.1.4.1. Pedestrians Matching excerpt #MZ5XFJ: When trail runners come to a curve in the trail they lower their center of gravity, lean to the inside of the curve, and transfer their weight to the inside of one shoe and the outside of the other. These actions transfer the weight of the user to the sides of the feet, which increases the pounds per square inch applied to the trail tread. The angle of the foot also becomes more acute, increasing the angle of impingement. 44. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 5 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #JGKFAU 4.2 Discretizing Advection Matching excerpt #VFBFKJ: where \mathcal{A}_{bc} is the interpolation of the discretized \mathcal{A} with fixed angle \theta_b and wavenumber k_c , \hat{\mathbf{k}}_b = (\cos \theta_b, \sin \theta_b) is the wave direction determined by angle \theta_b , and \mathbf{x}_a = (x_a, y_a) . 45. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 4 Context: #57PDWB Interactive Procedural Street Modeling #QNKCB5 5 Tensor Field Generation #4XDKA4 5.3 Modifying Tensor Fields Using Rotation Fields Matching excerpt #UWWD8Z: In real street networks we observe various forms of irregularities that seem to have stemmed from slight distortions of regular or smooth patterns. Additionally, given a symmetric tensor field T , the major and minor hyperstreamlines always intersect at a right angle except at the degenerate points where they are not well-defined. While orthogonal intersections are dominant and preferred for construction, we also need to take into account non-orthogonal intersections. To model these phenomena we make use of three different scalar fields R_1 , R_2 and R_3 that model rotations of the minor and major eigenvectors: 1) the first rotation field is used to rotate both major and the minor eigenvectors with R_1 degrees in opposite directions, i.e. the tensor value at (x, y) is altered such that the major and minor eigenvectors are rotated by an angle of R_1(x, y) and -R_1(x, y) , respectively, where R_1 \in [-\frac{\pi}{2}, \frac{\pi}{2}] . 2) R_2 rotates the major eigenvector only, and 3) R_3 rotates the minor eigenvector. While in theory only two scalar fields are necessary, we have found that the use of three scalar fields provide additional intuition. 46. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 3 Context: #57PDWB Interactive Procedural Street Modeling #QNKCB5 5 Tensor Field Generation #FCEMBJ 5.1 Generation of Basis Fields Matching excerpt #7R43W5: Heightfield: The natural elevation is an important constraint for most road construction. We observe that roads are often built by taking into account the gradient of the height field. To derive a tensor field from a heightfield H(x, y) , we compute the gradient \nabla H = (\partial H / \partial x, \partial H / \partial y) . We then use the tensor field T(x, y) = R \begin{pmatrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & -\cos 2\theta \end{pmatrix} whose minor eigenvector field matches the gradient of the heightfield everywhere, i.e. \theta = \arctan(\frac{\partial H / \partial y}{\partial H / \partial x}) + \frac{\pi}{2} and R = \sqrt{(\partial H / \partial x)^2 + (\partial H / \partial y)^2} . 47. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 4 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks Matching excerpt #Q847GQ: Recall that the discrete path is a rectilinear path composed of straight segments connecting sample points. Existing techniques only consider 4 or 8 connectivity between sample points. Therefore, the segments of the discrete path can only have 4 or 8 directions, with a maximal angle resolution of 45 degrees. Shift paths [JV04] can partially overcome this problem by allowing paths to shift away from the grid points, but require a computationally demanding relaxation step to shift path segments. 48. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 3 Context: #UR2SY7 Procedural Generation of Roads #RNR7U5 4. Cost functions #RUTEZU 4.1. Surface roads Matching excerpt #XDR4PZ: Slope Let s(\mathbf{p}, \dot{\mathbf{p}}) denote the slope of the terrain at point \mathbf{p} . If the slope is too steep, the transfer function should return infinity so as to prevent paths from climbing very steep slopes which would generate unrealistic roads. Otherwise, we use a function of the slope controlled by the maximum cost value \mu(\kappa_0) . 49. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 8 Context: #UR2SY7 Procedural Generation of Roads #SBCAWF 7. Results Matching excerpt #M8G6GC: Figure 22 shows the influence of the slope cost function over the trajectory. By setting the maximum authorized slope to a high value and lowering the influence of the slope cost function over the global cost, the generated path is a long surface road (left image). In contrast, if the maximum authorized slope is very low, it is no longer possible to create a road going up the hills and the algorithm creates a tunnel (right image). 50. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 4 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #SR7CUB 5.1. Path segment masks Matching excerpt #NSW89D: Influence of the size of the masks Increasing the size of the segment path masks enables us to detect paths with a better angle resolution and to reduce the limit on direction effect, at the cost of an increasing number of iterations in the shortest path algorithm. Table 1 reports the number of path segments n_k as well as the maximum angle \alpha . Approximate matches 1. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 8 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.029 Related excerpt #6N825C: rocks strength. We choose the minimal and maximal slope angles to be 6^\circ and 54^\circ respectively. This results in a more random distribution of the erosion patterns in valleys as shown in Figure 17. 2. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #7E86TB 5. Erosion Score: 0.019 Related excerpt #APLS5B: Given a node \mathcal{X}_k , we use its receiver \mathcal{X}_l stored in \tilde{\mathcal{T}} to compute the slope. Let \|\mathbf{p}_k - \mathbf{p}_l\| denote the distance between nodes \mathcal{X}_k and \mathcal{X}_l located at points \mathbf{p}_k and \mathbf{p}_l in the horizontal plane, we have: 3. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #7E86TB 5. Erosion Score: 0.018 Related excerpt #7HBEWM: This section describes the last two steps of our iterative algorithm: drainage and slope computation, and solving the stream power Equation (1). 4. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 7 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.016 Related excerpt #Z2BRQU: We note x the distance between \mathbf{p} and the corresponding outflow, and d the distance between ep and a ridge. Then we assume that A is proportional to (d-x)^2 . Recall that s = dh/dx , so we obtain: 5. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #JT9864 3.1. Geological Background Score: 0.014 Related excerpt #PGNGMP: The stream power equation states that the rate of change of surface topography h(\mathbf{p}) at a position \mathbf{p} is controlled by the balance between the surface uplift u(\mathbf{p}) and the fluvial erosion, which is a function of the local slope s(\mathbf{p}) and the drainage area A(\mathbf{p}) . The local slope s(\mathbf{p}) is defined as the surface topographic gradient: 6. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 8 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.012 Related excerpt #EUK7YL: We experimented by forcing the maximum slope to follow a 3D Perlin noise with a high persistence, to account for local different 7. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #7E86TB 5. Erosion Score: 0.011 Related excerpt #HUHFWU: Drainage and slope. Let \mathcal{N}_k denote a node of the graph-covering stream trees \tilde{\mathcal{T}} and C(\mathcal{N}_k) the set of its children nodes. The drainage area A_k can be computed using the recursive formula: 8. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #Z6DVCN 4. River Network Graph Score: 0.02 Related excerpt #HS22AT: Next, graph nodes are labeled with the terrain slope s and river flow \phi values at their cell position. The latter is a measure of the volumetric rate at which water is carried down the river and an accurate estimation is problematic, since it depends on parameters such as rainfall and soil composition. Instead, we apply a simplified model based on an empirical power law observed in geomorphology [Dun78]: from drainage area A_{ij} [ m^2 ], the flow \phi_{ij} of the river [ m^3 s^{-1} ] is approximated by \phi_{ij} = 0.42A_{ij}^{0.69} . This equation takes into account evaporation and infiltration, which is why the volume of flow is not preserved. 9. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Score: 0.025 Related excerpt #CLXYG3: where \lambda \in [0; 0.25] is another slope-magnitude function that describes if the terrain is mountainous. This terrain slope map can also be either generated 10. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 3 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #DBN56J 4.2 River Network Generation #VTGN6K 4.2.2 Node Expansion Score: 0.02 Related excerpt #BMNJ7A: River Slope map. During the expansion step, the elevation of each new node should be higher than its ancestors to guarantee a consistent water flow. This elevation is computed according to a local river slope-magnitude value that is provided either by the user (Fig. 1 and 17) or generated procedurally (Fig. 18). Either way, the river slope-magnitude (a scalar value) defines only the height variation and provides no information on the direction of the expansion. Mapped on the whole terrain, this river slope map provides an intuitive way to describe how the drainage network will expand. 11. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #DBN56J 4.2 River Network Generation #VTGN6K 4.2.2 Node Expansion Score: 0.012 Related excerpt #4ULQC7: the other nodes and higher than its ancestor node N_{\mathcal{X}} . We constrain the terrain generation so that the maximum local slope in the graph should be less than a given threshold \kappa depending on the location of the point. The constant \kappa represents an upper bound of the slope-mapping function. Therefore, we make sure that the new point \mathbf{p} will satisfy the Lipschitz condition: |\mathbf{p}_z - \mathbf{p}_z'| < \kappa(\mathbf{p}) \cdot d(\mathbf{p}, \mathbf{p}') . This condition prevents the creation of huge cliffs. 12. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #97YQQD 6. Other erosion factors #VEK6N9 6.2. Thermal erosion Score: 0.023 Related excerpt #XU4RDE: where s_c = \text{atan}(30^\circ) is the critical slope. We modify Eqn. 3 to add the contribution of the thermal erosion: 13. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #97YQQD 6. Other erosion factors #C4WS38 6.1. Hillslope erosion Score: 0.019 Related excerpt #FJ5WJ6: We integrate from s to the ridge r , where the slope vanishes; and use Hack's law [Hac57] to associate the distance to the ridge with the drainage A : r - s = CA(s)^h , where C is a constant in the range [1.4 – 2], and the exponent is usually set to h = 0.6 : 14. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 11 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #V6AZDH 7.3. Applicability of our method Score: 0.016 Related excerpt #CLYRVZ: Escarpments are steep slopes that separate flat areas of different elevations. The sudden change in elevation yields a strong erosive response, that illustrates the need for the advective component of the analytical solutions. Indeed, a simpler solution that would only model a progressive reduction of the slopes would only cause a local smoothing of the cliffs, while the stream power law predicts a retreat of the cliff along the drainage pattern at a speed that depends on the river discharge [SS20]. We illustrate this behavior in 15. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 10 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #BK5LST 7.2. Ablation study Score: 0.015 Related excerpt #3WX3ZE: Hillslope erosion stabilizes the slopes of the mountains and acts as the main erosion process at low drainage where the stream power law becomes negligible [LD03]. We show the impact of hillslope in Figure 9, where we show the analytical solutions of the stream power law only at \delta x = 50 m (left), compared with our modified formulation that includes the hillslope erosion (Section 6.1, right of Figure 9). Without hillslope, we observe the emergence of unrealistically sharp ridges and peaks. 16. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 7 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #97YQQD 6. Other erosion factors #C4WS38 6.1. Hillslope erosion Score: 0.013 Related excerpt #L42GEL: Hillslope processes encompass the weathering of the mountain slopes and the diffusion that results from the creep flow of the eroded material. It is often simplified as a linear diffusion of the terrain elevation [BS97, SPF + 23, CJP + 23]: 17. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 10 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #BK5LST 7.2. Ablation study Score: 0.012 Related excerpt #TMJFHY: in Figure 10 (left), but the stream power law does not let us control the steepness of the cliff, only the speed at which they propagate away from the low boundary node following the drainage patterns. In contrast, adding thermal erosion as explained in Section 6.2 allows us to adjust the critical angle, and hence the shape of the slopes (Figure 10, right). 18. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 13 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Score: 0.017 Related excerpt #AJSDD6: We complete our simulations using algorithm one, by examining walkers that travel consecutively up and down the incline. Results of the simulations can be seen in figure 7. A slightly different weathering time of T = 1500s was used. There is no requirement that the forbidden angles are the same for hikers moving up and down the incline. In general, we expect that the different mechanisms for walking up and down inclines lead to different forbidden angles. In this set of simulations, we choose a forbidden angle of \theta_1 = 25^\circ for walkers moving up the diagram (down the gradient). Those moving down the diagram (up the gradient) have a minimum safe angle of \theta_2 = 10^\circ . We run simulations for a range of \alpha . Some zig-zag patterns can be seen for low alpha, but patterns of decent size do not appear until \alpha \gtrsim 0.45 (panel d). Again, the sizes of the bends in the path increase in size with \alpha . The 19. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 1 Context: #G4BEE9 Mountain trail formation and the active walker model #2F9V87 1. Introduction Score: 0.016 Related excerpt #JWYPGD: On inclines, there is a third influence. Walkers may ascend slopes diagonally if the gradient of the incline becomes too steep to ascend directly. Walking at an angle to the line of fastest ascent has the effect of decreasing the effective gradient of the incline, permitting travel up steeper slopes. On descent, it may not be possible to walk directly down a very steep slope without becoming unbalanced, again leading walkers to take a diagonal path. Our aim in this article is to determine if the walkers' desire to avoid steep gradients, in combination with the rules of the active walker model, can be used to simulate the zigzag paths that can be observed in mountainous regions. 20. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 13 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Score: 0.012 Related excerpt #EDDBRC: As the minimum safe angle is increased to 15^\circ , we note that the minimum values of \alpha which are needed to generate zig-zag patterns decreases slightly. In Fig. 5(a) where \alpha = 0.4 , we observe that a single zigzag emerges in the path. As walkers get closer to their destination, the rate at which they change their walking direction increases. Fig. 5(b) shows a similar path for \alpha = 0.45 . In Fig. 5(c) we observe that when \alpha = 0.5 walkers take larger detours away from the direct path between entry and exit, with several changes of direction along the trail. Similar results were found when \theta = 25^\circ (Fig. 6). While zigzag forms develop during the simulations, the rather diffuse paths are not satisfactory representations of mountain trails. 21. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 6 Context: #G4BEE9 Mountain trail formation and the active walker model #MKLE5Y 4. A model of mountain walkers #U98348 4.1. New rules for mountain walking Score: 0.012 Related excerpt #BVT3JG: where \mathbf{i} and \mathbf{j} are unit vectors in the x (uphill) and y (horizontal) directions respectively. In the determination of \beta , care is taken to ensure that the angle is in the quadrant consistent with the signs of e_x and e_y . We take care to avoid any problems with branch cuts in equations 6 and 7. Strictly, \phi should relate to the direction of the walker over the time period just before 22. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 1 Context: #G4BEE9 Mountain trail formation and the active walker model #2F9V87 1. Introduction Score: 0.01 Related excerpt #GNDKEV: To demonstrate some examples of paths on inclines, we took photographs in the Lake District in Cumbria, England, which can be seen in Fig. 1. The upper panels Fig. 1(A1,A2) show spontaneously formed zig-zag paths on Wansfell. Two paths can be seen to the left and right hand sides of the picture, as highlighted in the figure on the right (A2). The left hand path has been augmented with rock since its formation, but still shows the characteristic zig-zag. To remove doubt on the origin of the zig-zags (for example, the stones might have been laid according to a plan) a second path can be seen to the right of the picture. The right hand path is spontaneously formed in the grass. Both have similar path angle and regularity of direction change. An example from further up the trail can be seen in panels B1 and B2. Here, there is additional wear to the side of the trail, indicating that the trail is still evolving. The paths are on inclines of around 1:8. The bottom path (C1 and C2) is on an incline of around 1:2, and was observed near Low Sweden Bridge which is close to the village of Ambleside. Trails of this type are not unique to England, and such paths can be seen in other locations, such as Smith Rock in the USA, where the bends in the paths are large enough to appear on trail maps 23. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 31 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades #7FRMWX 5.7.3.5. Percent of Hillslope Score: 0.027 Related excerpt #SFWHTE: The relationship between hillslope grade and linear trail grade is one of the most important factors in trail design. As hillslope grade increases, the linear trail grade can also increase up to the limit established by other variables discussed in this section. Correspondingly, as hillslope grade decreases, linear trail grade also needs to decrease. If linear trail grade begins to approach hillslope grade, the trail begins to align with the "fall line" of sheet flow drainage directed by the landform. A fall line trail will capture sheet flow and become a water conveyance. The recommended ratio of hillslope to linear trail grade is based on all the variables used to determine the maximum sustainable grade. In some locations, a 2:1 ratio of hillslope to linear grade may be adequate, while in other locations a 3:1 ratio may not be enough. The relationship between the two grades is critical to the long-term sustainability of the trail. 24. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 33 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #ZGJXBS 5.7.4. Designed Linear Grades Score: 0.026 Related excerpt #D33DUB: Sometimes a maximum sustainable grade may exceed the user's comfort level or needs. For example, if, due to favorable landform conditions, the maximum sustainable grade for a Class I pedestrian hiking trail ranges between 12 and 16% but the user group is largely young families, senior citizens, and casual hikers, continuous trail grades between 12% and 16% are too steep. A designed grade of 8% to 10% is more appropriate. The same 12% to 16% linear grade may be too steep for most Class I equestrian use as well since horses are usually not conditioned for unremitting steep grades. 25. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 32 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades #BRLU95 5.7.3.9. Evaluating and Interpreting the Criteria Score: 0.024 Related excerpt #53NYQ5: The above criteria can influence the maximum sustainable grade either positively or negatively. When using these criteria to determine the maximum sustainable linear grade it is important to note that they are very much inter-related. They can collectively increase or decrease the maximum linear grade. They may also offset each other when some of the criteria have a positive influence and others have a negative influence on the linear grade. For example, the proposed trail corridor may be located high in a watershed that receives a moderate amount of rainfall and has low intensity rainfall events. All of these conditions enhance the maximum linear grade capabilities of the trail. However, if the soils have low strength and durability characteristics and there is an absence of canopy cover, these negative conditions offset the positive criteria and the maximum linear grade would not increase and could even decrease. Interpreting these criteria is as much art as it is science and the more experience the trail designer has in laying out, constructing, and maintaining trails the better they will be able to evaluate the landform. As previously mentioned, some of these variables may change throughout the proposed alignment, which could alter the maximum sustainable grade. There may not be a single maximum sustainable grade for the entire alignment but several maximum linear grades along the proposed trail corridor. 26. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 56 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Score: 0.024 Related excerpt #8CNUPW: Once the flagger is on grade, the shooter and flagger use their clinometers or Abney hand levels to sight at the horizontal reference points on each other's bodies. The instruments should read the linear grade for that segment, and both team members must be within 1% of each other. If the two grades are off more than one percentage point, one person is reading their instrument incorrectly, shooting at the wrong reference point, or one instrument is defective. The team re-sights the grade to determine the cause of the error and takes the appropriate corrective action. On an ascending trail, if the instrument readings are within one percentage point of each other and the linear grade is too low, the flagger in front moves up the slope to increase the grade. If the linear grade is too high, the flagger in front moves down the slope to lessen the grade. 27. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 34 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #ZGJXBS 5.7.4. Designed Linear Grades Score: 0.024 Related excerpt #QAJC48: In most situations the maximum sustainable grade will not exceed the designed grade or the grade needed by the use type. However, when those conditions do exist, the linear grade should be adjusted (lowered) to meet the needs of the user. 28. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 59 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Score: 0.022 Related excerpt #CBKMJC: Photo 5.40 illustrates how, following traditional construction practices, a trail constructed on a 30% hillslope would be half native bench and half fill bench (yellow line). However, by constructing further into the hillslope the entire trail bed is comprised of native material (red line). 29. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 14 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #BUKYGV 5.5. Mechanical Wear #8BXTCV 5.5.4. Sudden Grade Changes Score: 0.022 Related excerpt #76WMXT: When trail users encounter a sudden change in linear grade they respond in the same manner as they do when accelerating or braking. (See Photo 5.11.) This response is more about gravity than speed. To compensate for traversing up a steep grade, pedestrians lower their center of gravity, lean forward, and push off with the balls of their feet. To compensate for traversing down a steep grade, they lean backward and dig in with their heels. When going uphill or downhill, horses lower their center of gravity, push off with their rear legs or dig in with their rear legs. Mountain bikers apply more force to the bike pedals (including standing on their pedals) when going uphill and apply the brakes to the front and rear tires when going downhill. OHV riders accelerate their vehicles when going uphill and apply the brakes when going downhill. 30. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 14 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #BUKYGV 5.5. Mechanical Wear #8BXTCV 5.5.4. Sudden Grade Changes Score: 0.022 Related excerpt #247BPE: It is not uncommon to have a sudden grade increase in a trail alignment. A sudden grade change occurs when the linear grade increases by a factor of two or three over a short distance without any transitional grade in between. Examples of sudden grade changes include going abruptly from a 5% to 10% grade or from a 7% to 20% grade. Sudden grade changes are often related to adjustments in the trail alignment to go above or below a control point or drop in or climb out of natural or constructed watercourse crossings, grade reversals, or rolling dips. They typically result from poor layout or construction practices. (See Photo 5.10.) 31. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 27 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #M2FCT4 5.6. Maintaining Natural Drainage Score: 0.022 Related excerpt #SW8LMB: Constructing a trail bed on a hillslope rather than flat ground will also enhance the trail's drainage performance. Constructing into the hillslope will facilitate more efficient overland sheet flow drainage. When the sheet flow runs down the cut bank in a thin film it accelerates, giving it the momentum to flow across the trail bed and down the hillslope. (See Photo 5.20.) Curvilinear alignment combined with sustainable linear grades, hillside construction, and outsloping prevents water diversion and accumulation. Retaining the landform's natural drainage patterns is the key to sustainable trails. 32. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 29 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #D9NVQC 5.7.2. Major Control Points and Average Linear Grades Score: 0.021 Related excerpt #56N3J2: Mapping software can also be used to calculate elevation changes and average linear grades. However, these programs provide only rough estimates and should only be used prior to field validation. Once this calculation is performed, the linear grade between the points is compared to the maximum sustainable linear grade of the landform and accessible trail design standards. By breaking the trail corridor into individual segments between control points, the trail alignment is divided into manageable units. Segmentation is an important step that greatly simplifies layout and design. 33. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 33 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades #BRLU95 5.7.3.9. Evaluating and Interpreting the Criteria Score: 0.02 Related excerpt #76SGWC: Once the maximum linear grade has been identified between the major control points, it can be compared to the average linear grade determined by the rise over run calculation. If the average grade is steeper than the maximum sustainable grade, the trail alignment needs to be adjusted (lengthened) to conform to the grade limit. Using the above example of two control points that are 2,000 feet apart with a 200 foot elevation difference, if the maximum sustainable linear grade is determined to be 8% and the average linear grade between the two control points is 10%, then additional linear run must be provided to reduce the average linear grade. To determine the additional linear run needed, divide the elevation difference between the two controls by the maximum sustainable linear grade (i.e., 200 \text{ ft} \div 0.08 = 2,500 \text{ ft} ), then subtract the existing distance between the two points to determine the additional length needed (i.e., 2,500 \text{ ft} - 2,000 \text{ ft} = 500 \text{ ft} ). To reduce the average linear grade to 8%, an additional 500 lineal feet of trail must be added to the alignment. If landbase, resource, aesthetic, or construction issues prohibit lengthening the trail in a curvilinear fashion, then trail features and structures such as topographic turns, climbing turns, and switchbacks may be needed. Steps may also be a potential solution. These trail features and structures must be placed at appropriate locations and become minor control points. 34. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 32 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades #DQ4WG4 5.7.3.8. Evaluation of Existing Trails Score: 0.018 Related excerpt #S3X7UU: An additional method of determining the maximum sustainable grade of a proposed trail is to evaluate existing trails in the same geographic area. Assuming that the existing trails have the same characteristics identified above as the proposed trail, they can be used as a tool to ground truth the maximum sustainable grade analysis. The key to using existing trails as indicators of maximum sustainable grades is that those trails or portions of those trails must possess the appropriate curvilinear alignment and proper trail construction characteristics. Unfortunately, there are very few trails that possess those qualities. However, you can usually find a segment or segments that meet these criteria. By knowing the use type, levels of use, and seasons of use, and by closely monitoring the linear grade, cross slope, and soil conditions, you can begin to establish the threshold of sustainable linear grade on these trail segments. 35. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 61 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Score: 0.018 Related excerpt #82N8XD: NOTE: AMOUNT OF TRAIL BENCH VARIES LINEARLY W/ % OF SIDE SLOPE. ALL SOIL SHOULD BE MINERAL AND CONTAIN NO ORGANIC MATERIAL. 36. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 29 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades Score: 0.018 Related excerpt #9ZJB62: The maximum sustainable grade is initially determined by evaluating information obtained during the literature research and from design standards. However, this initial grade needs to be refined and validated by field reconnaissance. The following variables determine the maximum sustainable grade of a trail. 37. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 29 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades Score: 0.017 Related excerpt #RCLS5L: Maximum sustainable linear grade is the linear grade of a trail that, when combined with proper layout and construction, will result in a trail bed that requires only routine maintenance and will not threaten resources, even when subjected to severe weather conditions or heavy use. All trails require some level of maintenance. However, a sustainable trail should perform its intended purpose without the need for non-cyclical maintenance and should not be subject to catastrophic failures during significant storm events. 38. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 32 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades #SB9AAG 5.7.3.6. Location on the Hillslope Score: 0.015 Related excerpt #EZKSLY: Generally, within a watershed, trail alignment at lower elevations will encounter more shallow groundwater and accumulate greater amounts of sheet flow than trails at higher elevations. The amount of sheet flow and shallow groundwater that accumulates on the trail is generally proportional to the watershed's surface area above the trail alignment. This concept is important to understand when designing trails on slopes because the more water the trail encounters, the lower the linear grade it can sustain. In addition, trails at the bottom of a watershed usually encounter less stable geology, as inner gorges undergo a more dynamic geomorphic process. Trail alignments at higher elevations in the watershed usually can sustain higher linear grades. 39. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 57 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Score: 0.014 Related excerpt #G9NCTS: Curvilinear alignment should be carefully followed during flagging. So that the trail is kept nearly perpendicular to overland sheet flow, linear grade shots should be taken between all topographic breaks in the landform including subtle breaks. To ensure the trail will not accumulate or divert water, natural drainage patterns should be maintained, including dipping the trail in and out of topographic watercourse features, such as small swales and undulations. Additionally, linear grades should be adjusted relative to changes in the percent of hillslope to prevent the trail from becoming fall line and able to capture and convey the hillside sheet flow. A properly laid out trail will be nearly hydrologically invisible on the landform and will prevent water from entering and running down the trail. 40. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 28 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #D9NVQC 5.7.2. Major Control Points and Average Linear Grades Score: 0.014 Related excerpt #S47DP4: Once the existing information is reviewed and assimilated, the major control points between the starting and ending of the trail are identified. These points are identified during the literature review process and confirmed by field reconnaissance. Major control points include highway accesses, railway crossings, large bodies of water, massive landslides, avalanche chutes, talus slopes, and steep cliffs. Generally, these points are where the new trail alignment must pass through (“positive controls”) or avoid (“negative controls”). After these points are confirmed and established, the broad trail corridor is narrowed and adjusted to accommodate these locations. Mapping software can be used to draw the trail corridor following the principles of curvilinear alignment. This corridor is adjusted to avoid or join the major points. Most mapping software will calculate the distance of the trail corridor drawn. The average linear grade between major control points is then calculated by dividing the elevation difference between two control points by the linear distance between the points. For example, if the elevation difference between the two control points is 200 feet and the linear distance between them is 2,000 feet, the average linear grade will be 10% (i.e., 200 \text{ ft.} \div 2,000 \text{ ft.} = 0.10 or 10%). 41. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 15 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #BUKYGV 5.5. Mechanical Wear #8BXTCV 5.5.4. Sudden Grade Changes Score: 0.014 Related excerpt #WHZ4PN: Because of the increased mechanical wear, sudden grade changes should be avoided by following the layout and design principles identified in this chapter and Chapter 14, Drainage Structures . If a drainage structure such as a grade reversal is used, the grades going into and out of the structure should be gradual and never exceed the maximum sustainable linear grade. 42. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 57 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process #SKHQPC SIGHTING FOR GRADE WITH CLINOMETER Score: 0.013 Related excerpt #537P9J: It is important to note that when placing a flag at a scuff marking the correct linear grade, its location represents the outboard hinge of the trail bed and not the centerline of the trail bed. In manuals following traditional trail construction practices, the centerline is influenced by the percent of grade of the hillslope where the trail is constructed. If the hillslope grade is 50% or steeper, the trail bed will be nearly 100% native bench, which means the flag represents the outside edge of the trail bed. For a hillslope grade of 30%, the trail bed is approximately 50% native bench and the flag represents centerline of the trail bed. For a hillslope grade of 10%, the trail bed is approximately 25% native bench and the flag represents the inside quarter of the trail bed. These estimates are based on using fill material for constructing the trail bed. (See Figure 5.13.) Partial bench construction is not a recommended practice as a trail bed comprised of fill material will be subject to differential settling, more susceptible to mechanical wear, and less sustainable. For these reasons trail designers should always strive for full bench construction. 43. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 52 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #NQEU6U 5.7.6. Final Grade Reconciliation Score: 0.013 Related excerpt #JTLEZB: Once all major and minor control points are located within the trail corridor, the average and maximum sustainable linear grades between control points are identified. These grades can then be compared to the designed trail grade. If there are no conflicts, the trail alignment can be finalized. The final linear grade between each control point must be equal to or less than the maximum sustainable linear grade and the designed grade, which may require reconciling segments where the average linear grade exceeds these limits. Additional linear run can be obtained through topographical turns, climbing turns, or switchbacks. Engineered and constructed solutions may also be necessary to work through minor controls and reduce linear grades, which can require many days in the field. By completing this trail design process, the designer will gain a thorough knowledge of the landform and be aware of all the issues and proposed design solutions. By the end of field reconnaissance, the designer should have explored every possible routing and selected one that represents the best possible alignment. For pedestrian trails, the designer can now determine if the proposed alignment meets accessibility standards. By now, every option should have been explored to design and construct an accessible trail. 44. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 54 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #8BZAPC 5.7.7. Flagging the Trail Alignment #AGRR47 5.7.7.1. Initial Flagging Process Score: 0.012 Related excerpt #74BTZF: Normally, two people are sufficient for flagging a trail alignment. They use clinometers or Abney hand levels to sight linear grades. Prior to starting, they stand on level ground and use their instruments to obtain a horizontal reference point on each other's bodies. They look through their instruments at 0% (level to eye height) and locate where that horizontal line is on the body part of the other person. People of similar height are usually partnered, so their reference points are on each other's faces. If one person is substantially taller than the other, the taller person will sight over the shorter person's head, and they will not have a horizontal reference point. When shooting grades in the field, both members of the flagging team must be able to sight on each other to validate the linear grade. The flagging team's linear grade measurements should be within 1% of each other, which cannot be accomplished if one partner is unable to sight on the other. If there is a significant difference in height between the two flaggers, the shorter person can carry a rod or pole that is long enough for the taller person to obtain a horizontal reference point. That location on the rod is then marked with colored tape and flagging for future reference. (See Figure 5.12 and Photo 5.36.) 45. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 51 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #XG25M6 5.7.5.2. Designed Control Points #AG3WMA 5.7.5.2.5. Orientation/Aspect Score: 0.012 Related excerpt #BMQNV9: Taking advantage of the landform's aspect can greatly improve the availability and performance of the trail and the comfort of the trail user. 46. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 46 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #XG25M6 5.7.5.2. Designed Control Points #9EED3X 5.7.5.2.2. Turns Score: 0.011 Related excerpt #EQ3H8H: It may not be possible to locate a turn where all of these features are present, but the more of these features that can be included the more functional and sustainable it will be. Photos 5.29 demonstrate the appropriate location for a climbing turn on a ridge nose with a slope less than 30% (left). Note no retaining wall was used at the bottom of the landing. On the right of Photo 5.29, the appropriate location of a switchback on the flank of a watercourse with a slope greater than 30% is shown. Note the retaining wall at the bottom of the landing. Photo 5.30 provides examples of using a break in the slope and natural barriers to prevent cutting of the turn by trail users. 47. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 7 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #BTBPNF Algorithm 6: Extracting a depression-free water surface Score: 0.021 Related excerpt #E7SE4R: Input : Terrain cells \mathcal{T} with elevation z , small slope \epsilon 48. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #53AQ2N Algorithm 7: Implicit fluvial erosion Score: 0.01 Related excerpt #VPGNAT: Fluvial erosion is not the only erosive process responsible for shaping terrain. Hillslope processes model the gradual accumulation of solid material at the base of mountains and hills [BS97] and is usually expressed as a diffusion equation. We follow Tzathas et al. [TGSC24] and approximate it by including additional terms in the Stream Power Equation, changing kQ^m to kQ^m + k_t + k_h A^{-h} , where k_t and h = 0.6 are hillslope erosion parameters, A is the drainage area (obtained via flow routing with precipitation set uniformly to p = \Delta x^2 ). The parameter k_t accounts for slope-dependent effects (landslides, debris-flow), regrouped in computer graphics under the catch-all term thermal erosion [MKM89]. 49. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 3 Context: #UR2SY7 Procedural Generation of Roads #RNR7U5 4. Cost functions #RUTEZU 4.1. Surface roads Score: 0.024 Related excerpt #XDR4PZ: Slope Let s(\mathbf{p}, \dot{\mathbf{p}}) denote the slope of the terrain at point \mathbf{p} . If the slope is too steep, the transfer function should return infinity so as to prevent paths from climbing very steep slopes which would generate unrealistic roads. Otherwise, we use a function of the slope controlled by the maximum cost value \mu(\kappa_0) . 50. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 8 Context: #UR2SY7 Procedural Generation of Roads #SBCAWF 7. Results Score: 0.011 Related excerpt #M8G6GC: Figure 22 shows the influence of the slope cost function over the trajectory. By setting the maximum authorized slope to a high value and lowering the influence of the slope cost function over the global cost, the generated path is a long surface road (left image). In contrast, if the maximum authorized slope is very low, it is no longer possible to create a road going up the hills and the algorithm creates a tunnel (right image). ### 9. Tool result: search_text Exact matches 1. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 4 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #JL4FVP 5 Wave Patch Generation: Matching excerpt #PRB2KL: Once the fluid represented by the wave patch is detached from the fluid below that represented by the shallow water simulation, its motion is primarily determined by its initial velocity and gravity. Thus, Euler steps are sufficient to integrate velocity and position over time. After the update, we perform a collision detection of the particle with the fluid surface of the shallow water simulation. When a collision is detected, we distort the shallow water simulation at the particle position \mathbf{x} with H(\mathbf{x}) = H(\mathbf{x}) - p_m , while the eight neighbors of the shallow water node at \mathbf{x} are displaced by p_m/8 . Note that we do not explicitly transport fluid with the wave patches, as a modification of the height field along the wave front would distort its motion. This leads to noise within the shallow water simulation, unless the modification along the whole region of the wave is very smooth. As mentioned below, correctly performing this mass transport and smoothing is a topic of future research. 2. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 1 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #LSRGTK 2 Related Work Matching excerpt #XYKATD: Full 3D simulations became popular with the methods developed in [19] and [4], and have by now been extended in numerous ways. Studies of breaking waves have likewise first been performed in 2D [1]. [16] on the other hand presented a full 3D treatment of breaking waves with a Volume-of-Fluid simulation. In [20] the visual impact of breaking waves has been improved by adding particles for sprays and foam. Similar to [16], an approach to use slices of 2D simulations for wave simulations in real-time is demonstrated in [23]. Recently, Full three-dimensional simulations have been combined with two-dimensional techniques to speed up simulations of large volumes. In [9], a 2D simulation is performed beneath a layer of full 3D simulation for the fluid surface, while [22] couple the 3D simulation region to a 2D shallow water simulation. While these approaches significantly lower the simulation time, they are still not suitable for real-time applications. 3. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 8 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Matching excerpt #76252N: Stream power erosion without the uplift. The stream power erosion can be used without the uplift and it adds a global hydrological realism to an existing scene as shown on an example of a fractal terrain enhanced with erosion in Figure 14. As the erosion converges toward a flat terrain, it is necessary to use small time steps and to stop the simulation after only a few iterations. 4. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 9 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #RRBERX 7. Conclusion Matching excerpt #5SD6KW: Contrary to previous erosion simulation methods, the user does not need to predefine an initial mountain on which erosion is applied, and which may affect the visual realism. In our approach the user paints a simple uplift map on a flat ground, enabling control of the shape of the main mountain ranges after a few iterations. Our simulation algorithm runs at interactive rates, and allows monitoring the results by tuning a single erosion parameter. Moreover, the erosion itself can be used without the tectonic uplift and it improves realism of existing terrain models. In addition to real-time visualization methods used during simulation, we can convert the vector 5. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 1 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #X3SQUZ 2. Related Work Matching excerpt #EXM5FG: Erosion is the most important geomorphological agent forming terrains and methods simulating erosion have been developed for many years in computer graphics. The seminal paper by Musgrave et al. [MKM89] introduced hydraulic and thermal erosion. Both approaches were coupled with fractal terrain generations. Chiba et al. [CMF98] and Benes and Forsbach [BF02] detailed the hydraulic erosion by using the simulation of water flow, followed by dissolution of soil, transportation and deposition. These methods were later improved by adopting the Navier-Stokes equations on a 3D voxel grid in [BTHB06] and by enabling the interactive sculpting of the input terrain through erosion strokes in [VBHS11]. Landslides (mass erosion) were modeled by combining discrete element methods and particle hydrodynamics [Hv11]. Various approaches apply small-scale erosion models such as weathering of statues [DEJP99], Voronoi-based block erosion for modeling cliffs [PGGM09], spheroidal erosion for modeling of goblins [BFO + 07], corrosion simulation [WCMT07], and small-scale volumetric mountains and rocks [T110]. 6. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #DH5T8U 3.2. Algorithm Overview Matching excerpt #A8CFAJ: Our algorithm proceeds in two main steps: erosion simulation computed on planar graph \mathcal{G} embedding elevation and flow information, called the stream graph , and conversion of this graph into an elevation model \mathcal{M} representing the terrain. 7. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results Matching excerpt #ZHQFZP: In all experiments, unless stated differently, we use a terrain size of 50 \times 50 \text{ km}^2 . We set the maximum tectonic uplift to \mathcal{U} = 5.0 \cdot 10^{-4} \text{ my}^{-1} (meters per year), which is the average uplift among earth mountains. The erosion rate depends on many factors, such as precipitation and rock strength. In order to get a more intuitive setting, we follow the relationship between height, uplift, and erosion detailed in Section 6.4. We set the erosion rate to k = 5.61 \cdot 10^{-7} \text{ y}^{-1} for mountains to culminate at about 2000m. We set the time step at the geological scale \delta t = 2.5 \cdot 10^5 \text{ y} to ensure a fast convergence while avoiding the appearance of high unnatural cliffs. 8. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 1 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #T4ZQ7N 1. Introduction Matching excerpt #DRDV94: The terrain at the right of Figure 1 was generated using our method from the simple uplift map depicted on the left. The simulation process runs at interactive rates. While individual iterations provide a real-time preview enabling user interaction, the method converges to a final solution in less than two minutes. The interactive visual feedback enables users to interrupt the process before convergence if they need to change control parameters. 9. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #DH5T8U 3.2. Algorithm Overview Matching excerpt #4Q2VY3: Erosion simulation. Starting from the input domain \Omega where the uplift \mathcal{U} \neq 0 , we initialize the stream-graph \mathcal{G} as a random planar graph defined by triangulating uniformly distributed terrain sample points \mathbf{p}_k in \Omega . We set the initial elevation of the nodes h_k of \mathcal{G} to zero. We then iterate the stream power equation until we get plausible elevation information (or water flow directions) associated to each node (or arc) of \mathcal{G} . This is done by iterating the following steps until convergence (Figure 4): 10. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #JT9864 3.1. Geological Background Matching excerpt #7GS7F8: Fluvial erosion is the erosion of the bedrock material and its transportation downhill by streams. It is caused by the shear stress exerted by running water and the sediment it contains onto the bed of a stream. The interaction between the fluvial erosion and the tectonic uplift has been studied for many years in geology and is usually modeled by the stream power equation [WT99]: 11. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 8 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Matching excerpt #TB8KR6: The algorithm for lakes flow connection decreases greatly the number of iterations needed to obtain a plausible terrain in terms of hydrology. Without the lake connections, the water eventually finds a flow out of the main local minima, but after 4-5 more iterations than the total convergence of the erosion with lake connection (Figure 16). Even after many iterations, a large number of local minima are still adding some discontinuities in the hydrology network. 12. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #63EVKU 6.1. Visual realism Matching excerpt #Z493FS: We compared our stream-erosion simulation to real mountain data sets where fluvial erosion is the dominant factor: the San 13. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 1 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #T4ZQ7N 1. Introduction Matching excerpt #XZGNXD: We present a novel method that generates large mountainous terrains with plausible large scale landform features and patterns. The input to our algorithm is an uplift map painted by the user that defines the speed at which mountains are lifted. From this input, and a random planar graph covering the region on the map, we iterate through elevation updates for graph nodes, using the stream power equation to simulate the interaction between tectonic uplift and fluvial erosion processes. The original method from [BW13] is extended to efficiently model water flowing from lakes. This simulation process produces a stream graph derived from the initial graph. The graph is augmented with stream directions along edges and elevation information at the nodes. The graph can either be converted into an elevation map by interpolating the elevation information between streams for real-time visualization, or converted into a primitive-based terrain model with a high level of detail embedding riverbeds, ridges and valleys, using a combination of parameterized terrain primitives introduced in [GGP + 15] and automatic terrain amplification [GDPG16]. 14. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 0 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #T4ZQ7N 1. Introduction Matching excerpt #KM8ZR7: There is a large body of previous work on terrain modeling going back nearly 35 years. The first algorithms were inspired by fractals and noise generators [FFC82, EMP + 02]. More realism was later achieved by using physical and geological considerations, such as simulating hydraulic erosion [MKM89, BF02] to improve existing terrains. Example-based algorithms [ZSTR07, GMM15] provide a high level of control but are limited to the landform features provided by exemplars and usually cannot generate new geological structures. In contrast, erosion simulations [BF02, BTHB06] di- 15. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 9 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #KNTPE7 7.3. Comparison to Other Techniques Matching excerpt #2KNSHV: During each iterative design cycle the expert spent approximately 2 hours sculpting the riverbed, adjusting simulation parameters and running individual frame tests, and this was then followed by 9 hours spent executing the simulation. The latter included initializing particles, simulating particle stabilization to obtain a pseudo-periodic state for the river, and then generating 20 seconds of fluid animation. Simulation precision was set at 3cm, resulting in a total of 4.5 million particles and 200 million voxels. We tried reducing accuracy to cut down iteration times, but this introduced significant artifacts and the approximate and accurate water surfaces were so uncorrelated as to make authoring unworkable. Finalizing the scene required 15 iterations, each with 2 hours of scene editing and 9 hours of simulation, for a total of 165 hours. Our method represents a tremendous improvement in terms of production time and memory footprint. 16. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 9 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Matching excerpt #EQTM8J: Table 2 shows the time required to reach these results for different resolutions. We keep the total extent of the terrain constant, therefore decreasing \delta x from 50 to 25 and 12m. We observe that we need to decrease the timestep proportionally to the cell size to prevent artifacts in the simulation, therefore the number of iterations increases in both the fixed point (43, 82, 156 iterations) and the simulation (230, 460, 980 iterations). In contrast, the multigrid methods only require the addition of one level of down/up-sampling, which leads to a complexity almost linear to the number of cells. We additionally show the performance of the optimization algorithm, in the worst case, which is when we adjust the elevations to the initial drainage (disabling the iterative approach). In practice, we observed that the optimization cleans all visible discontinuities after 50 iterations for all resolutions. Overall, we did not observe significant changes in performance with other erosion parameters. 17. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 0 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #TY8V58 1. Introduction Matching excerpt #HRH4UV: Our work comes from the observation that there exist analytical solutions to the mathematical equation that expresses the formation of large-scale landscapes resulting from the competition between tectonic uplift and fluvial incision. Thanks to an efficient implementation of these analytical solutions, we obtain a terrain modeling tool that shares the benefits of a physical simulation, but without the cost of thousands of time-stepping iterations. Instead, the temporal component of the simulation becomes another parameter provided to the user, that controls the real-world duration of the erosion process. 18. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 0 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #87Z54H Abstract Matching excerpt #T295H3: Terrain generation methods have long been divided between procedural and physically-based. Procedural methods build upon the fast evaluation of a mathematical function but suffer from a lack of geological consistency, while physically-based simulation enforces this consistency at the cost of thousands of iterations unraveling the history of the landscape. In particular, the simulation of the competition between tectonic uplift and fluvial erosion expressed by the stream power law raised recent interest in computer graphics as this allows the generation and control of consistent large-scale mountain ranges, albeit at the cost of a lengthy simulation. In this paper, we explore the analytical solutions of the stream power law and propose a method that is both physically-based and procedural, allowing fast and consistent large-scale terrain generation. In our approach, time is no longer the stopping criterion of an iterative process but acts as the parameter of a mathematical function, a slider that controls the aging of the input terrain from a subtle erosion to the complete replacement by a fully formed mountain range. While analytical solutions have been proposed by the geomorphology community for the 1D case, extending them to a 2D heightmap proves challenging. We propose an efficient implementation of the analytical solutions with a multigrid accelerated iterative process and solutions to incorporate landslides and hillslope processes – two erosion factors that complement the stream power law. 19. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Matching excerpt #74AXB7: The uplift is counteracted by erosion, which impacts the slopes of the mountain and therefore its maximal elevation. Erosion comes from many factors: water, glaciers, landslides, wind, and even anthropic or biological impact. Many models in geomorphology consider only erosion by water, also called fluvial erosion . Indeed, the fluvial network is considered the backbone of landscapes, and fluvial incision dictates the rate of landscape erosion [Whi04]. While simple to model, fluvial erosion explains the main topographical characteristics of most mountain ranges and has been the dominant erosion factor over many geological periods - with the notable exception of the last million years, where the Quaternary saw an important increase in glacial erosion that leaves specific marks in high altitude [PMD01, ENPL09, SHV + 12]. 20. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 1 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #TY8V58 1. Introduction Matching excerpt #MYMRA9: The stream power law is commonly used in geomorphology [WT99, BW13] and now in computer graphics [CBC*16, SPF*23] to model large-scale river erosion. Combined with uplift - the tectonically-driven rate of elevation change of the mountain - this results in a Partial Differential Equation (PDE) that describes the formation of the mountain ranges over geological time. Early studies in Earth sciences suggest that this equation admits analytical solutions [RTP13, Ste21] that readily provide a landscape at a time t (Figure 1), without requiring the lengthy iterations of a time-stepping scheme. However, these solutions use several simplifying assumptions, for instance, that the terrain is initially flat. We propose a new derivation and fast numerical implementation of these solutions for the more general case, which enables us to reach a larger range of applications, from the instantaneous generation of large-scale mountain ranges to the controllable aging of a user-provided terrain. Inspired by the implicit time-stepping scheme for the stream power law [BW13, CBC*16], our algorithm uses an ordering of the terrain grid cells, starting at the domain boundaries, and following the river network upstream. This strategy comes with a caveat illustrative of the challenges of porting the 1D solution to the 2D setting: elevations are computed based on an order that depends on the hydrology network, but the hydrology network itself depends on the elevations. Previous work [Ste21] developed a fixed-point algorithm that iterates over the successive computation of the river network and then the elevations. Yet, this algorithm converges slowly, requiring too many iterations to be applied in an interactive editing context and assumes flat initial topography. We therefore propose two solutions: one inspired by multigrid approaches to accelerate the convergence, and another that allows small deviations from the analytical solutions and uses optimization to enforce the smoothness of the terrain surface. This added freedom - without sacrificing the geological consistency - provides more flexibility and allows user control. Finally, we observe that the solutions to the stream power law yield a singularity that results in infinitely large slopes close to the ridges - where geologists suggest that other erosion processes dominate [LD03]. Therefore, we explore solutions to include approximations of other processes such as hillslope and thermal erosion. We demonstrate the applicability of our method through a variety of results, that show the versatility of the analytical solutions that are able to quickly generate large-scale mountains (Figure 1, right), as well as providing a fast physically-based erosion tool (Figure 1, center left). 21. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Matching excerpt #E6X4P6: Analytical solutions and simulation. The purpose of our algorithm based on analytical solutions is to quickly generate terrains that are similar to the results of a simulation of the stream power law. In Figure 5, we compare between our method (with multigrid, top left), a simulation [CBC + 16] (top right), and previous work in geology [Ste21] (Fixed point iteration, bottom left). The comparison is performed at steady-state ( t = 4.6 \text{ My} ) as the last method does not handle initial topography and, also, in order to limit the integration error of the simulation. In this example, we use a constant uplift modulated by a subtle noise on a 512 \times 512 terrain with \delta x = 50 \text{ m} . In the simulation, we use 460 iterations with dt = 10000 , which we found to be the maximal time-step that did not produce visible artifacts. The fixed-point algorithm required 43 iterations to converge. 22. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 1 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #2BWKC4 2. Previous Work Matching excerpt #SR5QZ4: Methods that simulate hydraulic erosion handle the water dynamics explicitly, which, in theory, increases the physical accuracy of the erosion but introduces numerical constraints that limit them to a smaller spatiotemporal extent. To compensate, the results are scaled up, which therefore reduces the overall plausibility. In contrast, fluvial erosion methods implement models developed in geomorphology, for instance, the stream power law [WT99]. These laws abstract water physics under simpler proxies, e.g., the drainage area that represents water flux (or discharge), which yields simulations that can efficiently cover much larger time spans. Therefore, fluvial erosion allows a tight coupling with the growth of the mountain under tectonic uplift [CBC + 16] to model the formation of large-scale mountain ranges. Uplift was also proposed as a guide for the user to shape the landscape [CCB + 17, SPF + 23]. We build our analytical model upon the laws introduced by fluvial erosion methods, but our mathematical treatment removes the need for costly iterations inherent to simulations. 23. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 9 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Matching excerpt #MAU7Q5: GPU simulations of the stream power law [SPF*23] might in some cases be faster than our method even though they require many iterations. There are, however, caveats inherent to the GPU architecture that prevent them from being used in all cases. First, GPU simulations use an explicit time-stepping scheme, which bounds the admissible time step and can yield a prohibitive number of iterations for small \delta x . Second, depressions in the topography lead to local minima that interrupt the river network. Similarly to other CPU algorithms, we use depression breaching [CBC*16, SD21] to enforce the continuity of the river across the depressions. The absence of such an algorithm on GPU implementations is particularly visible in cases where we erode without uplift - all the water is trapped within the depressions and the erosion only occurs in the vicinity of the topographic gradients. 24. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 0 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #TY8V58 1. Introduction Matching excerpt #EHZRW2: to the valley) [EMP + 02, BTH06, GMM15], for larger scales up to the scale of the mountain range they lack geological consistency which is prevailing in large mountain structures. Consistency is achieved by approaches based on physical simulations [CCB + 17] which are preminent in this case. However, physical simulations require the integration of the geological history of landscapes, leading in turn to long simulation time or numerous iterations before reaching a suitable result. 25. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 12 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #US5Z9M 8. Conclusion Matching excerpt #CEANXB: We proposed a new method to quickly erode large-scale terrains. Thanks to the analytical solution of the stream power law, we do not have to rely anymore on numerous iterations inherent in simulations. Instead, the time becomes another parameter that the user can explore without any incidence on the computation time. We proposed a derivation and implementation of these analytical solutions adapted to computer graphics applications, allowing the user to specify both an initial terrain to be eroded and an uplift map to control the emergence of a mountain range and explore any intermediate possibility. To the challenge of generating a terrain physically consistent with its river network, we propose two solutions that yield interactive performances: an accurate multigrid acceleration, and an optimization-based approach that preserves the initial river network. Eventually, we introduced new models for hillslope and thermal erosion that are easily integrable in our implementation. Our main limitation is the lack of time consistency at large time t , which motivates future work on a more conservative hydrology-based multigrid scheme, or alternative solutions where analytical solutions would control the procedural generation of river networks [GBG + 19]. 26. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Matching excerpt #ESC38J: A first common modeling approximation is to consider surface evolution as a detachment-limited process (as opposed to transport-limited) where the evolution of surface elevation z is directly related to the competition between rock uplift and erosion rate, and not to the capacity of the rivers to transport or deposit sediments [How94]. In this setting, erosion is generally described using the stream power incision model [HK83, How94, WT99, Lag14], where erosion rate is a power law of the surface slope \|\nabla z\| , and drainage area A that acts as a proxy for the river discharge. The drainage area A(\mathbf{x}) is defined at a position \mathbf{x} as the area of the drainage basin - or catchment - upstream of \mathbf{x} . Coupled with the uplift u , the Stream Power Law expresses the rate of change of surface elevation: 27. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 1 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #2BWKC4 2. Previous Work Matching excerpt #SKSHS3: Physically-based methods were inspired by the geological knowledge that landscapes are shaped by the combination of various processes [WT99, WHBY22]: climate which modulates the rates of erosion, and tectonics which controls the uplift rate (the rate of vertical growth of the mountain). In computer graphics, researchers initially modeled the most visible factor: erosion, which was first used as a post-process over a procedural or user-modeled terrain [MKM89]. This method was refined with data structures and algorithms for strength-varying layers of rocks [RPP93, BF01], and by improving the water model with Shallow Water equations [Ben07], Smoothed Particles Hydrodynamics [KBKv09] and GPU implementations [VBHS11]. 28. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 6 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #4VW4H2 5. Combining river network and elevations #JHZBJ3 5.1. Fixed-point algorithm Matching excerpt #NDJ2FL: The large number of iterations required limits the applicability of analytical solutions to interactive applications and hinders their benefits compared to a full simulation. Therefore, we propose two strategies: one inspired by the theory of multigrid – which still performs this iterative process but with fewer iterations at different scales, and the second using an optimization to reduce the discontinuities provoked by a mismatch between the ordering and the elevations. 29. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 8 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #W352NS 5 Algorithm Implementation and Simulated Results #MQ2VEA 5.4 Lap Time Convergence and Predicted Lap Time Matching excerpt #UCVJLC: Fig. 11 shows that the predicted lap time converges monotonically over four or five iterations, with significant improvements over the centerline trajectory occurring over the first two iterations. The predicted minimum lap time of 136.4 seconds is similar to the predicted lap time of 136.7 seconds from the nonlinear gradient descent approach, although in reality, the experimental lap time will depend significantly on unmodelled effects such as powertrain dynamics. 30. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Matching excerpt #YVMH2N: Interactive landscape authoring. To demonstrate the general applicability of our algorithms we provide extracts from an interactive landscape authoring session in Figure 7 and the accompanying video. Here, user-guided simulation is applied to a 512 \times 512 terrain, which, thanks to GPU acceleration combined with implicit time-stepping, requires only 10 iterations and 0.1s to capture 700,000 years of geomorphological evolution. For comparison, a CPU implementation [CBC*16] requires 2.6s. The user first defines the primary mountains by progressively painting on an uplift map, and can then freely change simulation parameters (here the deposition constant). Finally, the user advances the age of the mountain by increasing the number of iterations to 100, producing the result on the far right in 0.7 seconds. Note that lakes disappear over time as a consequence of filling by deposition and uplift, combined with erosion, which gradually removes the obstructions between them. 31. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 1 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #L8RWX4 1. Introduction Matching excerpt #XF6U9G: We demonstrate its practicality through three example applications: river generation, terrain erosion, and ecosystem simulation. These use cases illustrate that with minimal modification, our algorithms are applicable to terrain modeling, geospatial analysis, and simulation models in computer graphics, geomorphology, and ecology. In particular, we show how to adapt our GPU algorithm to an implicit time-stepping scheme for erosion simulation using the Stream Power Law. This reduces the number of required time steps and significantly enhances interactivity. We also present a new strategy to account for sediment deposition. 32. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 9 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Matching excerpt #N2QDLW: Comparative evaluation. An alternative strategy for landscape simulation on the GPU [SPF*23, JBC24] is to use explicit time-stepping for erosion combined with approximate flow routing, where the discharge is propagated by a single cell on each simulation step. This method requires many more iterations due to the stability conditions of the explicit scheme but does eventually converge to a solution qualitatively similar to ours. Crucially, there are several situations where this strategy cannot be applied. One case is the erosion of an existing terrain containing depressions. Another failure case (see Figure 12) occurs when noise is added to uplift to increase the diversity. The approximate solution relies on the assumption that the flow path weakly varies over time, which allows the approximation of the discharge to progressively improve. Adding noise invalidates this assumption and leads to a significant underestimation of drainage and, consequently, an underestimation of erosion. This is visible in Figure 12, where the maximal elevation depends on the amount of noise. In contrast, our combination of implicit-time-stepping and exact-flow does not suffer from this shortcoming. 33. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 7 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation Matching excerpt #V92Q79: Here we show how we apply flow and depression routing to accelerate landscape simulation, with use cases in river and lake modeling, terrain erosion, and ecosystem simulation. In particular, our GPU algorithms together provide the discharge necessary for erosion simulation. Furthermore, they enable a novel GPU-based solution for implicit time-stepping of erosion using the Stream Power Law, which we combine with a simulation of sediment deposition. 34. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Matching excerpt #M53PTE: Another consideration is the acceleration afforded by the larger timesteps of our implicit solution. We show in Figure 13 that a 512 \times 512 terrain with \Delta x = 32\text{m} obtained with an explicit scheme ( \Delta t = 1,000 years) is visually similar to the result of our implicit solution ( \Delta t = 20,000 years). Our implicit scheme allows an increase of the timestep by a factor of 20, which reduces, by the same factor, the iterations needed to achieve the same total geological timespan. With such timesteps, generating a 10 million year-old landscape requires 7.2s and .5s, for the explicit and our implicit scheme, respectively. Note that larger implicit timesteps are unconditionally stable, and only diverge slightly from the explicit solution. Note that explicit and implicit schemes in general do not yield identical solutions as they accumulate discretization error differently. 35. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 1 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #KDKKZ3 2. Related Work Matching excerpt #URD5LH: Instead, large-scale terrain erosion models [CBC + 16] take their inspiration from geomorphology [BW13] and directly compute total water discharge by accumulating precipitation from high (mountain ridges) to low elevations (the sea). This flow accumulation is communicated across large stretches of the terrain and is thus less local and less amenable to parallelisation [VBHS11] than direct water dynamics. However, this is more than offset by the sheer number of iterations required for a dynamics solution to reach steady-state. Schott et al. [SPF + 23] provide an approximate variant of discharge-based Stream Power erosion that propagates discharge by a few cells on each time step. While this strategy is trivially parallelizable, it requires a stable river network and thus precludes outside terrain forces such as time-dependent tectonics or sediment deposition. Furthermore, the underlying explicit time-stepping scheme requires many timesteps, while our method is amenable to an implicit scheme that overcomes this constraint. 36. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 7 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #BTBPNF Algorithm 6: Extracting a depression-free water surface Matching excerpt #J4QRW9: where the first term u is the tectonically induced uplift (or growth rate of the mountain), and the second term is the erosion, dependent on the discharge Q , erosion coefficients k and m , and the slope \partial z/\partial x . The discharge provided by flow routing is scale-independent, so to compensate we scale the discharge Q by accumulating \Delta x^2 p , where \Delta x is the cell size and p is the precipitation. The uplift is usually considered time-independent and therefore applied as a pre-process. This leaves an implicit solution to the second erosive part of Equation 2 as: 37. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 9 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Matching excerpt #44JH58: Our method scales to higher-resolution landscapes, as illustrated in Figure 8 for a 2048 \times 2048 terrain with 300,000 simulated years (200 iterations) generated in under 10 seconds. 38. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 1 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #KDKKZ3 2. Related Work Matching excerpt #9GS59V: Terrain Simulation. Methods for generating terrain for use in computer graphics can be broadly categorised [GGP + 19] into procedural (using algorithmic rules to mimic emergent properties), example-based (learning structure from existing terrain data), and simulation (mathematically emulating natural processes). Within terrain simulation, fluvial erosion is recognized as a primary force in shaping the topography of mountains. Early erosion methods in computer graphics [MKM89] simulated water dynamics directly using shallow water equations [Ben07] or smoothed particle hydrodynamics [KBKv09]. Unfortunately, water dynamics are very short term and need to be applied many thousands of times to capture long-term erosion processes. 39. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 0 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #5RMF3P Abstract Matching excerpt #BKN6BV: Terrain analysis plays an important role in computer graphics, hydrology and geomorphology. In particular, analyzing the path of material flow over a terrain with consideration of local depressions is a precursor to many further tasks in erosion, river formation, and plant ecosystem simulation. For example, fluvial erosion simulation used in terrain modeling computes water discharge to repeatedly locate erosion channels for soil removal and transport. Despite its significance, traditional methods face performance constraints, limiting their broader applicability. 40. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance Matching excerpt #PQTH4E: We also included 5 synthetic terrains at the same resolution levels, and each with a controlled proportion of depression coverage (at synth-1% , synth-5% and synth-15% levels). These were generated by erosion simulation (Section 6), followed by layering different amplitudes of uniformly distributed noise. Note that it is common practice to add this type of noise during erosion simulation to mimic natural stochastic processes. 41. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 7 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #BTBPNF Algorithm 6: Extracting a depression-free water surface Matching excerpt #F5SQR5: Ecosystem simulation. The water routes derived through river and lake modeling have direct application to ecosystem simulation. Water, along with sunlight and warmth, is a key requirement for plant growth, with different species having varied adaptation to water availability. Modeling water discharge is therefore a crucial element in ecosystem simulations. To demonstrate applicability, Figure 6 shows the outcome of an ecosystem simulation for a biome in the Pyrenees mountains [PGG*24] at the 50 year mark, with water accumulation provided by our flow and depression routing. For clarity, pioneer species with strong drought tolerance have been removed and what remains are species, such as Sessile Oak and European Beech, that require the greater moisture found in riparian areas. Most ecosystem simulations use a month as the timestep granularity, due in part to the overhead of calculating water flow. The acceleration provided here creates an opportunity for shorter, weekly, or even daily, timesteps with non-uniform rainfall across the landscape [PMG*22] and hence greater simulation accuracy. 42. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 6 Context: #RNVWWR Water Surface Wavelets #MU7P6S 5 ALGORITHM SUMMARY Matching excerpt #SK58YU: We divide our algorithm into a function TimeStep that does some pre-computation work once every time step, and a function WaterHeight that needs to be computed on-demand for each node of the finely-sampled grid and each pixel. TimeStep mainly solves the evolution equation 18 by splitting it into two parts: AdvectionStep , which computes the semi-Lagrangian advection in 43. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #9AHGRG: Varying these parameters has different effects on the visual results and performance of our method, and we explore each of them in our supplementary video. The number of \mathcal{A} samples in our simulation depends linearly on the resolution of our 4\text{D } X_{\mathcal{A}} \times X_{\mathcal{A}} \times \Theta_{\mathcal{A}} \times K_{\mathcal{A}} simulation grid, so doubling the resolution of any dimension will roughly increase the memory and the runtime by a factor of 2. Increasing the spatial resolution X_{\mathcal{A}} will allow the wavefronts to exhibit a higher curvature, allowing more detailed interactions with highly curved boundaries. Figure 8 shows the effect of X_{\mathcal{A}} on the simulation quality. Increasing the angular resolution \Theta_{\mathcal{A}} allows a more precise behavior in each direction. Increasing the wavenumber resolution K_{\mathcal{A}} allows more detailed dispersion of wave groups (different amplitude groups travel at different speeds). We show an example with K_{\mathcal{A}} = 4 simulated wave groups in Figure 9 and in our video, which shows more accurate wave group dispersion but roughly quadruples the run time (drops the frame rate from 70fps to 20fps). 44. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #WKY9MT: our results, we show a vast 4\text{km} \times 4\text{km} sea interacting with islands, floating barrels, actively moving boats, and a user-controlled jet-ski. Both the simulation and the heightfield evaluation are computed in parallel on the GPU in each time step. We provide a supplemental document that describes relevant implementation details for both parts. Our laptop with a NVIDIA Geforce GTX 1070 GPU achieves an average frame rate of 60fps with the parameters in Table 1, and this paper includes an interactive demo of our method which recreates this example. Table 2 displays the timing breakdown for an average frame of this animation; note that the timing for the computation of \eta depends on the number of pixels occupied by waves and may vary slightly. 45. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 0 Context: #RNVWWR Water Surface Wavelets Matching excerpt #56PPMK: Previous methods for simulating 2D water waves directly compute the change in height of the water surface, a strategy which imposes limitations based on the CFL condition (fast moving waves require small time steps) and Nyquist's limit (small wave details require closely-spaced simulation variables). This paper proposes a novel wavelet transformation that discretizes the liquid motion in terms of amplitude-like functions that vary over space , frequency , and direction , effectively generalizing Fourier-based methods to handle local interactions. Because these new variables change much more slowly over space than the original water height function, our change of variables drastically reduces the limitations of the CFL condition and Nyquist limit, allowing us to simulate highly detailed water waves at very large visual resolutions. Our discretization is amenable to fast summation and easy to parallelize. We also present basic extensions like pre-computed wave paths and two-way solid fluid coupling. Finally, we argue that our discretization provides a convenient set of variables for artistic manipulation, which we illustrate with a novel wave-painting interface. 46. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 29 Context: #EAB6Y7 V EXAMPLES OF HARMONY-SEEKING COMPUTATIONS FROM DIFFERENT FIELDS #5MUWW2 Example 13. Formation Of Giant Voids In The Universe: A Very Large Example of a Generated Wholeness Matching excerpt #MLT8LP: The actual physical diameter of one of these voids, is unimaginably huge, about 100 million light years. It is in miles, 186,000 * 3600 * 365 * 24 * 100,000,000 = 5865696 * 10^6 * 10^8 \approx 6 * 10^6 * 10^6 * 10^8 = 6 * 10^{20} miles. A jet plane flying at 600 mph, would take a 10^{14} years to cross this void – something like 5000 times the age of the universe itself. I say this only to emphasize the truly huge size of the voids that we are talking about, and in particular to draw attention to the fact that if it is that huge, the ring thickness could be almost anything, and the ratio of ring thickness to ring diameter could have a large range of possible values. 47. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 9 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #QGEMMG 4.3 Player Physics #ACMUGX 4.3.6 Dynamics Update Matching excerpt #UF5N8K: so the controller accelerates and decelerates with a time constant of approximately 0.1 s. Here, runSpeed is the configured running speed, v_z the current forward velocity, \Delta t the physics timestep, and the factor 10 controls the rate at which the velocity approaches its target. 48. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 4 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #CSD47K Impulse Driven NS Matching excerpt #JDXE4W: Before applying the impulses an initial state must be computed so that we know which direction and with what magnitude the impulses should be applied. We refer to this process as priming the flow which is depicted in Figure 3. First, an impulse field is propagated across the simulation grid over a number of steps starting with an initial impulse hint from the user at one edge of the river which dictates the basic direction of the river. The first time step causes the impulses to be applied as the fluid is solved. At any cell where the velocity is not zero, that velocity vector is normalized and saved as the flow hint for that cell. In the next time step impulses are applied to the initial cells given by the user and those cells already affected by the simulation. The algorithm sweeps across the river in successive time-steps from the user specified source location. This is repeated until all cells have a flow hint associated with them. In the second phase of the flow priming procedure the simulation is run with flow hinting enabled until one “advection particle” is able to travel the length of the river. 49. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 4 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #PVQNK6 Bootstrapping the Hydrostatic Pressure Columns Matching excerpt #UJWCSS: The HSP computations are dependent on the velocity in the previous time step. Therefore in order to generate an HSP pressure map we simply substitute the initial phase of NS velocity output into the velocity component, u_0 , of the HSP velocity update equation. This bootstrapping procedure only provides the HSP simulation with the initial flow rate and direction of each hydrostatic pressure column cell. Once these values are input into the HSP solver, the resulting 3D flow information is entirely based on the 3D terrain underneath and inside the fluid volume. 50. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 6 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Matching excerpt #K7SCA8: where a_c is the particle's current age, a_b its birth time, while l_c and l_b denote the particle's current and birth locations. A is a constant defining the average age of a particle and L determines the maximum distance a particle can be from its birth location without being transparent. For all our simulations we set A to be 1.5 seconds and L to be 5% of the total length of the river. Approximate matches 1. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results Score: 0.028 Related excerpt #ZHQFZP: In all experiments, unless stated differently, we use a terrain size of 50 \times 50 \text{ km}^2 . We set the maximum tectonic uplift to \mathcal{U} = 5.0 \cdot 10^{-4} \text{ my}^{-1} (meters per year), which is the average uplift among earth mountains. The erosion rate depends on many factors, such as precipitation and rock strength. In order to get a more intuitive setting, we follow the relationship between height, uplift, and erosion detailed in Section 6.4. We set the erosion rate to k = 5.61 \cdot 10^{-7} \text{ y}^{-1} for mountains to culminate at about 2000m. We set the time step at the geological scale \delta t = 2.5 \cdot 10^5 \text{ y} to ensure a fast convergence while avoiding the appearance of high unnatural cliffs. 2. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #JT9864 3.1. Geological Background Score: 0.028 Related excerpt #MSXUGH: Note that, when applied at the right temporal and spatial scales (typically between 10^5 and 10^7 years and a few tens to hundreds of kilometers), the stream power equation does not only model erosion, but also captures the way a complex relief emerges from a supposedly flat part of the continental crust [How94]. 3. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 6 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.023 Related excerpt #MNZNZU: The erosion parameters in the stream power erosion are not intuitive to set. Even in geology, the impact of these coefficients is not well-understood. The erosion coefficient k and the uplift u are both subject to a multiplication by dt , so only their ratio is relevant. However, its value has a strong influence on the mountain height. We made a series of experiments in order to find a relationship between this ratio and the maximum mountain height. It turned out this relation is linear and the height in kilometers follows the rule h_{max} = 2.244 u/k . 4. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #JT9864 3.1. Geological Background Score: 0.019 Related excerpt #EKXATA: The constants m and n depend on rock strength, climate, and the topology of river networks. While the values of those parameters are poorly understood, the ratio m/n is constrained by the shape of the stream profiles and is thought of being m/n \approx 0.5 [WT99]. As in most geomorphological studies, we use n = 1 and m = 0.5 . Moreover, some geological studies attempt to tune these parameters by example [CB14] and a recent survey [Lag14] studies the limit of geological knowledge regarding the parameters of the stream power equation. 5. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #7E86TB 5. Erosion Score: 0.018 Related excerpt #ECXQM8: Correction based on thermal erosion. While the simulation of the stream power equation works efficiently for carving the bottom of the rivers, other phenomena may be predominant in some cases, in particular for low drainage areas. In such cases, the stream erosion equation produces unrealistic sharp and high peaks. 6. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #DH5T8U 3.2. Algorithm Overview Score: 0.017 Related excerpt #4Q2VY3: Erosion simulation. Starting from the input domain \Omega where the uplift \mathcal{U} \neq 0 , we initialize the stream-graph \mathcal{G} as a random planar graph defined by triangulating uniformly distributed terrain sample points \mathbf{p}_k in \Omega . We set the initial elevation of the nodes h_k of \mathcal{G} to zero. We then iterate the stream power equation until we get plausible elevation information (or water flow directions) associated to each node (or arc) of \mathcal{G} . This is done by iterating the following steps until convergence (Figure 4): 7. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 8 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.016 Related excerpt #76252N: Stream power erosion without the uplift. The stream power erosion can be used without the uplift and it adds a global hydrological realism to an existing scene as shown on an example of a fractal terrain enhanced with erosion in Figure 14. As the erosion converges toward a flat terrain, it is necessary to use small time steps and to stop the simulation after only a few iterations. 8. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #7E86TB 5. Erosion Score: 0.015 Related excerpt #QZCCTD: We correct this effect by using a thermal erosion mechanism [MKM89]. Thermal erosion embeds the set of processes that causes rocks to break because of the thermal shocks caused by the infiltrated water and changes in temperature. The eroded material is transported down-slope. We modify our algorithms as follows: if the result of the stream power equation leads to slopes higher than 30^\circ , we reduce the change of elevation so as to keep slopes in the prescribed range. 9. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 6 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #2RYGP7 6.3. Performance Score: 0.014 Related excerpt #W7JZEK: The number of iterations needed to obtain a fully-formed mountain chain is difficult to estimate because it depends on a number of input parameters (see the discussion below). Yet, thanks to the implicit resolution, it does not depend on the resolution of the terrain. In our experiments, the mountains were fully shaped after 50 iterations and the geometry stops evolving after 100 – 300 iterations, as shown in Figure 12. A solution to accelerate convergence could be to progressively refine the sampling grid. Note that this refinement needs to be uniform, in order to preserve the possible emergence of local stream and the details in the shape of rivers. 10. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 2 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #ZRSZUM 3. Background and Overview #JT9864 3.1. Geological Background Score: 0.012 Related excerpt #PGNGMP: The stream power equation states that the rate of change of surface topography h(\mathbf{p}) at a position \mathbf{p} is controlled by the balance between the surface uplift u(\mathbf{p}) and the fluvial erosion, which is a function of the local slope s(\mathbf{p}) and the drainage area A(\mathbf{p}) . The local slope s(\mathbf{p}) is defined as the surface topographic gradient: 11. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #7E86TB 5. Erosion Score: 0.012 Related excerpt #7HBEWM: This section describes the last two steps of our iterative algorithm: drainage and slope computation, and solving the stream power Equation (1). 12. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 8 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #AWRWEN 6.4. Stream power erosion Score: 0.009 Related excerpt #6N825C: rocks strength. We choose the minimal and maximal slope angles to be 6^\circ and 54^\circ respectively. This results in a more random distribution of the erosion patterns in valleys as shown in Figure 17. 13. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Score: 0.011 Related excerpt #VG86AP: We use a simplified model based on an empirical power law observed in geomorphology [Dunne and Leopold 1978]. Let A [m 2 ] be the watershed area. The mean flow \phi of the river [m 3 s -1 ] is given by \phi = 0.42 \cdot A^{0.69} . The watershed area A is approximated by the sum of the areas of cells connected to s in the graph, and it allows calculation of the outgoing flow \phi of any cell V (Fig. 10). This equation takes into account evaporation and infiltration, and that is why the volume flow is not preserved. 14. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 9 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Score: 0.027 Related excerpt #EQTM8J: Table 2 shows the time required to reach these results for different resolutions. We keep the total extent of the terrain constant, therefore decreasing \delta x from 50 to 25 and 12m. We observe that we need to decrease the timestep proportionally to the cell size to prevent artifacts in the simulation, therefore the number of iterations increases in both the fixed point (43, 82, 156 iterations) and the simulation (230, 460, 980 iterations). In contrast, the multigrid methods only require the addition of one level of down/up-sampling, which leads to a complexity almost linear to the number of cells. We additionally show the performance of the optimization algorithm, in the worst case, which is when we adjust the elevations to the initial drainage (disabling the iterative approach). In practice, we observed that the optimization cleans all visible discontinuities after 50 iterations for all resolutions. Overall, we did not observe significant changes in performance with other erosion parameters. 15. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 10 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #V6AZDH 7.3. Applicability of our method Score: 0.024 Related excerpt #LBNKBW: We now illustrate the versatility of our method through several applications. Fig 1 shows a landscape initialized with Perlin noise and eroded at different user-provided times to illustrate the range of possible effects, from a short post-process that carves only the main slopes (at t = 200ky ) to the complete formation of a new mountain range ( t = 1.6My ). 16. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 11 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #V6AZDH 7.3. Applicability of our method Score: 0.024 Related excerpt #Z3MXM7: User-made terrains can be authored through a combination of procedural techniques, noise and modeling tools ( i.e. , extrusion, smoothing). In Figure 11, we asked a user to produce a coarse terrain ( \delta x = 30\text{m} , top left) and use our method (without uplift) to add erosion details. We observe the different patterns produced by varying the erosion time ( 100\text{ky} , 200\text{ky} , and 300\text{ky} ), and notice in particular that both the incision depth and the shape of the eroded cavities are affected – shorter time caves numerous small gullies, which deepen and merge into fewer large valleys at a longer erosion time. 17. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 3 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law Score: 0.023 Related excerpt #2ZH6S2: Analytical solutions of the stream power law describe elevations of an eroded terrain at a given time t , without requiring the many iterations of a time-stepping scheme. Existing 1D analytical solutions in Earth sciences [RTP13] simplify the derivation thanks to dimensionless variables, which complicates their algorithmic treatment. We instead describe how to derive the solutions with the natural variables and how to infer an efficient algorithm to evaluate them. 18. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Score: 0.022 Related excerpt #NYZKTL: which competes with erosion and can lead to a progressive increase in the surface altitude, called surface uplift [EM90]. Rates of rock uplift and erosion vary in space and time and achieve values up to a few millimeters per year in some mountain ranges. 19. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 6 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #4VW4H2 5. Combining river network and elevations #JHZBJ3 5.1. Fixed-point algorithm Score: 0.021 Related excerpt #BNNDD5: We observed that this algorithm converges for the steady state case (large t ), but could sometimes oscillate, especially for small t , small uplift, and large discontinuities in the initial topography. We address this issue with an exponential moving average (at each iteration, we average the topography predicted by the steady state with the elevations resulting from the previous iteration.) 20. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 4 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law #QR788H 4.1. The method of characteristics for the stream power law Score: 0.02 Related excerpt #P8246L: where a(s) = kA(s)^m . Note that we assume that A does not depend on time – we observed that, after some time, the drainage A stabilizes in the main river channels. A solution of Eqn. 3 was proposed in Earth sciences [Ste21] with the assumption that u is constant in space and varies in time, which is important for geomorphologists who study the erosional response to tectonic perturbations. We prefer an orthogonal approach where the uplift varies in space but not in time, as we expect the uplift to be easier to control for the user as a function of space alone [SPF + 23]. 21. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Score: 0.02 Related excerpt #2DEC4W: where k , m and n are erosion coefficients. Throughout the paper, we will use some of the common values: m = 0.4 and n = 1 . The choice of n = 1 , also commonly used in geomorphology, makes the equation linear and therefore simplifies the derivation of the analytical solutions. While this choice barely impacts the result as the valley profiles are mostly directed by the ration m/n , we acknowledge that the actual values of m and n remain an open question in geomorphology [Lag14]. 22. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 11 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #V6AZDH 7.3. Applicability of our method Score: 0.019 Related excerpt #7G84VM: Figure 12, where we start from a procedurally generated cliff that separates two areas with uniform elevation (left). Then we apply our method without uplift and observe the cliff retreating after 200 and 500\text{ky} . Note that without uplift, without deposition, and with flat boundary conditions, the retreating cliff leaves open a flat area around the main rivers. 23. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Score: 0.019 Related excerpt #ESC38J: A first common modeling approximation is to consider surface evolution as a detachment-limited process (as opposed to transport-limited) where the evolution of surface elevation z is directly related to the competition between rock uplift and erosion rate, and not to the capacity of the rivers to transport or deposit sediments [How94]. In this setting, erosion is generally described using the stream power incision model [HK83, How94, WT99, Lag14], where erosion rate is a power law of the surface slope \|\nabla z\| , and drainage area A that acts as a proxy for the river discharge. The drainage area A(\mathbf{x}) is defined at a position \mathbf{x} as the area of the drainage basin - or catchment - upstream of \mathbf{x} . Coupled with the uplift u , the Stream Power Law expresses the rate of change of surface elevation: 24. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #97YQQD 6. Other erosion factors #VEK6N9 6.2. Thermal erosion Score: 0.017 Related excerpt #5WP8EC: above the critical angle, we change u and a to incorporate the thermal erosion with Eqns. 28 and 29, and use the new values to re-estimate the elevation z(x) . Note that changing a also change D_{x,t} , which slightly change the algorithm summarized at the end of Section 4.2: instead of computing first D_{x,t} for all x , then S(x) for all and finally z(x) , we interleave them to compute together D_{x,t} , S(x) , and z(x) from their values at x - \delta x . 25. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #97YQQD 6. Other erosion factors #VEK6N9 6.2. Thermal erosion Score: 0.017 Related excerpt #XU4RDE: where s_c = \text{atan}(30^\circ) is the critical slope. We modify Eqn. 3 to add the contribution of the thermal erosion: 26. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 1 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #2BWKC4 2. Previous Work Score: 0.016 Related excerpt #SR5QZ4: Methods that simulate hydraulic erosion handle the water dynamics explicitly, which, in theory, increases the physical accuracy of the erosion but introduces numerical constraints that limit them to a smaller spatiotemporal extent. To compensate, the results are scaled up, which therefore reduces the overall plausibility. In contrast, fluvial erosion methods implement models developed in geomorphology, for instance, the stream power law [WT99]. These laws abstract water physics under simpler proxies, e.g., the drainage area that represents water flux (or discharge), which yields simulations that can efficiently cover much larger time spans. Therefore, fluvial erosion allows a tight coupling with the growth of the mountain under tectonic uplift [CBC + 16] to model the formation of large-scale mountain ranges. Uplift was also proposed as a guide for the user to shape the landscape [CCB + 17, SPF + 23]. We build our analytical model upon the laws introduced by fluvial erosion methods, but our mathematical treatment removes the need for costly iterations inherent to simulations. 27. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 4 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law #QR788H 4.1. The method of characteristics for the stream power law Score: 0.016 Related excerpt #SP6MM5: Compared to previous simulation-based methods that required iterating over time, this solution directly expresses the elevation of the terrain from the uplift and drainage area. This is why we follow geology literature [Ste21] to call this an analytical solution (with respect to time), even if we need to resort to a numerical evaluation of the integral over space. 28. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #2BWKC4 2. Previous Work Score: 0.015 Related excerpt #KZXFJV: Early analytical solutions were introduced, first on models that simplify the treatment of the water discharge [Luk72, Luk74] and introduce the method of characteristics for erosion equations. This idea was later extended to the stream power law [RTP13] that simplifies the problem thanks to a translation to dimensionless variables. Eventually, Steer [Ste21] proposed a solution to the 2D problem and tested it with several scenarios, to study in particular the response of the landscape to temporal variations in the uplift, which is an important question in geomorphology. However, some questions were left open and we to answer them in this work, such as the case where the initial terrain is not flat, which allows us to erode existing terrains. Furthermore, their method used an iterative algorithm to enforce the convergence of the analytical solution, which we accelerate with an approach inspired by multigrid. 29. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Score: 0.014 Related excerpt #E6X4P6: Analytical solutions and simulation. The purpose of our algorithm based on analytical solutions is to quickly generate terrains that are similar to the results of a simulation of the stream power law. In Figure 5, we compare between our method (with multigrid, top left), a simulation [CBC + 16] (top right), and previous work in geology [Ste21] (Fixed point iteration, bottom left). The comparison is performed at steady-state ( t = 4.6 \text{ My} ) as the last method does not handle initial topography and, also, in order to limit the integration error of the simulation. In this example, we use a constant uplift modulated by a subtle noise on a 512 \times 512 terrain with \delta x = 50 \text{ m} . In the simulation, we use 460 iterations with dt = 10000 , which we found to be the maximal time-step that did not produce visible artifacts. The fixed-point algorithm required 43 iterations to converge. 30. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 4 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law #QR788H 4.1. The method of characteristics for the stream power law Score: 0.013 Related excerpt #24U9NL: As we seek the elevation at time t and position x , we only consider the curve that includes the point x, t . For this curve, the space-time relationship is expressed by \tau_{x,t}(s) defined such as \tau_{x,t}(x) = t , which gives after integration: 31. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #97YQQD 6. Other erosion factors #C4WS38 6.1. Hillslope erosion Score: 0.013 Related excerpt #SH59MV: An analytical solution including the hillslope erosion would require joining the stream power law (Eqn. 1) with Eqn. 23 which results in an advection-diffusion equation. Solving this equation needs a global 2D treatment, preventing our decomposition to a set of 1D solutions on the stream tree, and the complexity of the derivations and implementation of the solutions even in the 1D case challenges their usability in a terrain modeling framework. 32. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 10 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #BK5LST 7.2. Ablation study Score: 0.013 Related excerpt #3WX3ZE: Hillslope erosion stabilizes the slopes of the mountains and acts as the main erosion process at low drainage where the stream power law becomes negligible [LD03]. We show the impact of hillslope in Figure 9, where we show the analytical solutions of the stream power law only at \delta x = 50 m (left), compared with our modified formulation that includes the hillslope erosion (Section 6.1, right of Figure 9). Without hillslope, we observe the emergence of unrealistically sharp ridges and peaks. 33. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 9 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Score: 0.012 Related excerpt #4MTZXN: We illustrate this problem in the inset figure, where we use a simulation without depression filling to erode an escarpment for 500ky. While the result should be similar to Figure 12 (right), the erosion remained local to the initial cliff and did not expand toward wide canyons. 34. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 9 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Score: 0.011 Related excerpt #MAU7Q5: GPU simulations of the stream power law [SPF*23] might in some cases be faster than our method even though they require many iterations. There are, however, caveats inherent to the GPU architecture that prevent them from being used in all cases. First, GPU simulations use an explicit time-stepping scheme, which bounds the admissible time step and can yield a prohibitive number of iterations for small \delta x . Second, depressions in the topography lead to local minima that interrupt the river network. Similarly to other CPU algorithms, we use depression breaching [CBC*16, SD21] to enforce the continuity of the river across the depressions. The absence of such an algorithm on GPU implementations is particularly visible in cases where we erode without uplift - all the water is trapped within the depressions and the erosion only occurs in the vicinity of the topographic gradients. 35. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 5 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law #S7W7HC 4.2. Recursive algorithm for the 1D analytical solutions Score: 0.011 Related excerpt #8QNMBB: which gives the time required for the elevation to be advected from position x to y . The first step of our algorithm is to compute D_{x,t} , defined implicitly by \tau_{x,t}(D_{x,t}) = 0 , or 36. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #2BWKC4 2. Previous Work Score: 0.011 Related excerpt #233A3P: Earth sciences commonly use simulations to understand the formation of mountains. The variety of models adapted to many use cases is immense [CDM14] and out of the scope of the paper. Therefore, we will focus on the family of methods shared with computer graphics that build upon the stream power law [HK83, WT99]. Several implementations were proposed: fast implementations of implicit solutions [BW13], enhancement of a numerical model with analytical solution near the ridges [GWHB14], or the inclusion of sediment deposition. 37. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 4 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law #QR788H 4.1. The method of characteristics for the stream power law Score: 0.011 Related excerpt #SYQLY9: Note that \tau_{x,t}(s) parameterizes time, and therefore should remain positive. The function \tau_{x,t} being strictly increasing, we define a point D_{x,t} by \tau_{x,t}(D_{x,t}) = 0 , such that the characteristic curve is only defined when s \geq D_{x,t} . This is illustrated in the right of Figure 3 by the curve associated with (x, t_1) . The other curve – going through (x, t_2) – shows a case where \tau_{x,t}(D_{x,t}) = 0 does not have a solution, and for which we set D_{x,t} = 0 . 38. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 2 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #QW6CT7 3. Background and overview #MYA2EJ 3.1. Landscape dynamics in geology Score: 0.011 Related excerpt #74AXB7: The uplift is counteracted by erosion, which impacts the slopes of the mountain and therefore its maximal elevation. Erosion comes from many factors: water, glaciers, landslides, wind, and even anthropic or biological impact. Many models in geomorphology consider only erosion by water, also called fluvial erosion . Indeed, the fluvial network is considered the backbone of landscapes, and fluvial incision dictates the rate of landscape erosion [Whi04]. While simple to model, fluvial erosion explains the main topographical characteristics of most mountain ranges and has been the dominant erosion factor over many geological periods - with the notable exception of the last million years, where the Quaternary saw an important increase in glacial erosion that leaves specific marks in high altitude [PMD01, ENPL09, SHV + 12]. 39. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 4 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law #QR788H 4.1. The method of characteristics for the stream power law Score: 0.01 Related excerpt #GNAVAZ: If this happens for all cells in the terrain, this solution corresponds to the steady state of the stream power law. 40. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 5 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #UE2TM4 4. Analytical solutions of the stream power law #S7W7HC 4.2. Recursive algorithm for the 1D analytical solutions Score: 0.01 Related excerpt #6EG6ZV: Eqn. 11 is not well defined for small x or large t , which are cases where the information would need to be advected from beyond the boundaries of the domain. To detect this situation, we set T(0, 0) = 0 and parse the array from the bound, progressively evaluating T(0, x) = T(0, x - \delta x) + \delta x/a(x) until we find the first x_0 for which T(0, x_0) > t . We set D_{x,t} = 0 for x < x_0 , and, assuming that 1/a is locally constant near x = 0 : 41. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 3 Context: #G4BEE9 Mountain trail formation and the active walker model #A5Y7MA 2. Active walker model for human trails Score: 0.023 Related excerpt #YF42TP: The rate of change of G(\mathbf{r}, t) depends on weathering (the first term on the right hand side of the equation) and wear by walkers (the second term). The rate of weathering is governed by the parameter 1/T , where T sets the time scale of path decay back to the undisturbed ground condition G_0 . The saturation value is denoted G_{\max} . The parameter controlling the damage caused by a footprint is denoted I . Walkers are located at positions \mathbf{r}_{\mu} , and \delta(\mathbf{r}) is the Dirac delta function. In the presence of more than one walker, \mu is an index corresponding to the walker being considered. Note that G is a positive quantity in this study. 42. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 13 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Score: 0.017 Related excerpt #AJSDD6: We complete our simulations using algorithm one, by examining walkers that travel consecutively up and down the incline. Results of the simulations can be seen in figure 7. A slightly different weathering time of T = 1500s was used. There is no requirement that the forbidden angles are the same for hikers moving up and down the incline. In general, we expect that the different mechanisms for walking up and down inclines lead to different forbidden angles. In this set of simulations, we choose a forbidden angle of \theta_1 = 25^\circ for walkers moving up the diagram (down the gradient). Those moving down the diagram (up the gradient) have a minimum safe angle of \theta_2 = 10^\circ . We run simulations for a range of \alpha . Some zig-zag patterns can be seen for low alpha, but patterns of decent size do not appear until \alpha \gtrsim 0.45 (panel d). Again, the sizes of the bends in the path increase in size with \alpha . The 43. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Score: 0.026 Related excerpt #M53PTE: Another consideration is the acceleration afforded by the larger timesteps of our implicit solution. We show in Figure 13 that a 512 \times 512 terrain with \Delta x = 32\text{m} obtained with an explicit scheme ( \Delta t = 1,000 years) is visually similar to the result of our implicit solution ( \Delta t = 20,000 years). Our implicit scheme allows an increase of the timestep by a factor of 20, which reduces, by the same factor, the iterations needed to achieve the same total geological timespan. With such timesteps, generating a 10 million year-old landscape requires 7.2s and .5s, for the explicit and our implicit scheme, respectively. Note that larger implicit timesteps are unconditionally stable, and only diverge slightly from the explicit solution. Note that explicit and implicit schemes in general do not yield identical solutions as they accumulate discretization error differently. 44. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 7 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #BTBPNF Algorithm 6: Extracting a depression-free water surface Score: 0.018 Related excerpt #J4QRW9: where the first term u is the tectonically induced uplift (or growth rate of the mountain), and the second term is the erosion, dependent on the discharge Q , erosion coefficients k and m , and the slope \partial z/\partial x . The discharge provided by flow routing is scale-independent, so to compensate we scale the discharge Q by accumulating \Delta x^2 p , where \Delta x is the cell size and p is the precipitation. The uplift is usually considered time-independent and therefore applied as a pre-process. This leaves an implicit solution to the second erosive part of Equation 2 as: 45. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #BTBPNF Algorithm 6: Extracting a depression-free water surface Score: 0.014 Related excerpt #9VLUV9: As with water surface extraction, we can compute z_t using a simple modification of basin identification (see Algorithm 7). The outcome of applying our accelerated method of fluvial erosion is illustrated in Figure 8. Note that Equation 2 is a special case of the Stream Power Law with the slope exponent set to one. Further research is required to adapt our solution to the general case, for instance with a global Newton-Raphson's algorithm. 46. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #53AQ2N Algorithm 7: Implicit fluvial erosion Score: 0.012 Related excerpt #VPGNAT: Fluvial erosion is not the only erosive process responsible for shaping terrain. Hillslope processes model the gradual accumulation of solid material at the base of mountains and hills [BS97] and is usually expressed as a diffusion equation. We follow Tzathas et al. [TGSC24] and approximate it by including additional terms in the Stream Power Equation, changing kQ^m to kQ^m + k_t + k_h A^{-h} , where k_t and h = 0.6 are hillslope erosion parameters, A is the drainage area (obtained via flow routing with precipitation set uniformly to p = \Delta x^2 ). The parameter k_t accounts for slope-dependent effects (landslides, debris-flow), regrouped in computer graphics under the catch-all term thermal erosion [MKM89]. 47. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 1 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #KDKKZ3 2. Related Work Score: 0.01 Related excerpt #URD5LH: Instead, large-scale terrain erosion models [CBC + 16] take their inspiration from geomorphology [BW13] and directly compute total water discharge by accumulating precipitation from high (mountain ridges) to low elevations (the sea). This flow accumulation is communicated across large stretches of the terrain and is thus less local and less amenable to parallelisation [VBHS11] than direct water dynamics. However, this is more than offset by the sheer number of iterations required for a dynamics solution to reach steady-state. Schott et al. [SPF + 23] provide an approximate variant of discharge-based Stream Power erosion that propagates discharge by a few cells on each time step. While this strategy is trivially parallelizable, it requires a stable river network and thus precludes outside terrain forces such as time-dependent tectonics or sediment deposition. Furthermore, the underlying explicit time-stepping scheme requires many timesteps, while our method is amenable to an implicit scheme that overcomes this constraint. 48. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 7 Context: #RNVWWR Water Surface Wavelets #MU7P6S 5 ALGORITHM SUMMARY #AJK8ET Algorithm 1 Pseudocode for the algorithms used in our paper Score: 0.009 Related excerpt #NGXPFF: 1: function TIMESTEP( t ) 2: AdvectionStep( t ) 3: WavevectorDiffusion( t ) 4: \bar{\Psi} \leftarrow PrecomputeProfileBuffers( t ) 5: end function 6: function WATERHEIGHT( \mathbf{x}, t ) 7: \eta \leftarrow 0 8: for b \leftarrow 1, \Theta_\eta do 9: \theta_b \leftarrow \frac{2\pi}{\Theta_\eta} b 10: \hat{\mathbf{k}} \leftarrow (\cos \theta_b, \sin \theta_b) 11: \mathbf{p} \leftarrow \hat{\mathbf{k}} \cdot \mathbf{x} + \text{rand}(b) 12: for c \leftarrow 1, K_\eta do 13: \eta \leftarrow \eta + \mathcal{A}(\mathbf{x}, k_c \hat{\mathbf{k}}) \cdot \bar{\Psi}_c(\mathbf{p}, t) 14: end for 15: end for 16: end function 49. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 6 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Score: 0.022 Related excerpt #K7SCA8: where a_c is the particle's current age, a_b its birth time, while l_c and l_b denote the particle's current and birth locations. A is a constant defining the average age of a particle and L determines the maximum distance a particle can be from its birth location without being transparent. For all our simulations we set A to be 1.5 seconds and L to be 5% of the total length of the river. 50. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 6 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Score: 0.013 Related excerpt #WTCDC3: The average lifespan, A , of the particles can be adjusted depending on how turbulent and quickly the river is moving. Our system provides a graphical particle display that assists in the adjustment of this value, as seen in Figure 5. By representing each particle as a color determined by its birth location it is easy to see how far the particles remain traveling in groups of similar color. We note that there is significant leeway in choosing good settings for these parameters; finding a single optimum setting for these constants is not required since the system is not overly sensitive to the tuning of this parameter. Moreover, we use a pseudo-random function with values in the range of (0.5, 2.0) to scale each particle's life span with respect to the average, A . The aim being to avoid situations in which many particles are dying or spawning simultaneously. ### 10. Tool result: search_text Exact matches 1. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 11 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #MHMBEA 5. Implications of the computational approach and future work Matching excerpt #F2DH4H: The measure of structural beauty ( L ), as defined by S (substructures) times H (hierarchy), reminds us of the classic work on aesthetic measure (Birkhoff 1933). The classic work had the same motivation as our computational approach; it was aimed to quantify the degree of beauty by disregarding colors and materials, as well as human aspects such as cultures, education, and ethnicities. The aesthetic measure ( M ) considers the two notions of order ( O ) and complexity ( C ) and combines them together into a single formula: M = O/C . The formula shows an inverse relationship between the degree of beauty and that of complexity, M \propto 1/C , which is against the notion of organized complexity. Eysenck (1942) changed the initial formula to M = O \times C , which makes better sense, at least from the point of organized complexity because the more complex something is, the more beautiful it is. The biggest problem of the classic measure is that it has never been verified by any psychological study (Douchova 2015). On the other hand, the degree of beauty based on living structure is well supported by the mirror-of-the-self experiments mentioned above. 2. Source: Water-rendering literature overview (#4CB2WQ) Matching note #4CB2WQ: The water-rendering corpus organizes around a recurring hybrid strategy: simulate only the low-frequency/structural behavior needed for motion, then add high-frequency visual detail and optical cues cheaply. The survey separates deep-water parametric/spectral methods from shallow-water fluid methods and identifies foam, spray, and light interaction as separate realism layers (#4S5XNT, #CZNWCP). River methods use coarse or procedural velocity fields plus advected wave textures: Arnold et al. combine 2D Navier–Stokes, hydrostatic pressure columns, and texture advection (#8KBMFE, #T9Y2PR); Yu et al. compute local steady flow and use screen-space sampled wave sprites for huge terrains (#3UZ7TP, #AL6YQ9); their later Lagrangian texture-advection method uses deformable particle grids to preserve both flow and texture spectrum (#DZCPD6, #KSH8JS). Vlachos's Portal 2 production method is the cheapest end of this continuum: artist-authored flow maps distort two normal-map layers, with offsets and noise hiding repetition/pulsing (#6ELMAT, #XVFV3N). Shallow-water work adds effects a height field cannot express: Thürey et al. detect steep fronts and spawn connected-particle sheets for overturning waves, drops, and foam (#KHRCTA, #XFKY8Q); Ojeda and Susín layer FFT/noise normals, advected foam, photon caustics, and screen-space reflection/refraction over a shallow-water simulation (#BVUXWL, #PBZNNB). Scherzer et al. target fully dynamic particle fluids, using screen-space depth/thickness layers, adaptive curvature-flow smoothing, and Weber-number-based volumetric foam (#G3TYUA, #YJNSYU). Surface Wavelets is the strongest large-scale wave paper: it simulates slowly varying amplitudes over space/frequency/direction on a coarse grid, reconstructs detailed waves separately, supports obstacles and artistic control, and runs a 4 km × 4 km scene at 60 fps (#RFLQDX, #764D8D, #WKY9MT); it cannot handle breaking waves or splashes because it is linear (#YWWZAM). Specialized cheap methods include halftone-mask foam dissipation with under 3% overhead (#KFWVK3, #V5XDSY), Bézier-curve river networks with streaming normal maps (#QGESFA, #MSQQ8G), and distance-dependent switching among Stokes, cosine, and bump-mapped wave models (#H2E2UR, #EYM9N6). 3. Source: Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning (#869NHK), Ian Parberry, Jennifer R. Alford, Mary Yingst, p. 2 Context: #5R6DEX Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning #UQWEYD Overview of Our Approach #Z6PB8R The Saturation Function Matching excerpt #4EFZBU: where \vec{v} = (x, z) is position, \vec{k} is the wave direction, s is the speed of the wave, t is time, K is wave slope, A is wave amplitude, \lambda_{adj} is wavelength adjusted for ocean depth, and \lambda is original wavelength. 4. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 4 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #JL4FVP 5 Wave Patch Generation: Matching excerpt #PRB2KL: Once the fluid represented by the wave patch is detached from the fluid below that represented by the shallow water simulation, its motion is primarily determined by its initial velocity and gravity. Thus, Euler steps are sufficient to integrate velocity and position over time. After the update, we perform a collision detection of the particle with the fluid surface of the shallow water simulation. When a collision is detected, we distort the shallow water simulation at the particle position \mathbf{x} with H(\mathbf{x}) = H(\mathbf{x}) - p_m , while the eight neighbors of the shallow water node at \mathbf{x} are displaced by p_m/8 . Note that we do not explicitly transport fluid with the wave patches, as a modification of the height field along the wave front would distort its motion. This leads to noise within the shallow water simulation, unless the modification along the whole region of the wave is very smooth. As mentioned below, correctly performing this mass transport and smoothing is a topic of future research. 5. Source: Water Flow in Portal 2 (#A2QB8L), Alex Vlachos, p. 38 Context: #S2CBRT Water Flow in PORTAL 2 #XAMC76 Water Speed Affects Normals Matching excerpt #6HNB2U: We scale down the strength of the normal in tangent space by the flow speed (Flow speed is the length of the 2D flow vector) 6. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 5 Context: #JJE8HN Procedural Riverscapes #TFD8TX 5. River Network Amplification #U4VCJG 5.3. Seeding Riverflow Primitives Matching excerpt #5NJY7V: In terms of the impact of Rosgen type on the choice of water primitives, for type A we assign near constant height over each basin and then add fall primitives where basins intersect. Next, we place downstream turbulence primitives based on the waterfall drop and average flow velocity. These decrease in amplitude and frequency with increasing distance from the waterfall. For type C , the bends have high turbulence and velocity in deeper areas with calmer primitives placed in the shallows. The straights are seeded with high turbulence primitives to emulate rapids. For type D , the velocity and turbulence parameters of water primitives are keyed to channel depth and distance from the center of the nearest channel. 7. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 6 Context: #JJE8HN Procedural Riverscapes #9ZYJP2 6. Animated Procedural River Model #U6BTCY 6.1. Riverflow Primitives Matching excerpt #MYB6GF: In turn, the function \delta h is defined as an n -fold sum of scaled noise functions n , referred to as fractional Brownian motion m , and characterized by several parameters (persistence p , lacunarity l , and frequency f ): 8. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #Z6DVCN 4. River Network Graph Matching excerpt #HS22AT: Next, graph nodes are labeled with the terrain slope s and river flow \phi values at their cell position. The latter is a measure of the volumetric rate at which water is carried down the river and an accurate estimation is problematic, since it depends on parameters such as rainfall and soil composition. Instead, we apply a simplified model based on an empirical power law observed in geomorphology [Dun78]: from drainage area A_{ij} [ m^2 ], the flow \phi_{ij} of the river [ m^3 s^{-1} ] is approximated by \phi_{ij} = 0.42A_{ij}^{0.69} . This equation takes into account evaporation and infiltration, which is why the volume of flow is not preserved. 9. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 6 Context: #JJE8HN Procedural Riverscapes #9ZYJP2 6. Animated Procedural River Model #U6BTCY 6.1. Riverflow Primitives Matching excerpt #X2XX5X: All primitives are also characterized by a set of input parameters, which control the output functions ( f_i , \mathbf{u}_i , s_i ) and include: average elevation e_i , amplitude a_i , and average flow velocity \mathbf{u}_i . For readability we drop the subscript i hereafter. 10. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 6 Context: #JJE8HN Procedural Riverscapes #9ZYJP2 6. Animated Procedural River Model #U6BTCY 6.1. Riverflow Primitives Matching excerpt #GU2NEL: We have implemented a range of procedural primitives with characteristic dynamics (Figure 16), namely: calm, turbulent, wave, cascade, vortex, and ripple primitives (see the accompanying video for their animation). Calm water primitives are generated in regions with low turbulence and produce only swells and damped ripples. In contrast, turbulent water primitives are created where the water is agitated and the velocity high. Wave primitives approximate local crests and troughs, often dictated by the riverbed topography. Cascade primitives represent a more extreme version of this effect and include a corresponding plunge pool. Vortex primitives produce swirling that typically occurs downstream of under-water obstacles, such as rocks. Finally, ripples capture high frequency disturbance of the water surface from crosswinds and other sources. We also designed particular primitives for specific effects, such as echoing water ripples that approximate the complex movement of water interacting with river banks. By design it is easy to code new waterflow primitives for inclusion in the blend-flow tree. 11. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 3 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #96ENPE 2.2. Fourier domain approaches #Z39SP2 2.2.1. General methods Matching excerpt #956825: where \alpha = 0.0081 is called Phillips' constant, g is the gravitation constant. The frequency peak f_m is defined by: 12. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Matching excerpt #VG86AP: We use a simplified model based on an empirical power law observed in geomorphology [Dunne and Leopold 1978]. Let A [m 2 ] be the watershed area. The mean flow \phi of the river [m 3 s -1 ] is given by \phi = 0.42 \cdot A^{0.69} . The watershed area A is approximated by the sum of the areas of cells connected to s in the graph, and it allows calculation of the outgoing flow \phi of any cell V (Fig. 10). This equation takes into account evaporation and infiltration, and that is why the volume flow is not preserved. 13. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 8 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #LGLUMA 6 Experimental Validation Matching excerpt #3LSFWC: Autonomous closed-loop following of the racing trajectory is accomplished by using an integrated Differential Global Positioning System (DGPS) and Inertial Measurement Unit (IMU) to obtain the global vehicle position and velocity. A localization algorithm is applied to find the vehicle's position along the desired path ( s ) and lateral/heading deviation ( e and \Delta\Psi ) from the path. A previously developed feedback-feedforward steering algorithm [10] is then applied to keep the vehicle following the desired path at high lateral and longitudinal accelerations. By locating the desired position along the path, the current vehicle speed can be referenced to the desired vehicle speed from Fig. 12, and a simple proportional speed tracking controller with feedforward can be applied to track the desired speed profile. The same controller setup is also used to experimentally drive the trajectory generated by the nonlinear gradient descent algorithm. Closed loop control is applied at a sample rate of 200 Hz using a dSPACE MicroAutobox unit. The experimental data 14. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 3 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #G64TVV 4 Updating Path Given Fixed Velocity Profile #U4YF4Y 4.1 Overall Approach and Minimum Curvature Heuristic Matching excerpt #K2FUXE: The second step of the trajectory generation algorithm takes the original reference path K(s) and corresponding velocity profile U_x(s) as inputs, and modifies the reference path to obtain a new, ideally faster, racing line. Sharp [12] suggests a general approach for modifying an initial path to obtain a faster lap time by taking the original path and velocity profile and incrementing the speed uniformly by a small, constant “learning rate.” An optimization problem is then solved to find a new reference path and control inputs that allow the vehicle to drive at the higher speeds without driving off the road. If a crash is detected, the speed inputs are locally reduced around the crash site and the process is repeated. 15. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 12 Context: #G4BEE9 Mountain trail formation and the active walker model #NBFQAN 5. Results #TPVRFV 5.1. Algorithm one Matching excerpt #WUZ6YE: In this section, results from the mountain walker extension to the active walker model are shown. We begin by considering only walkers traveling down the slope. The following parameters were used for the simulations: the maximum ground potential was set to G_{\max} = 200\text{m}^{-1} (the units of G are set by Eq. 3 and Eq. 4) while the minimum ground potential was set to G_0 = 0 . Larger values of G_{\max} lead to larger attraction to the path. A new walker descended the inclined area as soon as the existing walker reached the destination (tests showed that there was little difference between this scheme and starting a walker every 100s). The visibility, \sigma of the paths was set to 10m and the intensity, I was set to l^2 G_{\max}/N , where N is the number of footprints needed to wear the ground condition to 1/e of its maximum value. N was set to 50 footfalls and the weathering parameter was initially set to T = 1000\text{s} . The values of N and T are smaller than in a real trail system, where N would be of the order of several hundred footfalls and T would be of the order of a few days. This still leads to realistic simulations since Helbing et al. have found that a combination of several parameters of the active walker model could be represented by the single parameter \kappa = IT/\sigma = G_{\max}T/N\sigma 7 . Individual walkers were assigned a random speed between 0.5m/s and 1.5m/s. In the simulation, walkers were given the starting position \mathbf{r}_{\text{initial}} = (0\text{m}, 5\text{m}) and a destination of \mathbf{r}_{\text{final}} = (25\text{m}, 5\text{m}) with the x -direction being the distance down the incline and y -direction the distance across the incline. Initially, 25000 walkers traversed the incline in each simulation. 16. Source: Recommended water renderer for procedural hydrological terrain (#JVRSKS) Matching note #JVRSKS: For a game with precomputed geological erosion and hydrology, the best fit is a stylized data-driven hybrid rather than runtime CFD. Reuse channel topology, banks, flow direction, discharge/drainage area, slope, depth/width, curvature, drops, junctions, obstacles, and distance-to-shore as shader/control fields. This closely matches the input assumed by scalable river animation (#QXYWAJ) and Procedural Riverscapes, which derives per-cell slope, volume, and velocity (#X3RVN8) and selects calm, turbulent, wave, cascade, vortex, and ripple primitives from terrain and flow conditions (#GU2NEL, #5NJY7V). Recommended architecture: one shared water material; rivers use generated flow maps to advect two offset normal/detail layers as in Portal 2 (#6ELMAT, #XVFV3N); lakes use low-speed wind ripples and shoreline masks; ocean uses a few art-directed Gerstner/spectral bands plus shore foam. Generate masks for turbulence/foam from normalized stream power, slope, curvature, constriction, drops, and obstacles; use depth for color/opacity and shallow-ground blending; use local feature primitives only at visually important events such as waterfalls, rapids, confluences, and rocks. Apply screen- or distance-dependent LOD, retaining flow direction and wind at distance while removing displacement and local effects (#H2E2UR, #EYM9N6). 17. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 10 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #PD667Q 6. Empirical Testing Matching excerpt #8ERHN4: Due to long run-times, two test sites were chosen for comparing the speed of the improved Priority-Flood algorithm against the TauDEM 5.0.6 parallel implementation of the Planchon–Darboux algorithm. Test Site A was Minnesota’s Steele County and Test Site B was Minnesota’s Nicollet County. The two test sites represent counties with an average (35%) and a large (61%) number of depressions, respectively. Thus, the results of the test should not be biased by the choice of counties. The test sites were also representative in terms of size. Test Site A was a 3 m DEM of 10891 \times 13914 cells ( 152 \cdot 10^6 total) and Test Site B was a 3 m DEM of 24140 \times 13183 cells ( 318 \cdot 10^6 total). 18. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 13 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #9D8AS4 8. Coda Matching excerpt #ED94U3: An improvement to the Priority-Flood priority queue (Alg. 2) has been described and tested. It runs in O(m \log_2 m) time, where m \leq n , on floating-point data and in O(n) time on integer data. By comparison, the Planchon–Darboux Algorithm has a time complexity of at least O(n^{1.2}) and the generalized Priority-Flood Algorithm has a time complexity of O(n \log_2 n) for floating-point DEMs and O(n) for integer DEMs. Under testing, the new algorithm outperformed the generalized Priority-Flood Algorithm in all cases. Improvements were often greater than 16% and were as high as 37%. In addition, a parallel implementation of the Planchon–Darboux Algorithm required upwards of six processors to match the improved Priority-Flood’s speed with a single processor. 19. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 7 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #BTBPNF Algorithm 6: Extracting a depression-free water surface Matching excerpt #J4QRW9: where the first term u is the tectonically induced uplift (or growth rate of the mountain), and the second term is the erosion, dependent on the discharge Q , erosion coefficients k and m , and the slope \partial z/\partial x . The discharge provided by flow routing is scale-independent, so to compensate we scale the discharge Q by accumulating \Delta x^2 p , where \Delta x is the cell size and p is the precipitation. The uplift is usually considered time-independent and therefore applied as a pre-process. This leaves an implicit solution to the second erosive part of Equation 2 as: 20. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation #53AQ2N Algorithm 7: Implicit fluvial erosion Matching excerpt #VPGNAT: Fluvial erosion is not the only erosive process responsible for shaping terrain. Hillslope processes model the gradual accumulation of solid material at the base of mountains and hills [BS97] and is usually expressed as a diffusion equation. We follow Tzathas et al. [TGSC24] and approximate it by including additional terms in the Stream Power Equation, changing kQ^m to kQ^m + k_t + k_h A^{-h} , where k_t and h = 0.6 are hillslope erosion parameters, A is the drainage area (obtained via flow routing with precipitation set uniformly to p = \Delta x^2 ). The parameter k_t accounts for slope-dependent effects (landslides, debris-flow), regrouped in computer graphics under the catch-all term thermal erosion [MKM89]. 21. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 2 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #SD69QC 3. Overview #8JBDT4 3.1. Flow routing Matching excerpt #HTY8YZ: Rain falling on a landscape flows downstream and progressively accumulates into streams and rivers. The volume of water flowing through a river cross-section per unit of time is called the discharge. Equivalently, the discharge is the upstream integral of the precipitation map. Flow routing involves the computation of this discharge for each cell of the terrain grid. 22. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 1 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #L8RWX4 1. Introduction Matching excerpt #K9JLST: For clarity, we define flow routing as the computation of the discharge – or any other material flux – over the terrain, and depression routing as the computation of the water flow path out of depressions. 23. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 7 Context: #RNVWWR Water Surface Wavelets #MEQNZV 6 EXTENSIONS #UTTFQ9 6.3 Solid-Fluid Coupling Matching excerpt #LLRQ8C: To add waves to the rigid body simulation, we calculate the change in energy of the rigid body caused by the water \Delta E_{RB} , where the rigid body's energy E_{RB} is equal to m\mathbf{v}^2/2 + mgh , with body mass m , velocity magnitude v , and gravity magnitude g . Linear wave theory tells us that water wave energy in deep water is proportional to the squared amplitude: 24. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 2 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #9RASZL 3.1 Motivation Matching excerpt #ZM4ETE: where the right hand side is defined by the particular wave model (shallow water equations, Bernoulli equation, etc.), and environmental interactions are encoded in the PDE’s boundary conditions. These discretizations sample \eta(\mathbf{x}, t) over space with a grid spacing equal to \Delta x . In order to avoid aliasing and faithfully reproduce high-frequency details, The Nyquist-Shannon sampling theorem [Shannon 1949] requires that \Delta x is less than half of the shortest wavelength in \eta(\mathbf{x}, t) . If \eta(\mathbf{x}, t) contains interesting high-frequency details, then the samples of \eta(\mathbf{x}, t) must be very close together, and thus \Delta x must be very small. Practically, decreasing \Delta x requires either more samples or a smaller simulation domain, so the Nyquist theorem effectively limits the visual detail that a simulator can produce. Highly detailed visuals can be obtained by decreasing \Delta x at the expense of vastly increased computation time and memory. 25. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #8PTY3G: Note that none of these resolution parameters affect the resolution of the waves themselves; they only affect the resolution of the wave groups , and thus induce higher-order indirect effects like curvature and speed of the wave groups, instead of affecting more visible cues like the frequency or speed of the wave crests. Instead, the frequency of the waves is controlled by the resolution of the heightfield evaluation, \eta(\mathbf{x}, t) , and the relative speed of the waves is fixed by the dispersion relation \omega . 26. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 10 Context: #RNVWWR Water Surface Wavelets #W3R46F 9 DISCUSSION Matching excerpt #BEDUYL: samples would have a grid cell spacing of 25 cm, even ignoring that it needs to store 2 values per grid cell. Following the Nyquist theorem, the smallest possible wavelength would be 0.5 m. By comparison, we animate wavelengths down to 2 cm. 27. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 1 Context: #RNVWWR Water Surface Wavelets #MGX8HM 2 RELATED WORK #2W6Q6T 2.1 Spectrum-based approaches Matching excerpt #3HBNML: We call this technique of discretizing a Fourier-transform the “spectrum-based” approach. These methods exhibit theoretically unlimited visual detail, in the sense that they can animate arbitrarily high frequency waves without impacting the method’s accuracy or stability. Similarly, fast wave speeds are trivial to simulate, because the motion is independent of the time step size. However, because the derivation of these methods makes several assumptions about the underlying flow, they tend to have limitations like the inability to realistically interact with complex boundaries. 28. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 1 Context: #RNVWWR Water Surface Wavelets #ZTWDW3 1 INTRODUCTION Matching excerpt #RFLQDX: Our work proposes a novel transformation to speed up the computation of water surface waves. Instead of discretizing the wave height and momentum at each point on a grid (like previous finite-difference methods), or discretizing wave amplitudes as a function of frequency and direction (like previous Fourier-based methods), we introduce a wavelet transformation that discretizes the wave amplitudes as a function of space, frequency, and direction combined . The variables resulting from this discretization change much more slowly over space than the original water wave height function, so we can represent the same amount of information with fewer variables. The new lower-frequency simulation is also less sensitive to traditional frequency-based limitations like the CFL condition and the Nyquist limit, which convert the maximum spatial frequency into limitations on time step size and visual detail. As a consequence, our discretization permits both high-resolution wave details (like Fourier-based methods) as well as local wave interactions with moving obstacles. 29. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 3 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #34V9L7 4. Adaptive Curvature Flow Matching excerpt #QUJBJA: One possible solution would be to remap the curvatures into a common reference coordinate system, for example by dividing H_s by z for each evaluation of H_s . However, our experiments have shown that this makes the integration very unstable, because the screen-space evaluation for larger particles is very noisy due to depth quantization. On the other hand, depth correction would make the resulting curvatures large in magnitude, leading to oscillation. 30. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 1 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #VR4JRQ 3. Overview Matching excerpt #QM2MGL: Our method builds on the screen space fluid rendering approach with curvature flow [vdLGS09]. Similar to this method, we start from an SPH simulation calculated using a hardware physics engine (PhysX), which provides a non-sorted 3D point cloud as input. Apart from the particle's position x we will also use the density \rho and velocity v for foam thresholding and the lifetime for varying the Perlin noise on a foam particle. 31. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 2 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #34V9L7 4. Adaptive Curvature Flow Matching excerpt #EHVCUP: where H is the mean curvature of a pixel, which is a function of the partial derivatives at the pixel and the depth value itself (for details see [vdlGS09]): 32. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 8 Context: #57PDWB Interactive Procedural Street Modeling #RXG48N References Matching excerpt #ZCBDT2: FISHER, M., SCHRÖDER, P., DESBRUN, M., AND HOPPE, H. 2007. Design of tangent vector fields. ACM, New York, NY, USA , vol. 26, 56. 33. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 18 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #D886YY 5 Analysis and Evaluation #PNAHWM 5.3 Ground Agent #63LCV9 5.3.1 Navigation and Behaviour Matching excerpt #KPQBVZ: The ground agent speed is adjusted according to the player’s forward velocity: 34. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 9 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #QGEMMG 4.3 Player Physics #ACMUGX 4.3.6 Dynamics Update Matching excerpt #UF5N8K: so the controller accelerates and decelerates with a time constant of approximately 0.1 s. Here, runSpeed is the configured running speed, v_z the current forward velocity, \Delta t the physics timestep, and the factor 10 controls the rate at which the velocity approaches its target. 35. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 16 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #D886YY 5 Analysis and Evaluation #Q7EX3B 5.1 Aerial Agent #MAX58R 5.1.2 Speed Control Matching excerpt #E29T3R: Here, p_f(t) is the current aerial agent position, p_{\text{aerial,target}} is the target position calculated ahead of the player, v_f is the current velocity reference used by the smoothing function, T_s is the smoothing time, and v_{\text{max}} is the maximum speed allowed for the aerial agent. 36. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 10 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #QGEMMG 4.3 Player Physics #ACMUGX 4.3.6 Dynamics Update Matching excerpt #U8EZM5: with y_0 the vertical position at the start of the jump, y(t) the position at time t , and v_y the vertical velocity immediately after lift-off. A linear damping coefficient of c = 2 \text{ s}^{-1} is applied through the Rigidbody, so that any unforced velocity decays as v(t) = v_0 e^{-2t} . This prevents residual drift after input release without producing an abrupt stop. If the player falls below y = -8 \text{ m} , the controller triggers a respawn that teleports the character back to the configured spawn point and resets the velocity. Up to nine respawns are permitted per run before the game-over state is entered. This safeguard is required because the procedural ground occasionally contains transient gaps between tile boundaries during navigation rebakes. 37. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 5 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Matching excerpt #FD4PEN: where h is the height field, \omega is the angular wave frequency, H(\mathbf{k}) contains amplitude and phase information, \mathbf{k} is a 2D vector such that k_x = 2\pi n / L_x , k_y = 2\pi m / L_y and (n, m) are integers with bounds -N/2 \leq n < N/2 and -M/2 \leq m < M/2 . 38. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 5 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #CSD47K Impulse Driven NS Matching excerpt #BMKDJR: where v is the cell's velocity, and f is the flow hint. We then check if d is greater than or equal to a cutoff deviance value and if so we calculate an impulse for the cell using the cell's current velocity vector and the cell's previously calculated flow hinting value. From our experiments, we found values around 15^\circ to be an effective cutoff value that works across different simulations. With numbers significantly less than 15^\circ the visual diversity of the simulation is impacted as the ability for opposing flows or fluidic shearing is overly constrained. Conversely, as the value is relaxed the general flow of the river becomes too variable and less visually realistic. A compromise between flow diversity and the general river flow is therefore necessary. 39. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 5 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #CSD47K Impulse Driven NS Matching excerpt #JWPTFC: The direction of the impulse is then modified based on the deviation between the flow hint vector and the current velocity vector. In order to calculate the cell's directional deviance, d , from the flow hint we use the standard geometric angle difference: 40. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 4 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #CSD47K Impulse Driven NS Matching excerpt #6PLNP5: Equipped with the flow hinting field and a primed fluid volume we begin adding impulses to each cell in the simulation as it runs. As we do so we need to ensure the simulation stability is not compromised, complex flows can still be visualized and the overall flow does not exhibit incorrect flow behavior such as a river reversing its direction. To accomplish this, the magnitude of the impulse added to a cell is made proportional to the cell’s velocity in relation to the desired flow volume. For example, if two cells had the same flow hint, with one having a velocity of 1.0 units of flow and the other 0.5, the faster moving cell would be affected twice as much as the slower moving cell during the application of the impulse. In this way, the impulse application scales linearly and the ratio between one cell and another does not change after the impulses are applied (given equal circumstances the difference in rate of flow between once cell and the next will have the same ratio after the impulse application). 41. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 5 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #CSD47K Impulse Driven NS Matching excerpt #FC4B98: where l_{ij} is the new impulse magnitude for cell at index (i, j) , \mathbf{u}_{ij} is the cell's velocity, p is the HSP pressure, P is the maximum pressure the HSP simulation can contain and z is a user defined value such that 0 \leq z < \infty . By changing z with a slider one can influence how much the HSP information affects the simulation. However, for all our simulations we keep z at 1.0. The sum of all these modified impulses is then equal to the desired flow velocity. 42. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 6 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #N4M5TN 5.4. Stochastic sampling Matching excerpt #WJSTC2: Table 5 reports statistics corresponding to the shortest paths illustrated in Figure 15 and demonstrating the efficiency of the sampling technique. The tunnel and bridge mask areas were set with r_i = 50 m and r_e = 300 m over a 300 \times 300 grid with a sampling grid size of 10 m. The corresponding number of grid points visited at every iteration was equal to \#T = 2728 . In contrast, the number of sample grid points in the stochastic approach was set to \#S = 50 . Timings demonstrate that the speed up is proportional to the ratio \#S/\#T . 43. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 8 Context: #B9LYTR Scalable real-time animation of rivers #TJAYJS 7. Discussion and limitations Matching excerpt #4Y2DNV: 2D flow hypothesis and terrain slope Our 2D flow hypothesis is valid for constant water depth (and homogeneous velocity profile along each water column). To account for depth h(x,y) variations we should simply conserve q(x,y) = v(x,y)h(x,y) instead of v \cdot \nabla \cdot q = 0 , q = \nabla \times \psi , v = q/h . This supposes either to know h or to deduce it from the terrain elevation z(x,y) . In our static case, the Chézy law provides a convenient approximation: v = C\sqrt{Rs} with C the Chézy constant, s the slope, v = Q/S the average velocity in a vertical section of surface S , perimeter P , and hydraulic radius R = S/P . Assuming the section has a known shape, e.g., a rectangle of known length l and height h , this yields h as a function of s, l, Q . 44. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 8 Context: #B9LYTR Scalable real-time animation of rivers #TJAYJS 7. Discussion and limitations Matching excerpt #PB35WU: Limitations of texture frequency range For very close views the sprite diameter in world space is smaller than the maximum wavelength of the reference wave texture. Hence our sprites cannot reproduce the low frequencies of this texture in this case. The solution is to represent these low frequencies with a scalar value attached to each sprite, sampled from a low pass filtered version of the wave texture. Approximate matches 1. Source: Real-time River Representation by Dynamic Control of Data on Waves (#5MGCZ5), Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato, p. 1 Context: #RNRNU8 Real-time River Representation by Dynamic Control of Data on Waves #7TBW6W 4. 水面波の生成 #7L3GHL 4.1 水面波の物理モデル Score: 0.029 Related excerpt #ETMUEY: ここで, x は水面波の進行方向における位置, t は時刻, z は川底からの水面波の高さ, H は波高(波の振幅)であり, C と L は上記のとおり,流速と波長である。 2. Source: Real-time River Representation by Dynamic Control of Data on Waves (#5MGCZ5), Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato, p. 1 Context: #RNRNU8 Real-time River Representation by Dynamic Control of Data on Waves #7TBW6W 4. 水面波の生成 #7L3GHL 4.1 水面波の物理モデル Score: 0.025 Related excerpt #HBX6M7: 本稿では,下流における比較的穏やかな水面波を対象とするため,波は規則波と仮定し,微小振幅波の理論 12) を適用する。つまり,水深に比べて波高が充分小さいとき,流速 C ,波長 L ,および周期 T の関係は次式(3)となり,式(3)を用いて流速 C を計算することができる。ただし, g は重力加速度である。 3. Source: Real-time River Representation by Dynamic Control of Data on Waves (#5MGCZ5), Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato, p. 2 Context: #RNRNU8 Real-time River Representation by Dynamic Control of Data on Waves #7TBW6W 4. 水面波の生成 #PN4DGU 4.3 風による波の変化 Score: 0.021 Related excerpt #ASNEB8: る。また、風力の大きさを波高 H に反映させることにより、波の振幅を変更することも可能である。なお、近距離景の場合、式(4)に対して上記位相 e を考慮することで、風により変化する波の表現が可能となる。 4. Source: Real-time River Representation by Dynamic Control of Data on Waves (#5MGCZ5), Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato, p. 2 Context: #RNRNU8 Real-time River Representation by Dynamic Control of Data on Waves #7TBW6W 4. 水面波の生成 #PN4DGU 4.3 風による波の変化 Score: 0.019 Related excerpt #CJYTFT: 図4において、風向きに直交し原点 o を通過する直線 m は次式(6)となるから、任意の点 (x_0, y_0) の直線 m からの距離 e は次式(7)となる。したがって、直線 m からの距離 e を風波の位相と考え、風向きが水面波の進行方向と逆向きであることを考慮すれば、風波は次式(8)となる。 5. Source: Real-time River Representation by Dynamic Control of Data on Waves (#5MGCZ5), Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato, p. 2 Context: #RNRNU8 Real-time River Representation by Dynamic Control of Data on Waves #7TBW6W 4. 水面波の生成 #PN4DGU 4.3 風による波の変化 Score: 0.015 Related excerpt #KMNNY2: 水面波の進行方向は風により時々刻々と変化するため、厳密には風のモデルを検討して水面波に適用する必要がある。しかしながら、風の物理モデルは確立されていないため、本研究では風により生成される波としての風波を近似的に考える。風波もストークス波による近似が最適と思われるが、風の影響は遠距離でも観察されること、また本研究では、リアルタイム表現を目的としていることから、風波はストークス波ではなく、余弦波としてモデル化する。図4に示すように、 x 軸の正方向に水面波が進行し、 x 軸と \theta の傾きを持つ方向から風が吹いていると仮定する。 H を波高、 L を波長、 C を流速、 x を水面波の進行方向における位置、 t を時刻とすると、水面波は次式(5)で近似的に表現できる。 6. Source: Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning (#869NHK), Ian Parberry, Jennifer R. Alford, Mary Yingst, p. 2 Context: #5R6DEX Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning #UQWEYD Overview of Our Approach #Z6PB8R The Saturation Function Score: 0.027 Related excerpt #4EFZBU: where \vec{v} = (x, z) is position, \vec{k} is the wave direction, s is the speed of the wave, t is time, K is wave slope, A is wave amplitude, \lambda_{adj} is wavelength adjusted for ocean depth, and \lambda is original wavelength. 7. Source: Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning (#869NHK), Ian Parberry, Jennifer R. Alford, Mary Yingst, p. 2 Context: #5R6DEX Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning #UQWEYD Overview of Our Approach #Z6PB8R The Saturation Function Score: 0.009 Related excerpt #XFF5YH: We use the following formulae from Van Dresek III, Bookout, and Lake [9] for the height y of the wave: 8. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 4 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #JL4FVP 5 Wave Patch Generation: Score: 0.012 Related excerpt #9UATCT: For the computation of the velocities of the wave patch particles, we use the velocity of the source point on the line \mathbf{u}_l . The actual overturning of a wave results in a significantly higher velocity at the top of the wave than at its bottom. We assume that this forward acceleration is proportional to the potential energy, in relation to the initial fluid height H_i . Thus, the velocity of a wave sheet particle at position \mathbf{x} is given by 9. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 6 Context: #JJE8HN Procedural Riverscapes #9ZYJP2 6. Animated Procedural River Model #U6BTCY 6.1. Riverflow Primitives Score: 0.008 Related excerpt #X2XX5X: All primitives are also characterized by a set of input parameters, which control the output functions ( f_i , \mathbf{u}_i , s_i ) and include: average elevation e_i , amplitude a_i , and average flow velocity \mathbf{u}_i . For readability we drop the subscript i hereafter. 10. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 5 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #XKG89F 3. Ocean dynamics simulation in shallow water Score: 0.021 Related excerpt #FNK3PH: with \vec{U} = (u, v, w) the velocity of the fluid, \mu its viscosity, p its pressure, \rho its density, and \vec{g} representing gravity (0, 9.81, 0) . Operator \nabla \vec{U} (resp. \nabla^2 \vec{U} ) is the gradient (resp. Laplacian) of \vec{U} and is defined by \nabla \vec{U} = (\frac{\partial u}{\partial x}, \frac{\partial u}{\partial y}, \frac{\partial u}{\partial z}) (resp. \nabla^2 \vec{U} = \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} ). The first equation guarantees mass conservation, i.e. the density of the fluid remains constant over time. The second one guarantees moment conservation: the acceleration \frac{\partial \vec{U}}{\partial t} of the fluid is equal to the sum of the applied forces weighted by its density. Other formulations for fluid behavior include shallow water equations (or Saint-Venant equations), preferably used whenever the horizontal scale is greater than the vertical one. 11. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 1 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #B9SCHY 2.1. Spatial domain approaches #3VTQEF 2.1.1. Early works Score: 0.02 Related excerpt #ALV78Q: where N_w is the total number of waves, A_i is the amplitude of the i -th wave, \vec{k}_i = (k_{ix}, k_{iz}) its wave vector, \omega_i its pulsation and y_0 is the height of the free surface. The x-axis is oriented horizontally and points towards the coastline, the y-axis is vertical, and the z-axis is horizontal and aligned with the coastline. For each wave, the shape of the curve defined by the motion of a single point depends directly on the product between the amplitude A_i and the wave number k_i = \|\vec{k}_i\| . If k_i A_i < 0.5 , this path is similar to a trochoid. If k_i A_i = 0.5 , the shape is a cycloid. In all other cases ( k_i A_i > 0.5 ), this path cannot represent a realistic motion (see Figure 2). 12. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 3 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #96ENPE 2.2. Fourier domain approaches #Z39SP2 2.2.1. General methods Score: 0.017 Related excerpt #2QEJGC: where C is a constant, \vec{k} is the wave vector, k is the wave number, \vec{w} is the wind direction, V is its speed and L = \frac{V^2}{g} . The choice of a random generator is justified by the Gaussian distribution of waves often observed in deep sea areas. In order to obtain fine details on the surface, each component is slightly perturbed by a noise function, producing more or less crested waves at any resolution (see Figure 4). Cieutat et al [CGG03] enhance this model in order to take in account water waves forces applied to a ship, implemented in a ship training simulator. 13. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 2 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #B9SCHY 2.1. Spatial domain approaches #3VTQEF 2.1.1. Early works Score: 0.016 Related excerpt #8D4U3R: with g the gravitation constant and L_i the wavelength of each individual wave. 14. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 3 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #96ENPE 2.2. Fourier domain approaches Score: 0.016 Related excerpt #A6RD53: where N_s is the number of spectral components, \vec{k} is the wave vector and \tilde{h}(\vec{k}, t) is the amplitude of the Fourier component obtained from a theoretic wave spectrum. 15. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 6 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #XKG89F 3. Ocean dynamics simulation in shallow water #7C4MCW 3.1. Eulerian approaches Score: 0.011 Related excerpt #9TLBXN: where, as in [TDG00], A is the amplitude of a wave, \vec{k} = (k_x, k_z) its characteristic vector and w its pulsation. The user can obtain any type of shore-break by choosing from a library of precomputed profiles. The full 3D simulation is then computed by extruding the desired profile along the parallel direction to the shore (see Figure 6). 16. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 3 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #96ENPE 2.2. Fourier domain approaches #Z39SP2 2.2.1. General methods Score: 0.01 Related excerpt #956825: where \alpha = 0.0081 is called Phillips' constant, g is the gravitation constant. The frequency peak f_m is defined by: 17. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 2 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #D9SXF3 1. Introduction #RNG4NC 1.1. Related Work #ESVL3G 119 2. Fluid simulation Score: 0.024 Related excerpt #V5K24C: 120 where \lambda_i = 1 for i = 1..4 and \lambda_i = 1/4 for i = 5..8 . g is 121 the gravity and h and \mathbf{u} are the fluid properties: height level 122 from the underlying terrain and velocity, respectively. They are 123 calculated as 18. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #TRR58W 5.1 Segmentation and Elevation of Crests Score: 0.008 Related excerpt #KHSN48: River flow evaluation contributes to the definition of the water-course. The exact computing is a complex problem that depends on multiple parameters, such as the climate and the soil composition. 19. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #DBN56J 4.2 River Network Generation #VTGN6K 4.2.2 Node Expansion Score: 0.008 Related excerpt #68SYWN: value \eta (we use \eta = 3/4 e = 1500[\text{m}] in our implementation): 20. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 1 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #KDKKZ3 2. Related Work Score: 0.008 Related excerpt #HGN9Y8: While the task of computing water flow over a terrain is a mainstay of hydrology and geomorphology, it is also directly applied in com- 21. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 3 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #9RASZL 3.1 Motivation Score: 0.029 Related excerpt #JDJC9N: Here, \eta_c(\mathbf{x}, t) is a complex function that varies over two-dimensional space and time, and we can get the wave height by taking its real part, \eta(\mathbf{x}, t) = \text{Re } \eta_c(\mathbf{x}, t) . The wavevector \mathbf{k} is a two-dimensional frequency function, the wavenumber k = |\mathbf{k}| represents a scalar frequency, and \mathbf{k} = \mathbf{k}/k is the wave direction. The exponential term in this equation represents a traveling wave, and A(\mathbf{k}) represents its amplitude. The angular frequency 22. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 3 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #ARD5T6 3.2 Derivation Score: 0.027 Related excerpt #K7F9J3: which tells us that our amplitude function \mathcal{A}(\mathbf{x}, \mathbf{k}, t) gets advected in space in the direction \hat{\mathbf{k}} with speed \omega'(\mathbf{k}) . Note that this speed corresponds exactly to the group speed which transports water wave energy [Johnson 1997] and wave packets [Jeschke and Wojtan 2017]. We provide a more detailed derivation of this equation in Appendix A. 23. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 3 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #9RASZL 3.1 Motivation Score: 0.025 Related excerpt #GM3U3W: encodes the speed of each wave based on its wavenumber k , gravity g , and surface tension \sigma . Spectrum-based methods compute the wave height by discretizing the integral over all of these two-dimensional waves, instead of discretizing a differential equation. This solution works perfectly for ideal situations with periodic domains, and no boundaries or interacting obstacles. However, these spectrum-based methods become impractical or impossible in less constrained scenarios. 24. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 7 Context: #RNVWWR Water Surface Wavelets #MEQNZV 6 EXTENSIONS #B6SYLX 6.1 Dissipation Score: 0.022 Related excerpt #NHQBFC: The first term models dissipation due to water viscosity \nu ( 10^{-6} \text{m/s} ), which affects mostly waves with small wavelengths. The second term accounts for surface contamination such as oil, dirt or algae and it affects larger waves as well. 25. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Score: 0.022 Related excerpt #8PTY3G: Note that none of these resolution parameters affect the resolution of the waves themselves; they only affect the resolution of the wave groups , and thus induce higher-order indirect effects like curvature and speed of the wave groups, instead of affecting more visible cues like the frequency or speed of the wave crests. Instead, the frequency of the waves is controlled by the resolution of the heightfield evaluation, \eta(\mathbf{x}, t) , and the relative speed of the waves is fixed by the dispersion relation \omega . 26. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 4 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION Score: 0.019 Related excerpt #WKDEGY: Section 3.2 introduced a new amplitude function \mathcal{A}(\mathbf{x}, \mathbf{k}, t) , an equation for evolving it over time (Equation 10), and an equation for computing the water wave height (Equation 7). The remainder of this section explains how we discretize these ideas to efficiently simulate water waves. 27. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 4 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #6AJDFD 4.1 Discretizing \mathcal{A} Score: 0.019 Related excerpt #HPVT4Q: The amplitude \mathcal{A}(\mathbf{x}, \mathbf{k}, t) is a function in 4 + 1 dimensions: two in space, two in wavevector, and one in time. We find it intuitive and computationally convenient to represent the wavevector in polar coordinates \mathbf{k} = (k \cos \theta, k \sin \theta) , where k is the magnitude of \mathbf{k} , and \theta is the angle made by \mathbf{k} and the x -axis. We represent \mathcal{A} on a four-dimensional grid [x_{\min}, x_{\max}] \times [y_{\min}, y_{\max}] \times [0, 2\pi] \times [k_{\min}, k_{\max}] , which spans two spatial coordinates x and y , the angular coordinate \theta , and the wavevector coordinate k . We store samples of \mathcal{A} on each of the nodes in this 4D grid, indexed by the coordinates a, b, c . We use the notation \mathcal{A}_{abc} to represent the discrete amplitude sample of the wave at grid node position \mathbf{x}_a = (x_a, y_a) , traveling at angle \theta_b , with wavenumber k_c . Figure 2 illustrates the grid used for our discretization. 28. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 3 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #ARD5T6 3.2 Derivation Score: 0.019 Related excerpt #U7CY32: so the number \zeta(\mathbf{x}, \mathbf{k}, t) tells how much the water height \eta_c behaves like a wave with wave-vector \mathbf{k} in the vicinity of point \mathbf{x} . 29. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 6 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #KQNQXW 4.3 Height field evaluation Score: 0.016 Related excerpt #TM83X4: To calculate the actual water height we numerically evaluate the integral in Equation 12. We evaluate the wavenumber in polar coordinates 30. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 5 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #6AJDFD 4.1 Discretizing \mathcal{A} Score: 0.016 Related excerpt #C2DP29: The wavenumber basis \psi_c(k) has a special physical interpretation; it symbolizes the spectrum of the waves represented by amplitude \mathcal{A}_{abc} . If we continue with our wave packet analogy, then \psi_c(k) describes the shape in frequency-space of the wave packet at position \mathbf{x} traveling in direction \theta with representative wavenumber k_c . Thus, a piecewise-constant \psi_c(k) implies that the wave packet has a flat spectrum, with all wavenumbers similar to k_c having the exact same amplitude; a piecewise-linear \psi_c(k) gives the packet a bit more of a localized wave packet-like shape with its peak at k_c ; and a Gaussian \psi_c(k) resembles the typical wave packet derivation. We are free to assign any wave spectrum we wish to this function, and, since we are modeling water waves in this paper, we found it appropriate to use an actual ocean wave spectrum for \psi_c(k) . Our examples set \psi_c(k) equal to the directional spectrum in Equation 32 of [Horvath 2015], normalized such that \mathcal{A}(x_a, \theta_b, k_c, t) = \mathcal{A}_{abc}(t) . 31. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 1 Context: #RNVWWR Water Surface Wavelets #ZTWDW3 1 INTRODUCTION Score: 0.016 Related excerpt #EMZ6QE: water height itself, so we can represent them on lower resolution grids. This change of variables allows more efficient computation and larger computational domains (Figure 1). 32. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 2 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #9RASZL 3.1 Motivation Score: 0.015 Related excerpt #CHFYEX: Current numerical methods for water wave simulation rely either on discretizations of partial differential equations (PDEs), or on spectrum-based methods. Methods based on discretized PDEs approximate some differential equation that describes how the wave height \eta(\mathbf{x}, t) evolves over time: 33. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 7 Context: #RNVWWR Water Surface Wavelets #MU7P6S 5 ALGORITHM SUMMARY #AJK8ET Algorithm 1 Pseudocode for the algorithms used in our paper Score: 0.015 Related excerpt #NGXPFF: 1: function TIMESTEP( t ) 2: AdvectionStep( t ) 3: WavevectorDiffusion( t ) 4: \bar{\Psi} \leftarrow PrecomputeProfileBuffers( t ) 5: end function 6: function WATERHEIGHT( \mathbf{x}, t ) 7: \eta \leftarrow 0 8: for b \leftarrow 1, \Theta_\eta do 9: \theta_b \leftarrow \frac{2\pi}{\Theta_\eta} b 10: \hat{\mathbf{k}} \leftarrow (\cos \theta_b, \sin \theta_b) 11: \mathbf{p} \leftarrow \hat{\mathbf{k}} \cdot \mathbf{x} + \text{rand}(b) 12: for c \leftarrow 1, K_\eta do 13: \eta \leftarrow \eta + \mathcal{A}(\mathbf{x}, k_c \hat{\mathbf{k}}) \cdot \bar{\Psi}_c(\mathbf{p}, t) 14: end for 15: end for 16: end function 34. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 7 Context: #RNVWWR Water Surface Wavelets #MEQNZV 6 EXTENSIONS #UTTFQ9 6.3 Solid-Fluid Coupling Score: 0.014 Related excerpt #LLRQ8C: To add waves to the rigid body simulation, we calculate the change in energy of the rigid body caused by the water \Delta E_{RB} , where the rigid body's energy E_{RB} is equal to m\mathbf{v}^2/2 + mgh , with body mass m , velocity magnitude v , and gravity magnitude g . Linear wave theory tells us that water wave energy in deep water is proportional to the squared amplitude: 35. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 2 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #9RASZL 3.1 Motivation Score: 0.013 Related excerpt #4DTJUL: Spectrum-based methods for animating water waves [Tessendorf 2004b] remove these problems by avoiding a spatial discretization altogether. They rely on linear wave theory [Johnson 1997], which describes the wave height dynamics in terms of frequencies instead of partial derivatives: 36. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 6 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #KQNQXW 4.3 Height field evaluation Score: 0.012 Related excerpt #5RPTRF: Our examples also extend the water height field to mimic trochoidal Gerstner waves [Tessendorf 2004b] by computing horizontal displacements in addition to the vertical ones in the profile buffer \bar{\Psi}_c(p, t) . We then include these horizontal displacements in the final summation of \eta . 37. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 10 Context: #RNVWWR Water Surface Wavelets #W3R46F 9 DISCUSSION Score: 0.012 Related excerpt #BEDUYL: samples would have a grid cell spacing of 25 cm, even ignoring that it needs to store 2 values per grid cell. Following the Nyquist theorem, the smallest possible wavelength would be 0.5 m. By comparison, we animate wavelengths down to 2 cm. 38. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 8 Context: #RNVWWR Water Surface Wavelets #8LZWQ3 7 ARTISTIC CONTROL #CXPF2K 7.1 Selecting the basis function \psi(k) Score: 0.011 Related excerpt #ZJSEMQ: The basis function \psi(k) controls the wave spectrum which is visualized in the final results. The spectrum can either be determined by physics or tuned by hand to create more stylized results. Figure 6 shows how changing this function affects the visualized wave heights. Regardless of the chosen spectrum, the waves will travel at the correct phase speed due to the dispersion relation in Equation 21. 39. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 5 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #6AJDFD 4.1 Discretizing \mathcal{A} Score: 0.011 Related excerpt #UG8PZG: in Section 8. As mentioned above, \mathcal{A} varies slowly over space, so we do not require much spatial resolution either. In our implementation we allocate X_{\mathcal{A}} = 4096 grid cells for each spatial dimension, which defines a grid cell spacing of approximately one meter. 40. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 3 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #ARD5T6 3.2 Derivation Score: 0.01 Related excerpt #2UA5FQ: now with \mathcal{A} playing the role of an amplitude that varies over space and time as well as wavevector. By plugging Equation 2 into Equation 5, we obtain an equation for the time evolution of \mathcal{A} : 41. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 4 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #6AJDFD 4.1 Discretizing \mathcal{A} Score: 0.009 Related excerpt #DSH4YY: where \phi_a(\mathbf{x}) is a basis function in position, \theta_b(\theta) is a basis function in angle, \psi_c(k) is a basis function in wavenumber coordinates, and C(\mathcal{A}_{abc}, t) is a coefficient function weighting various values of 42. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 11 Context: #RNVWWR Water Surface Wavelets #FFTTEG B \mathcal{A} IS LOWER FREQUENCY THAN \eta Score: 0.009 Related excerpt #E892ZC: First, express \mathcal{A} by combining Equation 5 and \mathcal{A}(\mathbf{x}, \mathbf{k}, t) = \zeta(\mathbf{x}, \mathbf{k}, t) e^{i\omega(\mathbf{k})t} : 43. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 3 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #ARD5T6 3.2 Derivation Score: 0.008 Related excerpt #52L883: \mathcal{A}(\mathbf{x}, \mathbf{k}, t) = \mathcal{A}_{\text{ambient}}(\mathbf{x}, \mathbf{k}, t) on transmitting boundary 44. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 3 Context: #RNVWWR Water Surface Wavelets #5EX6YK 3 THEORY #ARD5T6 3.2 Derivation Score: 0.008 Related excerpt #8EVKHR: which reminds us of a Fourier transform with \zeta acting like an amplitude that now depends on \mathbf{x} and t as well as \mathbf{k} . We introduce the change of variables \mathcal{A}(\mathbf{x}, \mathbf{k}, t) = \zeta(\mathbf{x}, \mathbf{k}, t) e^{i\omega(\mathbf{k})t} to obtain an analogue to the dynamic wave evolution in Equation 2: 45. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 6 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #KQNQXW 4.3 Height field evaluation Score: 0.008 Related excerpt #7T5ZQF: Now we can see more explicitly how the basis function \psi_c(k) relates to the spectrum associated with amplitude \mathcal{A}_{abc} ; Equation 21 treats \psi_c(k) as the amplitude function for each wavelength k in the heightfield evaluation. 46. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 5 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #B2JVNM River Surface Advection Score: 0.019 Related excerpt #FD4PEN: where h is the height field, \omega is the angular wave frequency, H(\mathbf{k}) contains amplitude and phase information, \mathbf{k} is a 2D vector such that k_x = 2\pi n / L_x , k_y = 2\pi m / L_y and (n, m) are integers with bounds -N/2 \leq n < N/2 and -M/2 \leq m < M/2 . 47. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 5 Context: #JCB5RE Advected river textures #G2SPEY Previous Work #CSD47K Impulse Driven NS Score: 0.009 Related excerpt #JS4LBU: It should also be noted that the flow speed of the river itself should be set in accordance to the grid cell size of the river in order to maintain grid size independent flow rates. For example, if the desired flow rate is 1.3 meters per second and the cell width is 1.0 unit, the flow rate should be set to one half the value of the same flow rate on a grid with a cell width of 2.0 units. 48. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 6 Context: #B9LYTR Scalable real-time animation of rivers #NRD5JU 5. Adaptive texture advection #KWALBE 5.2. Sprite-based texturing Score: 0.009 Related excerpt #U5WBC5: Wave patterns. In this work we focus on statistical wave patterns populating the surface and advected with the flow, 49. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 8 Context: #B9LYTR Scalable real-time animation of rivers #TJAYJS 7. Discussion and limitations Score: 0.008 Related excerpt #4Y2DNV: 2D flow hypothesis and terrain slope Our 2D flow hypothesis is valid for constant water depth (and homogeneous velocity profile along each water column). To account for depth h(x,y) variations we should simply conserve q(x,y) = v(x,y)h(x,y) instead of v \cdot \nabla \cdot q = 0 , q = \nabla \times \psi , v = q/h . This supposes either to know h or to deduce it from the terrain elevation z(x,y) . In our static case, the Chézy law provides a convenient approximation: v = C\sqrt{Rs} with C the Chézy constant, s the slope, v = Q/S the average velocity in a vertical section of surface S , perimeter P , and hydraulic radius R = S/P . Assuming the section has a known shape, e.g., a rectangle of known length l and height h , this yields h as a function of s, l, Q . 50. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 3 Context: #B9LYTR Scalable real-time animation of rivers #S3P9T2 4. Computing flow velocities Score: 0.008 Related excerpt #WR3N89: The stream function is related to the volumetric flow rate inside each branch of the hydrographic network: \psi must be constant along every connected boundary of the system, and the volumetric flow rate Q inside a given channel is equal to the difference between the values of \psi on each bank (see Figure 3): ### 11. Tool result: search_text Exact matches 1. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 6 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #CC4RWZ 8 Results Matching excerpt #RTYCL9: The results discussed in this section were calculated on a common PC with an Intel Core 2 Duo CPU (2.13 GHz), and a Nvidia Geforce 7950 GPU. As our implementation is not yet parallelized, it only makes use of one of the cores of the CPU. The actual frame rates of the different cases are given in Table 2. All test cases use between 160k and 200k grid points, and run with 40 to 75 frames per second, including rendering. The distribution of the computational time for the different parts of our algorithm can be found in Table 1. For this measurement a typical wave, as shown in Figure 6, was simulated. Overall, the fluid simulation amounts for 80% of the run time, while the rendering and overhead introduced by the graphics engine require the remaining 20%. Roughly half of the simulation time is spent on the shallow water simulation itself, while the wave simulation algorithm requires circa one fourth of the time. The creation of the surface mesh and the computation of the normals again requires roughly one fourth of the computations. 2. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Matching excerpt #VDK3Z2: The reasons for the difference of performance are twofold. First, we are in the worst case for indirect reconstruction and the best case for the direct reconstruction: the entire fluid domain is displayed on screen, and we use a very simple shader. Second, our GPU implementation of virtual textures is not optimized: we simply implemented a regular tiling with a fixed number 3. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 10 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #3HGSTC 4.4 Discussion Matching excerpt #QJAHFJ: Flow-guided texture synthesis algorithms [15], [16], [18] preserve large-scale features of the input texture but loose other texture properties, do not conform accurately to the input flow, and in some cases require a long pre-computation and several minutes per frame [15], [16]. We think that both algorithms have their benefits, depending on the application requirements and the input textures. 4. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #BWJ55J 3 OUR ALGORITHM #W6ZWF7 3.5 Reconstruction and Rendering #9GCRR9 3.5.3 Discussion Matching excerpt #R85SZH: accounted for. In this situation the memory and computational cost of the direct method become prohibitive. It gets worse for a large number of channels a_j . 5. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 1 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #T4ZQ7N 1. Introduction Matching excerpt #DRDV94: The terrain at the right of Figure 1 was generated using our method from the simple uplift map depicted on the left. The simulation process runs at interactive rates. While individual iterations provide a real-time preview enabling user interaction, the method converges to a final solution in less than two minutes. The interactive visual feedback enables users to interrupt the process before convergence if they need to change control parameters. 6. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results Matching excerpt #65MEBV: Our system is developed in C++ and uses OpenGL and GLSL for rendering. High quality image output were directly streamed to Vue 2015® ( http://www.e-onsoftware.com ). All examples in this paper were created on a desktop computer equipped with an Intel Core i7 CPU, clocked at 3GHz with 16GB of RAM. 7. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 9 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #KNTPE7 7.3. Comparison to Other Techniques Matching excerpt #2KNSHV: During each iterative design cycle the expert spent approximately 2 hours sculpting the riverbed, adjusting simulation parameters and running individual frame tests, and this was then followed by 9 hours spent executing the simulation. The latter included initializing particles, simulating particle stabilization to obtain a pseudo-periodic state for the river, and then generating 20 seconds of fluid animation. Simulation precision was set at 3cm, resulting in a total of 4.5 million particles and 200 million voxels. We tried reducing accuracy to cut down iteration times, but this introduced significant artifacts and the approximate and accurate water surfaces were so uncorrelated as to make authoring unworkable. Finalizing the scene required 15 iterations, each with 2 hours of scene editing and 9 hours of simulation, for a total of 165 hours. Our method represents a tremendous improvement in terms of production time and memory footprint. 8. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 8 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #FYBSSG 7.1. Performance Matching excerpt #9DU2N2: Table 2 reports timings and statistics for our method for the examples from this paper. Our implementation supports both real-time GPU and high-quality offline photon-traced rendering. The final model has a compact memory footprint: we are able to represent meandering rivers several kilometers in length with complex water effects in less than a few megabytes. Memory consumption is as low as 22 kilobytes for short rivers (of 50m) up to 2.7 megabytes for longer rivers ( \approx 4 km). Even without memory optimization, individual primitives range from 50 bytes to at most 90 bytes. 9. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 7 Context: #JJE8HN Procedural Riverscapes #9ZYJP2 6. Animated Procedural River Model #J5P42U 6.2. Operators Matching excerpt #46PS6V: In order to evaluate the surface characteristics at a given point \mathbf{p} , we query the construction tree and recursively traverse it to find local primitives that contribute to the water elevation f(\mathbf{p}, t) , velocity \mathbf{u}(\mathbf{p}, t) and effervescence s(\mathbf{p}, t) . On the CPU, the hierarchical nature of the blend-flow tree provides an implicit spatial acceleration structure. However, this is ill-suited to the graphics hardware, where we instead use a regular grid (as detailed in Section 7.1). Because the overlap between each primitive is calibrated by the river generation step, we achieve real-time performance when querying surface characteristics. 10. Source: The Topography of Minoan Peak Sanctuaries (#ARP5U7), A. A. D. Peatfield, p. 3 Context: #S9HW3P THE TOPOGRAPHY OF MINOAN PEAK SANCTUARIES Matching excerpt #R7HRDE: Reference to the varying altitudes of peak sanctuaries can be misleading. It is better to speak of distance relative to the nearest settlements, as they display a remarkable consistency. Most peak sanctuaries are within reasonable walking distance even of modern villages. There is no reason to suppose that Minoan settlements and villages were further away; indeed, Faure's surveys make a point of noting Minoan remains which are usually closer than modern settlements. Throughout their work, Faure and Rutkowski state walking times from villages up to the sites. The average quoted time is about one hour. While most of these times are quite possible, it should be understood that these are the optimum times, given the most favourable circumstances—that is, reasonable fitness, knowledge of the quickest route, good weather (not too hot or too windy), etc. It is only our speed-obsessed society that measures time so precisely; so, to people for whom walking was the usual mode of transport, a leisurely climb of several hours would not have seemed a great hardship. For modern mountain chapel festivals (particularly those dedicated to Aphendis Christos on 6 August each year), many people from all over the district gather to make the pilgrimage up the mountain. Only the very old, the very young, and the sick exclude themselves, but even then few people are inclined to race up the mountain. So it seems that a more realistic definition of an average climb is one that takes several hours. 11. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 8 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #XKG89F 3. Ocean dynamics simulation in shallow water #WB9J3L 3.2. Lagrangian approaches Matching excerpt #FK33M9: Adaptive schemes were proposed to reduce the number of particles and limit computation and memory costs for simulating large volumes of fluid. Desbrun and Cani [DC99] merge or split particles according to their density. The overall mass of the system is kept constant by re-computing particle masses as soon as they are subjected to one of these operations. In order to guarantee symmetric interactions between particles with different masses, a shooting / gathering scheme ensures that attraction or repulsion forces are equal. Although this approach reduces computation costs, visual artifacts can be observed during animations because of instantaneous merging or splitting of particles near the surface. The adaptive scheme proposed by Hong et al [HHK08] consists in varying the size and number of particles according to their position relative to a fixed set of layers defined by the user in a preprocessing step. Finally, Adams et al [APKG07] obtain adaptively sized particles by defining merging or splitting processes, depending on the distance to the viewer or to the surface. This ensures that visual artifacts are avoided near the surface since only particles deep inside the fluid can be modified. This approach was implemented on GPU by Yan et al [YWH + 09] to simulate breaking waves in real-time. 12. Source: A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics (#C4AY2M), B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato, p. 2 Context: #QZPELE A survey of ocean simulation and rendering techniques in computer graphics #JPY4VD 2. Ocean dynamics simulation in deep water #B9SCHY 2.1. Spatial domain approaches #W9ZUCV 2.1.2. GPU implementations Matching excerpt #GFZ39R: Series of periodic functions are particularly well suited to GPU computations, and in the last few years research works describing real time implementations have emerged. 13. Source: Procedural Content Generation via Machine Learning (PCGML) (#CQBDX4), Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass, p. 9 Context: #6EE2TX Procedural Content Generation via Machine Learning (PCGML) #6BC6KQ III. METHODS OF PCGML #PQ6DK6 D. Discussion of Approaches Matching excerpt #D6MLXP: It is hard to compare and contrast the different approaches’ performance as there is no agreed upon test for generator “goodness” (i.e. Playability of levels? Capturing of original levels’ style? etc.) and the different approaches do not list the time it takes to train or generate a level. However, a few general statements can be made. The LSTM approaches [21], [42] will nearly certainly take more time to train and generate than the MdMC approaches. Both generate one tile at a time, but the LSTM approach inherently requires more computation to generate. Furthermore, the MdMC can be trained in a single pass over the levels, but it is highly unlikely that training of the LSTM can be stopped after a single training epoch. We note that the Matrix Factorization approaches have potentially the worst memory usage, as all levels must be held in memory at once. In practice, given the relatively small datasets, this is unlikely a concern, but could pose an issue for situations that call for much larger or many more levels. The back-propagation neural network approaches assume a fixed architecture and as such are the only training size independent approach. In practice, the generator size for the other approaches (MdMC, latent style-graph, evolved neural network, matrix factorized) are likely to be smaller than the back-propagated neural network, but there are no guarantees. A similar concern for the latent style-graph approach is that generation time is dependent on the complexity of the training data (more dense, less regular levels will have more latent nodes and subsequently more relative position edges) unlike the other approaches which perform the same generation act at each step of generation. 14. Source: Procedural Content Generation via Machine Learning (PCGML) (#CQBDX4), Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass, p. 8 Context: #6EE2TX Procedural Content Generation via Machine Learning (PCGML) #6BC6KQ III. METHODS OF PCGML #FFTSJC C. Graphs #7EXCGN 1) Expectation Maximization Matching excerpt #MCNRDS: Individual parsed frames could then combine to form chunks of level geometry, which served as the input to the model construction process. In total Guzdial and Riedl made use of nine gameplay videos for their work with Super Mario Bros. , roughly 4 hours of gameplay in total. 15. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 6 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #XHMJUD 7. Conclusions Matching excerpt #SJKG3H: The complex light-related effects like caustics, refractions and reflections have been addressed using raycasting techniques which ensure a more realistic simulation and the constraint of the algorithms to be in screen-space keeps the quantity of memory used low enough. 16. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 7 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #SZAWPC 8 Results Matching excerpt #HYEVFY: We have attempted to recreate a model of an existing island using our approach as shown in Fig. 19. Having a given example, we have defined interactively the main domain and sketched the principal river streams. The system then automatically completed the terrain. The results are visually similar though they are not exact because of the stochastic nature of our algorithm. The overall time necessary to create the input slope maps was less than five minutes. Default parameters were used to generate these images. 17. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 9 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Matching excerpt #MAU7Q5: GPU simulations of the stream power law [SPF*23] might in some cases be faster than our method even though they require many iterations. There are, however, caveats inherent to the GPU architecture that prevent them from being used in all cases. First, GPU simulations use an explicit time-stepping scheme, which bounds the admissible time step and can yield a prohibitive number of iterations for small \delta x . Second, depressions in the topography lead to local minima that interrupt the river network. Similarly to other CPU algorithms, we use depression breaching [CBC*16, SD21] to enforce the continuity of the river across the depressions. The absence of such an algorithm on GPU implementations is particularly visible in cases where we erode without uplift - all the water is trapped within the depressions and the erosion only occurs in the vicinity of the topographic gradients. 18. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results Matching excerpt #YRYPF7: We prototyped our algorithm in Python with numpy (the code will be released with the paper). Our algorithms require several tree operations that are not trivially parallelizable, therefore we improved the performance of Python loops with just-in-time compilation provided by the package numba . We used an Intel Xeon E5-2650 v4 CPU with 64 GB RAM to compute all the results and timings reported in this section. We interfaced our code with Houdini [Sid23] to showcase the use of our approach in an interactive editing session (see the companion video) and we use Terragen [Sof23] to produce the final renderings. The parameter values used throughout our experiments are the ones shown in Table 1 and the uplift is constant, unless otherwise mentioned. The code, Houdini file, and heightfields are available at https://gitlab.inria.fr/landscapes/analytical-terrains . 19. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 10 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #66SM5X 7 Discussion and Future Work Matching excerpt #CK2TWF: The primary benefit of the proposed algorithm is not improved lap time performance over the nonlinear algorithm but rather a radical improvement in computational simplicity and speed. Each two-step iteration of the full course takes only 26 seconds on an Intel i7 processor, whereas the nonlinear algorithm from [5] typically runs over the course of several hours on the same machine. The most significant computational expense for the proposed algorithm is solving the convex curvature minimization problem for all 1843 discrete time steps T over the 4.5 km racing circuit. 20. Source: A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories (#G3TBNG), J. Christian Gerdes, John Subosits, Nitin R. Kapania, p. 10 Context: #AP8Y4X A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories #66SM5X 7 Discussion and Future Work Matching excerpt #MR4QDN: to run at the same sample time as the vehicle controller. Instead, the planner would operate on a separate CPU and provide a velocity profile and racing line for only the next 1-2 kilometers of the race track every few seconds, or plan a path for the next several hundred meters within a second. 21. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 51 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #9WNHGK 5.7.5. Field Reconnaissance #XG25M6 5.7.5.2. Designed Control Points #AG3WMA 5.7.5.2.5. Orientation/Aspect Matching excerpt #BMQNV9: Taking advantage of the landform's aspect can greatly improve the availability and performance of the trail and the comfort of the trail user. 22. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 1 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #8AC6U8 1. Background Matching excerpt #DAJKCD: DEMs have increased in resolution from thirty-plus meters in the recent past to the sub-meter resolutions becoming available today. Increasing resolution has led to increased data sizes: current data sets are on the order of gigabytes and increasing, with billions of data points. While computer processing and memory performance have increased appreciably during this time, legacy equipment and algorithms suited to manipulating smaller DEMs with coarser resolutions make processing these improved data sources costly, if not impossible. Therefore, improved algorithms are needed. 23. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 9 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #MCXU94 5. Analysis Matching excerpt #F37J93: Based on these tests, Luengo Hendriks recommended the implicit heap as the best choice for a priority queue: it used the least memory of all the algorithms tested and operated the fastest, though it does use a strict weak ordering. Hierarchical heaps and ladder queues operated faster for very large data sets (greater than 10^6 elements), but used significantly more memory. 24. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 1 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #Z3MQUT 2. Alternative Algorithms Matching excerpt #GDQUCW: Arge et al. [2003] describes a specialized O(n \log_2 n) procedure to perform watershed labeling, determine flow directions, and calculate flow accumulation on massive grids in situations where I/O must be minimized. Although parts of this procedure share sufficient similarities with Priority-Flood to be considered related, the combinations of algorithms used and the way in which they are specialized place it outside the scope of this paper. It is expected that the algorithm by Arge will run slower than that described here due to the greater overhead involved in explicit data management; however, this efficiency of memory may allow the algorithm by Arge to run better in situations where memory is limited. 25. Source: Real-time Rendering of River Networks (#MVUJ8Z), Quintijn Hendrickx, Rafael Bidarra, Ruben M. Smelik, p. 0 Context: #BTQCB6 Real-time Rendering of River Networks Matching excerpt #MSQQ8G: A commonly used method to visualize Bézier curves is to sample along the curve at a fixed rate, and then tessellate these samples into a geometric structure. However, to achieve smooth results, many samples are needed, resulting in a high vertex count. Because this is often not desirable in real-time rendering, we render the Bézier curves with bounding quads using only four vertices per curve. An implicitly defined distance field is used to project each pixel in the quad onto the nearest point on the curve. Using only quadratic order Bézier curves allows us to define the distance field as a function of the Bézier control points, which does not require any iterative algorithms. As a result this function is, due to its parallel nature, particularly suited for being evaluated on the GPU. Because of the low vertex count, no LOD techniques are necessary for large scale river networks, and rendering performance depends mostly on the total surface of visible water in screen-space. 26. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance Matching excerpt #THUW3K: Our performance tests were executed on a computer equipped with an Nvidia RTX A6000 GPU with 48GB of memory and used 20 cores of an Intel Xeon Gold CPU clocked at 2.10GHz with 128GB RAM. 27. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 1 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #L8RWX4 1. Introduction Matching excerpt #8QGM6W: Finally, we benchmark our solution against CPU and distributed computing variants, as well as previous GPU solutions. Our GPU implementation for flow routing provides a 5\times speed up on a 1024 \times 1024 resolution terrain over competing GPU implementations, while depression routing gains 34\times to 52\times speedup compared to parallel CPU approaches, depending on the variant of our algorithm. This improvement in performance enables applications in natural phenomena including river and lake modeling, terrain erosion, and sediment deposition, to cross the threshold and achieve interactive response times, especially when flow and depression routing need to be recomputed over many iterations. 28. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #C5KA2A 7.1. Implementation Matching excerpt #YGVPCZ: In terms of optimization, we reduce memory allocations and copying and prevent CPU-GPU communication in the control flow. We found that allowing the GPU to run for the maximum number of iterations ( e.g. , \log_2 n for flow routing) was more efficient than checking for early convergence. The only exception is in depression routing, where we halt the algorithm when no depressions remain. 29. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance Matching excerpt #KB2K8H: In this section, we compare our approach against other parallel GPU and CPU implementations of flow and depression routing. 30. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #B5KJYH 8. Conclusion Matching excerpt #292LBY: In comparative terms, our GPU implementation for depression routing outperforms an optimized parallel CPU algorithm by 34\times to 52\times on a 1024^2 resolution terrain, depending on the strategy for recipient correction. We also improve on previous GPU methods for flow routing [Bar19, SPF + 23] by a factor of 5\times . 31. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance #SKBWC5 7.3.1. Spatial scaling Matching excerpt #22P7V2: We show in Figure 16 the relationship between performance and terrain size, for resolutions ranging (logarithmically) from 64 \times 64 to 8192 \times 8192 . We observe that parallelism is limited by the maximum simultaneous threads in our GPU model at around 8192 \times 8192 , where performance follows a near-linear trend. 32. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 1 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #L8RWX4 1. Introduction Matching excerpt #FREQHT: While previous work has addressed both flow and depression routing, with optimal solutions for the CPU [CBB19], and a separate focus on distributed computing [Bar16], existing solutions for the GPU [Bar19, SPF + 23] are inefficient for flow routing and typically do not consider depression routing at all. 33. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 2 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #KDKKZ3 2. Related Work Matching excerpt #RV854H: There have been previous efforts to accelerate this problem by exploiting parallelism, either on CPU [Bar17] or GPU [Bar19, SPF 23 ]. These approaches parallelize the propagation of flow among independent flow paths but do not accelerate propagation within the paths themselves, leading to \mathcal{O}(l) iterations, where l \approx \sqrt{n} is the length of the longest channel and n the number of cells. In contrast, our approach requires \mathcal{O}(\log(n)) iterations. 34. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #B5KJYH 8. Conclusion Matching excerpt #BDZQP4: In terms of raw performance, our GPU implementation executes in under 55ms on terrains up to 4096^2 sample resolution. This opens up new opportunities and research avenues for the future use of flow and depression routing in an interactive context. Further work on our algorithm is also required to reach more general applications, for instance by allowing for multiple recipients (Multiple Flow Directions). 35. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 2 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #KDKKZ3 2. Related Work Matching excerpt #XA7N24: Barnes et al. [BLM14] proposed the use of a priority queue in progressively flooding from the boundary to the interior, filling depressions in the process, leading to a \mathcal{O}(n \log(n)) algorithm. Subsequent work reduced dependence on the priority queue data structure [ZSF16, WZF18] and investigated CPU parallelization [DLM11, Bar16, ZLFS17, BCW20]. Ultimately, the priority queue was dispensed with altogether by exploiting the observation that depression routing is an instance of a Minimum Spanning Tree search, which can be found in linear time on a planar graph [CBB19]. We build on this idea and adapt it to the GPU. 36. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #B5KJYH 8. Conclusion Matching excerpt #CADAM6: Algorithms for evaluating water flow over terrains are a staple of geo-analysis, with applications in computer graphics and beyond. Consequently, any improvement in their run-time performance is worth serious consideration. In this paper, we provide improved algorithms for solving both flow and depression routing problems, with, respectively, O(\log n) and O(\log^2 n) complexity for a terrain with n nodes. This is an improvement on previous methods, which usually require as many iterations as the length of the longest river ( \sim \sqrt{n} ). Most importantly, we are the first to propose a GPU solution for both flow and depression routing. 37. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Matching excerpt #YVMH2N: Interactive landscape authoring. To demonstrate the general applicability of our algorithms we provide extracts from an interactive landscape authoring session in Figure 7 and the accompanying video. Here, user-guided simulation is applied to a 512 \times 512 terrain, which, thanks to GPU acceleration combined with implicit time-stepping, requires only 10 iterations and 0.1s to capture 700,000 years of geomorphological evolution. For comparison, a CPU implementation [CBC*16] requires 2.6s. The user first defines the primary mountains by progressively painting on an uplift map, and can then freely change simulation parameters (here the deposition constant). Finally, the user advances the age of the mountain by increasing the number of iterations to 100, producing the result on the far right in 0.7 seconds. Note that lakes disappear over time as a consequence of filling by deposition and uplift, combined with erosion, which gradually removes the obstructions between them. 38. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 7 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #34USBX 6. Application to landscape simulation Matching excerpt #V92Q79: Here we show how we apply flow and depression routing to accelerate landscape simulation, with use cases in river and lake modeling, terrain erosion, and ecosystem simulation. In particular, our GPU algorithms together provide the discharge necessary for erosion simulation. Furthermore, they enable a novel GPU-based solution for implicit time-stepping of erosion using the Stream Power Law, which we combine with a simulation of sediment deposition. 39. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results Matching excerpt #3Q9YB8: In this section, we show the results of our method applied to the use cases detailed in section 6, and then demonstrate this performance against competitor methods. 40. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance #6RG72Z 7.3.2. Flow routing Matching excerpt #35RRR7: Topographic variation does not have a significant impact on the performance of flow routing, so we benchmark flow routing solely on real terrains. We compare our algorithm against: 41. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 6 Context: #RNVWWR Water Surface Wavelets #MU7P6S 5 ALGORITHM SUMMARY Matching excerpt #ES924P: This section gives an overview of the steps necessary to implement our algorithm. Our project webpage 1 also provides example code for a straightforward (CPU-only) implementation of the algorithm as well as an executable file which demonstrates our GPU-optimized implementation. 42. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #DWR9FU: The performance of our method comes from a few sources. First, the fact that \mathcal{A} is low resolution allows us to discretize it on a coarse grid, so we don't need an expensive simulation of \mathcal{A} to get detailed visual results. We can exploit this coarse grid by either using a huge simulation domain (as in the above example), or by using very few degrees of freedom to make the simulation faster. Next, the pre-computed profile buffer \Psi saves us two orders of magnitude in computation by reducing a 2D integral to a 1D integral with a texture lookup. Lastly, both the simulation and the wave height evaluation are embarrassingly parallel operations spread out among many points in space, so they greatly benefit from GPU acceleration. 43. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 6 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #KQNQXW 4.3 Height field evaluation Matching excerpt #82HGFN: The pre-computation of the profile buffer in Equation 21 is largely responsible for the performance of our method. For comparison, the evaluating \eta at all points in space using the naive 2D integral in Equation 19 costs O(K_\eta \Theta_\eta X_\mathcal{A}^2) operations, where X_\mathcal{A}^2 is the total number of spatial locations where \eta is computed. Our speedup using the profile buffer reduces this computation by two orders of magnitude to O(K_\eta + \Theta_\eta X_\mathcal{A}^2) . Distributing this computation over G GPU cores reduces the cost further to O(K_\eta + \Theta_\eta X_\mathcal{A}^2/G) . In practice, the introduction of the profile buffer in our implementation raised the frame rate from 1.8 to 275 – a speed-up factor of 233 for evaluating \eta . 44. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #9AHGRG: Varying these parameters has different effects on the visual results and performance of our method, and we explore each of them in our supplementary video. The number of \mathcal{A} samples in our simulation depends linearly on the resolution of our 4\text{D } X_{\mathcal{A}} \times X_{\mathcal{A}} \times \Theta_{\mathcal{A}} \times K_{\mathcal{A}} simulation grid, so doubling the resolution of any dimension will roughly increase the memory and the runtime by a factor of 2. Increasing the spatial resolution X_{\mathcal{A}} will allow the wavefronts to exhibit a higher curvature, allowing more detailed interactions with highly curved boundaries. Figure 8 shows the effect of X_{\mathcal{A}} on the simulation quality. Increasing the angular resolution \Theta_{\mathcal{A}} allows a more precise behavior in each direction. Increasing the wavenumber resolution K_{\mathcal{A}} allows more detailed dispersion of wave groups (different amplitude groups travel at different speeds). We show an example with K_{\mathcal{A}} = 4 simulated wave groups in Figure 9 and in our video, which shows more accurate wave group dispersion but roughly quadruples the run time (drops the frame rate from 70fps to 20fps). 45. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 7 Context: #Q94AYK IV HARMONY-SEEKING COMPUTATIONS #W2TBVW The Essence Of Harmony-Seeking Computation #VRE3KE Example 1: Embryogenesis Matching excerpt #S3DMND: Consider an example of embryogenesis, a growing mouse foot. Here is how it grows in four days, from the 12 th day to the 15 th day. You see that each stage contains within it some structure that is defined, and some that is for the time being a vague and fuzzy mass of jelly, which anticipates the shape of the next step, which then consolidates and solidifies what was merely latent only hours before. 46. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 6 Context: #57PDWB Interactive Procedural Street Modeling #ZN73JY 7 Results Matching excerpt #2L8GVV: To demonstrate the capabilities of our approach we show a number of street graphs generated using our system. Figure 16 shows a section of downtown Taipei which we have modeled. In Figure 17, a section of the Willamette River in Portland, OR is modeled. A road network for Manhattan is shown in Figure 18. Note that our goal is to generate maps inspired by real world maps, but not to exactly replicate the existing cities. In our experiments, a city with reasonable complexity can be modeled within five minutes, such as the fictional city in Figure 1, and the cities in Figures 16 and 17 took about five minutes for the main layout, but required an additional thirty to sixty minutes to fine tune the details and to experiment with different designs. The final images of three-dimensional geometry were created using RenderMan with ambient occlusion. See Figure 19 for four frames of a fly through shown in the accompanying video. 47. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 12 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #GL8ZA2 4 Design, Methodology, and Implementation #5W8C4J 4.4 Procedural Terrain Generation #VN6M88 4.4.5 Clean-up of Procedural Terrain Matching excerpt #Z2L9FU: For smooth performance and optimal use of memory, every generated ground tile checks the player's current position and destroys itself after the player has safely moved ahead. This is required because the terrain is generated continuously, and keeping every old tile in the scene would slowly increase the number of active objects without adding anything useful to the current gameplay. 48. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 8 Context: #JCB5RE Advected river textures #HMVN46 Results Matching excerpt #PRVSL6: Level of Detail provides notable performance improvements as can be seen in Table 1. Even the modest LOD optimizations we have implemented make a significant difference to the frame rate and to the number of polygons rasterized per second. All screenshots and timings were produced on an off-the-shelf dual-core Athlon XP 3800+ computer with an nVidia 8600GT graphics card and 4GB RAM. However, the code has not been parallelized or GPU optimized, meaning that only one of the two cores on the CPU has been directly used. Most of example river beds used in this paper have been imported from DEM files of real rivers. 49. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 4 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #SR7CUB 5.1. Path segment masks Matching excerpt #N6Y9UZ: Since explicitly storing all the arcs between grid points would be memory consuming, we propose to store the connectivity information between grid points using a set of path segment masks, denoted as \mathcal{M}_k (Figure 8). 50. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 7 Context: #B9LYTR Scalable real-time animation of rivers #LQXUW2 6. Implementation and results Matching excerpt #R825Y2: pend on the complexity of the scene. In the test, we achieved real-time performance even in the worst case where the projected surfaces occupy the whole window. Certainly, the performance will decrease if we decrease the Poisson-disk radius. However, a moderate value as we used in this test is sufficient due to the adaptivity of the particles and the sprite-based rendering scheme. Approximate matches 1. Source: Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning (#869NHK), Ian Parberry, Jennifer R. Alford, Mary Yingst, p. 5 Context: #5R6DEX Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning #LP9TTY Results Score: 0.023 Related excerpt #V5XDSY: We performed some experiments to obtain a preliminary benchmark for the extra computation load required by our new halftoning technique (Figure 7(c)) to the traditional texturing technique (Figure 7(a)). We ran both algorithms for five minutes using NVidia Composer, using FRAPS to measure average frames-per-second. The scene rendered in all experiments is shown in Figure 8. The results are shown in Table 1. We conclude that the extra load on the video appears to be less than 3% higher than traditional texture-fading techniques, which is negligible. 2. Source: Real-time Breaking Waves for Shallow Water Simulations (#8SERGP), Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm, p. 6 Context: #FA7BE4 Real-time Breaking Waves for Shallow Water Simulations #CC4RWZ 8 Results Score: 0.024 Related excerpt #RTYCL9: The results discussed in this section were calculated on a common PC with an Intel Core 2 Duo CPU (2.13 GHz), and a Nvidia Geforce 7950 GPU. As our implementation is not yet parallelized, it only makes use of one of the cores of the CPU. The actual frame rates of the different cases are given in Table 2. All test cases use between 160k and 200k grid points, and run with 40 to 75 frames per second, including rendering. The distribution of the computational time for the different parts of our algorithm can be found in Table 1. For this measurement a typical wave, as shown in Figure 6, was simulated. Overall, the fluid simulation amounts for 80% of the run time, while the rendering and overhead introduced by the graphics engine require the remaining 20%. Roughly half of the simulation time is spent on the shallow water simulation itself, while the wave simulation algorithm requires circa one fourth of the time. The creation of the surface mesh and the computation of the normals again requires roughly one fourth of the computations. 3. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON Score: 0.022 Related excerpt #B3QB7D: All pictures and timings in this paper and in the companion video 2 were computed on an Intel Core i7, running at 2.67 GHz, with an Nvidia GeForce GTX 275. 4. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 7 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Score: 0.018 Related excerpt #FCMCYQ: Timing results for a zoom in the fire example, using a fixed-size viewport ( 256 \times 256 ). 5. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Score: 0.014 Related excerpt #FB5X95: For Fig. 4, 6, 7, 8 and most of the video sequences, we used a fluid covering the entire picture, an output texture size of 512 \times 512 , and 300 grids of 8 \times 8 vertices (including grids being faded in or faded out). The timings correspond to the fire example (Fig. 4). 6. Source: Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field (#92XRH7), Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch, p. 6 Context: #5948CH Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field #MUN6QE 4 RESULTS AND COMPARISON #6B4N32 4.2 Performance and Timings Score: 0.012 Related excerpt #VDK3Z2: The reasons for the difference of performance are twofold. First, we are in the worst case for indirect reconstruction and the best case for the direct reconstruction: the entire fluid domain is displayed on screen, and we use a very simple shader. Second, our GPU implementation of virtual textures is not optimized: we simply implemented a regular tiling with a fixed number 7. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 6 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results #2RYGP7 6.3. Performance Score: 0.017 Related excerpt #D6XHTB: Table 1 reports the performance of our method as a function of the number of sampling points. Although we did not fully optimize the implementation, our method provides interactive feedback at every time step which enables us to visualize a simulation at interactive rates and to tune parameters. 8. Source: Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion (#96ZMGK), Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin, p. 5 Context: #A48PSA Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion #A8NK92 6. Results Score: 0.015 Related excerpt #65MEBV: Our system is developed in C++ and uses OpenGL and GLSL for rendering. High quality image output were directly streamed to Vue 2015® ( http://www.e-onsoftware.com ). All examples in this paper were created on a desktop computer equipped with an Intel Core i7 CPU, clocked at 3GHz with 16GB of RAM. 9. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 8 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #FYBSSG 7.1. Performance Score: 0.024 Related excerpt #9DU2N2: Table 2 reports timings and statistics for our method for the examples from this paper. Our implementation supports both real-time GPU and high-quality offline photon-traced rendering. The final model has a compact memory footprint: we are able to represent meandering rivers several kilometers in length with complex water effects in less than a few megabytes. Memory consumption is as low as 22 kilobytes for short rivers (of 50m) up to 2.7 megabytes for longer rivers ( \approx 4 km). Even without memory optimization, individual primitives range from 50 bytes to at most 90 bytes. 10. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 9 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #KNTPE7 7.3. Comparison to Other Techniques Score: 0.019 Related excerpt #2KNSHV: During each iterative design cycle the expert spent approximately 2 hours sculpting the riverbed, adjusting simulation parameters and running individual frame tests, and this was then followed by 9 hours spent executing the simulation. The latter included initializing particles, simulating particle stabilization to obtain a pseudo-periodic state for the river, and then generating 20 seconds of fluid animation. Simulation precision was set at 3cm, resulting in a total of 4.5 million particles and 200 million voxels. We tried reducing accuracy to cut down iteration times, but this introduced significant artifacts and the approximate and accurate water surfaces were so uncorrelated as to make authoring unworkable. Finalizing the scene required 15 iterations, each with 2 hours of scene editing and 9 hours of simulation, for a total of 165 hours. Our method represents a tremendous improvement in terms of production time and memory footprint. 11. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 7 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results Score: 0.017 Related excerpt #YZRYCS: We implemented our method in C++. Experiments were performed on a desktop computer equipped with Intel ® Core i7, clocked at 4GHz with 16GB of RAM, and an NVidia GTX 970 graphics card. The output of our system was directly streamed into Vue Xstream ® to produce photorealistic images. 12. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 5 Context: #JJE8HN Procedural Riverscapes #TFD8TX 5. River Network Amplification #AZ7MGY 5.4. Rosgen Scene Statistics Score: 0.012 Related excerpt #YCESD5: Table 1 reports the parameters and primitives statistics for Figures 14. The generation time of the two construction trees (riverbed and water) is negligible for these scenes (around 15ms). The number of primitives is related to the average density, which has been set in these examples to a sample every 50cm. It is possible to optimize the construction trees by grouping equivalent parameter primitives into a larger one. 13. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 5 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #GKHL8Q 6. Results and Discussion Score: 0.029 Related excerpt #A3VUS3: We have tested the previous algorithms on an Intel Core2Duo E8400 with 4GB of RAM and a Nvidia GTX280 running Ubuntu 11.10. The resulting averaged timings of the caustics and refraction/reflection algorithms are shown in Table 1, as these are the ones that tax more on the GPU by the use of raycasting. 14. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 6 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #GKHL8Q 6. Results and Discussion Score: 0.016 Related excerpt #CLEMXK: For the caustics, as shown in Table 1 and concluded in [3], the performance of the caustics algorithm depends primarily on the size of the grid of photons, but in our case also on the direction of the light, which can cause more photons to miss the light space raycast and use the second camera space one, thus increasing the number of computations and texture fetches needed to try to find a final position for them. Also, as the raycasting is done in the vertex shader it is further slowed down because of the increased penalty of texture fetches in that shader stage. Although a direct comparison with [3] is difficult because of the different hardware used, they reported to achieve about 200fps with a 128 2 photon grid, which is the same that saying that each frame costs 5ms to compute. With newer hardware but the dual light and camera space raycasts we propose, the cost of computing caustics is, in our case, below 2ms for the same configuration. 15. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 6 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #GKHL8Q 6. Results and Discussion Score: 0.015 Related excerpt #68CY35: were captured with the fluid covering the whole viewport, and even in this case, the whole algorithm does not cost more than 10ms for a reasonably sized viewport. In perspective, [23] made total internal refraction available although without surface reflection which, in the best case, reported 138fps, i.e., 7.24ms per frame on a Nvidia 8800 GTX, using only one bounce for internal refraction on a viewport of 512 2 . Although our GPU is newer than theirs, in a similar scenario, we achieve less than half their time with both refraction and reflection. 16. Source: Real-time Rendering of Enhanced Shallow Water Fluid Simulations (#CWC7H9), Antonio Susín, Jesús Ojeda, p. 6 Context: #3XLN3C Real-time Rendering of Enhanced Shallow Water Fluid Simulations #GKHL8Q 6. Results and Discussion Score: 0.012 Related excerpt #HHS3QR: The performance of the refraction/reflection algorithm is quite variable, it depends on the size of the viewport as well as the coverage of the fluid in screen: the more visible pixels, the more rays are cast. For fair comparison, the results in Table 1 17. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 7 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #SZAWPC 8 Results Score: 0.019 Related excerpt #4RJDJ6: We have implemented our system in C++. Experiments have been performed on a desktop computer equipped with Intel ® Core i7, clocked at 3 GHz with 16GB of RAM. The output of our system was directly streamed into MentalRay ® to produce photorealistic images (Fig. 20, 22). 18. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 7 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #SZAWPC 8 Results Score: 0.014 Related excerpt #Y6MAJM: Performance. Our method generates a vector-based representation of large terrains (several hundreds of square kilometers) in a few seconds (Table 2) and, though it is based on principles from hydrology, it does not rely on complex numerical physics-based simulations. The novel description of the generated terrain 19. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 8 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results Score: 0.015 Related excerpt #YRYPF7: We prototyped our algorithm in Python with numpy (the code will be released with the paper). Our algorithms require several tree operations that are not trivially parallelizable, therefore we improved the performance of Python loops with just-in-time compilation provided by the package numba . We used an Intel Xeon E5-2650 v4 CPU with 64 GB RAM to compute all the results and timings reported in this section. We interfaced our code with Houdini [Sid23] to showcase the use of our approach in an interactive editing session (see the companion video) and we use Terragen [Sof23] to produce the final renderings. The parameter values used throughout our experiments are the ones shown in Table 1 and the uplift is constant, unless otherwise mentioned. The code, Houdini file, and heightfields are available at https://gitlab.inria.fr/landscapes/analytical-terrains . 20. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 9 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Score: 0.015 Related excerpt #EQTM8J: Table 2 shows the time required to reach these results for different resolutions. We keep the total extent of the terrain constant, therefore decreasing \delta x from 50 to 25 and 12m. We observe that we need to decrease the timestep proportionally to the cell size to prevent artifacts in the simulation, therefore the number of iterations increases in both the fixed point (43, 82, 156 iterations) and the simulation (230, 460, 980 iterations). In contrast, the multigrid methods only require the addition of one level of down/up-sampling, which leads to a complexity almost linear to the number of cells. We additionally show the performance of the optimization algorithm, in the worst case, which is when we adjust the elevations to the initial drainage (disabling the iterative approach). In practice, we observed that the optimization cleans all visible discontinuities after 50 iterations for all resolutions. Overall, we did not observe significant changes in performance with other erosion parameters. 21. Source: Physically-based analytical erosion for fast terrain generation (#DWXKYQ), Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer, p. 9 Context: #JDHNVB Physically-based analytical erosion for fast terrain generation #PZFF56 7. Results #4Q9G6F 7.1. Validation and comparison Score: 0.015 Related excerpt #MAU7Q5: GPU simulations of the stream power law [SPF*23] might in some cases be faster than our method even though they require many iterations. There are, however, caveats inherent to the GPU architecture that prevent them from being used in all cases. First, GPU simulations use an explicit time-stepping scheme, which bounds the admissible time step and can yield a prohibitive number of iterations for small \delta x . Second, depressions in the topography lead to local minima that interrupt the river network. Similarly to other CPU algorithms, we use depression breaching [CBC*16, SD21] to enforce the continuity of the river across the depressions. The absence of such an algorithm on GPU implementations is particularly visible in cases where we erode without uplift - all the water is trapped within the depressions and the erosion only occurs in the vicinity of the topographic gradients. 22. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 9 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #PD667Q 6. Empirical Testing Score: 0.016 Related excerpt #XR7Z7G: An implementation of the improved Priority-Flood was tested against an implementation of the unimproved Priority-Flood; both implementations are included in the Supplemental Materials. The C++ STL priority queue was chosen to simplify programming and the tests were conducted on floating-point DEMs using a 64-bit Intel Xeon X5560 2.8GHz 8192kB cache processor and 24GB of RAM. The results are shown in Fig. 3. LIDAR-based 3m DEMs of 44 counties in Minnesota were tested, comprising an area of approximately 72,500km 2 —one-third of the state—with approximately 111,111 cells per square kilometer for a total of approximately 8 \cdot 10^9 cells; the average county size was 1,741km 2 ( 2 \cdot 10^8 cells). The improved Priority-Flood Algorithm out-performed the unimproved algorithm in every case. The average speed-up over all the counties tested was 16.8%, while the median was 12.5%. The maximal speed-up was 37.2%. 23. Source: Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (#MTDKDE), Clarence Lehman, David Mulla, Richard Barnes, p. 10 Context: #XJ3LVD Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models #PD667Q 6. Empirical Testing Score: 0.012 Related excerpt #RFP6GK: As shown in Fig. 4, the parallel implementation of the Planchon–Darboux Algorithm required six processors in order to process Test Site A in the same time as the improved Priority-Flood algorithm did with one processor. The speed difference was even more striking in the case of Test Site B, where 11 processors were required. 24. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance Score: 0.03 Related excerpt #THUW3K: Our performance tests were executed on a computer equipped with an Nvidia RTX A6000 GPU with 48GB of memory and used 20 cores of an Intel Xeon Gold CPU clocked at 2.10GHz with 128GB RAM. 25. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance #SKBWC5 7.3.1. Spatial scaling Score: 0.027 Related excerpt #22P7V2: We show in Figure 16 the relationship between performance and terrain size, for resolutions ranging (logarithmically) from 64 \times 64 to 8192 \times 8192 . We observe that parallelism is limited by the maximum simultaneous threads in our GPU model at around 8192 \times 8192 , where performance follows a near-linear trend. 26. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #B5KJYH 8. Conclusion Score: 0.026 Related excerpt #292LBY: In comparative terms, our GPU implementation for depression routing outperforms an optimized parallel CPU algorithm by 34\times to 52\times on a 1024^2 resolution terrain, depending on the strategy for recipient correction. We also improve on previous GPU methods for flow routing [Bar19, SPF + 23] by a factor of 5\times . 27. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 9 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Score: 0.025 Related excerpt #44JH58: Our method scales to higher-resolution landscapes, as illustrated in Figure 8 for a 2048 \times 2048 terrain with 300,000 simulated years (200 iterations) generated in under 10 seconds. 28. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 1 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #L8RWX4 1. Introduction Score: 0.025 Related excerpt #8QGM6W: Finally, we benchmark our solution against CPU and distributed computing variants, as well as previous GPU solutions. Our GPU implementation for flow routing provides a 5\times speed up on a 1024 \times 1024 resolution terrain over competing GPU implementations, while depression routing gains 34\times to 52\times speedup compared to parallel CPU approaches, depending on the variant of our algorithm. This improvement in performance enables applications in natural phenomena including river and lake modeling, terrain erosion, and sediment deposition, to cross the threshold and achieve interactive response times, especially when flow and depression routing need to be recomputed over many iterations. 29. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance #6RG72Z 7.3.2. Flow routing Score: 0.024 Related excerpt #D6YHUW: Note that neither of these algorithms provides a solution for depression routing on the GPU. The results are illustrated in Figure 18, with an average speed-up of 10\times , 5\times , 3\times and 3\times against [Bar19] for each target resolution, respectively. 30. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #B5KJYH 8. Conclusion Score: 0.023 Related excerpt #BDZQP4: In terms of raw performance, our GPU implementation executes in under 55ms on terrains up to 4096^2 sample resolution. This opens up new opportunities and research avenues for the future use of flow and depression routing in an interactive context. Further work on our algorithm is also required to reach more general applications, for instance by allowing for multiple recipients (Multiple Flow Directions). 31. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Score: 0.018 Related excerpt #M53PTE: Another consideration is the acceleration afforded by the larger timesteps of our implicit solution. We show in Figure 13 that a 512 \times 512 terrain with \Delta x = 32\text{m} obtained with an explicit scheme ( \Delta t = 1,000 years) is visually similar to the result of our implicit solution ( \Delta t = 20,000 years). Our implicit scheme allows an increase of the timestep by a factor of 20, which reduces, by the same factor, the iterations needed to achieve the same total geological timespan. With such timesteps, generating a 10 million year-old landscape requires 7.2s and .5s, for the explicit and our implicit scheme, respectively. Note that larger implicit timesteps are unconditionally stable, and only diverge slightly from the explicit solution. Note that explicit and implicit schemes in general do not yield identical solutions as they accumulate discretization error differently. 32. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #C5KA2A 7.1. Implementation Score: 0.018 Related excerpt #YGVPCZ: In terms of optimization, we reduce memory allocations and copying and prevent CPU-GPU communication in the control flow. We found that allowing the GPU to run for the maximum number of iterations ( e.g. , \log_2 n for flow routing) was more efficient than checking for early convergence. The only exception is in depression routing, where we halt the algorithm when no depressions remain. 33. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 8 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Score: 0.016 Related excerpt #YVMH2N: Interactive landscape authoring. To demonstrate the general applicability of our algorithms we provide extracts from an interactive landscape authoring session in Figure 7 and the accompanying video. Here, user-guided simulation is applied to a 512 \times 512 terrain, which, thanks to GPU acceleration combined with implicit time-stepping, requires only 10 iterations and 0.1s to capture 700,000 years of geomorphological evolution. For comparison, a CPU implementation [CBC*16] requires 2.6s. The user first defines the primary mountains by progressively painting on an uplift map, and can then freely change simulation parameters (here the deposition constant). Finally, the user advances the age of the mountain by increasing the number of iterations to 100, producing the result on the far right in 0.7 seconds. Note that lakes disappear over time as a consequence of filling by deposition and uplift, combined with erosion, which gradually removes the obstructions between them. 34. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance #LVVQ29 7.3.3. Depression routing Score: 0.015 Related excerpt #GPHPTV: The comparative performance of these depression routing algorithms is shown in Figure 17. In particular, we note that our algorithms outperform previous work by one order of magnitude for terrains up to a resolution of 2048 \times 2048 . However, this gap narrows somewhat for the largest terrains, which indicates non-favorable scaling at the upper end. Also worth noting is that, with the exception of flat terrains, the comparative advantage of using depression jumping increases for larger terrains. 35. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance Score: 0.015 Related excerpt #KB2K8H: In this section, we compare our approach against other parallel GPU and CPU implementations of flow and depression routing. 36. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 0 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #5RMF3P Abstract Score: 0.013 Related excerpt #LS5PD7: In this paper, we propose a novel GPU flow routing algorithm that computes the water discharge in \mathcal{O}(\log n) iterations for a terrain with n vertices (assuming n processors). We also provide a depression routing algorithm to route the water out of local minima formed by depressions in the terrain, which converges in \mathcal{O}(\log^2 n) iterations. Our implementation of these algorithms leads to a 5\times speedup for flow routing and 34\times to 52\times speedup for depression routing compared to previous work on a 1024^2 terrain, enabling interactive control of terrain simulation. 37. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 2 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #KDKKZ3 2. Related Work Score: 0.012 Related excerpt #RV854H: There have been previous efforts to accelerate this problem by exploiting parallelism, either on CPU [Bar17] or GPU [Bar19, SPF 23 ]. These approaches parallelize the propagation of flow among independent flow paths but do not accelerate propagation within the paths themselves, leading to \mathcal{O}(l) iterations, where l \approx \sqrt{n} is the length of the longest channel and n the number of cells. In contrast, our approach requires \mathcal{O}(\log(n)) iterations. 38. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 11 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #B5KJYH 8. Conclusion Score: 0.011 Related excerpt #CADAM6: Algorithms for evaluating water flow over terrains are a staple of geo-analysis, with applications in computer graphics and beyond. Consequently, any improvement in their run-time performance is worth serious consideration. In this paper, we provide improved algorithms for solving both flow and depression routing problems, with, respectively, O(\log n) and O(\log^2 n) complexity for a terrain with n nodes. This is an improvement on previous methods, which usually require as many iterations as the length of the longest river ( \sim \sqrt{n} ). Most importantly, we are the first to propose a GPU solution for both flow and depression routing. 39. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 6 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #KQNQXW 4.3 Height field evaluation Score: 0.021 Related excerpt #82HGFN: The pre-computation of the profile buffer in Equation 21 is largely responsible for the performance of our method. For comparison, the evaluating \eta at all points in space using the naive 2D integral in Equation 19 costs O(K_\eta \Theta_\eta X_\mathcal{A}^2) operations, where X_\mathcal{A}^2 is the total number of spatial locations where \eta is computed. Our speedup using the profile buffer reduces this computation by two orders of magnitude to O(K_\eta + \Theta_\eta X_\mathcal{A}^2) . Distributing this computation over G GPU cores reduces the cost further to O(K_\eta + \Theta_\eta X_\mathcal{A}^2/G) . In practice, the introduction of the profile buffer in our implementation raised the frame rate from 1.8 to 275 – a speed-up factor of 233 for evaluating \eta . 40. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Score: 0.021 Related excerpt #WKY9MT: our results, we show a vast 4\text{km} \times 4\text{km} sea interacting with islands, floating barrels, actively moving boats, and a user-controlled jet-ski. Both the simulation and the heightfield evaluation are computed in parallel on the GPU in each time step. We provide a supplemental document that describes relevant implementation details for both parts. Our laptop with a NVIDIA Geforce GTX 1070 GPU achieves an average frame rate of 60fps with the parameters in Table 1, and this paper includes an interactive demo of our method which recreates this example. Table 2 displays the timing breakdown for an average frame of this animation; note that the timing for the computation of \eta depends on the number of pixels occupied by waves and may vary slightly. 41. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Score: 0.014 Related excerpt #DWR9FU: The performance of our method comes from a few sources. First, the fact that \mathcal{A} is low resolution allows us to discretize it on a coarse grid, so we don't need an expensive simulation of \mathcal{A} to get detailed visual results. We can exploit this coarse grid by either using a huge simulation domain (as in the above example), or by using very few degrees of freedom to make the simulation faster. Next, the pre-computed profile buffer \Psi saves us two orders of magnitude in computation by reducing a 2D integral to a 1D integral with a texture lookup. Lastly, both the simulation and the wave height evaluation are embarrassingly parallel operations spread out among many points in space, so they greatly benefit from GPU acceleration. 42. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Score: 0.013 Related excerpt #9AHGRG: Varying these parameters has different effects on the visual results and performance of our method, and we explore each of them in our supplementary video. The number of \mathcal{A} samples in our simulation depends linearly on the resolution of our 4\text{D } X_{\mathcal{A}} \times X_{\mathcal{A}} \times \Theta_{\mathcal{A}} \times K_{\mathcal{A}} simulation grid, so doubling the resolution of any dimension will roughly increase the memory and the runtime by a factor of 2. Increasing the spatial resolution X_{\mathcal{A}} will allow the wavefronts to exhibit a higher curvature, allowing more detailed interactions with highly curved boundaries. Figure 8 shows the effect of X_{\mathcal{A}} on the simulation quality. Increasing the angular resolution \Theta_{\mathcal{A}} allows a more precise behavior in each direction. Increasing the wavenumber resolution K_{\mathcal{A}} allows more detailed dispersion of wave groups (different amplitude groups travel at different speeds). We show an example with K_{\mathcal{A}} = 4 simulated wave groups in Figure 9 and in our video, which shows more accurate wave group dispersion but roughly quadruples the run time (drops the frame rate from 70fps to 20fps). 43. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 6 Context: #RNVWWR Water Surface Wavelets #MU7P6S 5 ALGORITHM SUMMARY Score: 0.012 Related excerpt #ES924P: This section gives an overview of the steps necessary to implement our algorithm. Our project webpage 1 also provides example code for a straightforward (CPU-only) implementation of the algorithm as well as an executable file which demonstrates our GPU-optimized implementation. 44. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 5 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #T8YYAV 6. Results Score: 0.024 Related excerpt #LUVPJR: We have used an Intel Q9450 CPU with a GeForce GTX 280 graphics card. The SPH simulation was done with NVIDIA PhysX. Particle counts range from 20k to 64k, depending on the scene. All images were taken at 1280 \times 720 resolution. The curvature flow filtering step was done at half resolution. We use off-screen buffers to store our various intermediate results: 32 bit float for the water depth, 16 bit float for the foam depth, and 16 bit each for T_{wb} , T_{wf} , T_f and T_{ff} . This results in a total of 112 bit per pixel. 45. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 5 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #T8YYAV 6. Results Score: 0.014 Related excerpt #754PPX: Table 1 compares the computational cost of [vdLGS09] with our method (SPH simulation time not included). The indicated running times are an average for a default camera movement. Our method has comparable performance with the benefit of improved image quality especially at near or far viewpoints. Even foam does not significantly increase running time for our method. Figure 6 presents the computational cost of [vdLGS09] and our method using the example of a camera zoom movement in the waterfall scene (like the one of the filter comparison shown in the accompanying video). It takes on average 23.12% of the computation time to render the water and foam depth, 24.4% for the thickness passes, 27.43% for the adaptive curvature flow filtering and 25.05% for the composition (including update of data structures). This measurement represents the mean breakdown of 6k frames used different viewpoints. Figure 1 46. Source: Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents (#WZ8DHP), Rishabh Kar, p. 5 Context: #MDEACB Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents #SRM4HZ 3 Objectives and Technical Specification #EPG8QB 3.1 Evaluation Questions, Hypotheses, and Metrics Score: 0.015 Related excerpt #EDMX8Z: RQ3 (Performance). Can both agents perform their per-tile inspection within the 16.66 ms frame budget associated with 60 FPS, or at least within the 33.33 ms budget associated with 30 FPS, as defined by Unity’s profiling guidance [12, 13]? Hypothesis H3: the per-segment cost is bounded by a small constant independent of run length, because the scanner is gated by an integer tile index and amortises the OverlapBox sweep across many ray probes. 47. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 8 Context: #JCB5RE Advected river textures #HMVN46 Results Score: 0.014 Related excerpt #PRVSL6: Level of Detail provides notable performance improvements as can be seen in Table 1. Even the modest LOD optimizations we have implemented make a significant difference to the frame rate and to the number of polygons rasterized per second. All screenshots and timings were produced on an off-the-shelf dual-core Athlon XP 3800+ computer with an nVidia 8600GT graphics card and 4GB RAM. However, the code has not been parallelized or GPU optimized, meaning that only one of the two cores on the CPU has been directly used. Most of example river beds used in this paper have been imported from DEM files of real rivers. 48. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 7 Context: #B9LYTR Scalable real-time animation of rivers #LQXUW2 6. Implementation and results Score: 0.019 Related excerpt #EUX776: In order to demonstrate the benefits of our method in real applications we tested it in a 25 \times 25 \text{ km}^2 scene with a river network, branchings and obstacles. We used a 800 \times 600 window with r = d = 20 pixels. We used two kinds of waves: noise perturbations and wind ripples. For the former, we used a precomputed Perlin noise reference texture. For the latter, we used Fourier generation using analytical time evolution [Tes04] for wind waves. Both reference textures contain height fields, that are used by the water shader for bump mapping and environment mapping. The test was done on an AMD Athlon 3200 processor at 1.8 GHz with a GeForce 8800 GTS graphics board. The particles and the final rendering results are shown in Figure 11. 49. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 7 Context: #B9LYTR Scalable real-time animation of rivers #LQXUW2 6. Implementation and results Score: 0.014 Related excerpt #R825Y2: pend on the complexity of the scene. In the test, we achieved real-time performance even in the worst case where the projected surfaces occupy the whole window. Certainly, the performance will decrease if we decrease the Poisson-disk radius. However, a moderate value as we used in this test is sufficient due to the adaptivity of the particles and the sprite-based rendering scheme. 50. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 7 Context: #B9LYTR Scalable real-time animation of rivers #LQXUW2 6. Implementation and results Score: 0.013 Related excerpt #K63RTB: We then measured the performance of our method. Figure 9 shows that given a Poisson-disk radius, the running time of our method depends linearly on the projected area of river surfaces in the window. Thus our method does not de- ### 12. Tool result: search_text Exact matches 1. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 4 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #85YSXN 3. A computational approach to the goodness or structural beauty of an image #3UYRFA 3.1 Head/tail breaks for deriving the underlying living structure Matching excerpt #MKYDT2: Head/tail breaks is a recursive function to derive the inherent hierarchy of a dataset. A dataset as a whole is divided into two parts: the head for those greater than the average, and the tail for those less than the average. The head as a subwhole is again divided around the new average of the subwhole into the head and the tail, and this process continues until the remaining data is no longer heavy-tailed or the head percentage is greater than 40%. Eventually, the dataset is considered as an iterative system, i.e., the head of the head of the head and so on. All the tails and the last head constitute individual classes or hierarchical levels of the dataset. 2. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 4 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #85YSXN 3. A computational approach to the goodness or structural beauty of an image #3UYRFA 3.1 Head/tail breaks for deriving the underlying living structure Matching excerpt #AUBQ8K: Let us use the dataset containing 10 numbers [1, 1/2, 1/3, \dots, 1/10] that exactly follows Zipf's law (1949) to show how the dataset can be classified (Figure 2) by the head/tail breaks, and why this dataset is more living than another dataset. The average of the 10 number is about 0.29, which partitions them into two sets: the head for those greater than the average [1, 1/2, 1/3] and the tail for those less than the average [1/4, 1/5, \dots, 1/10] . For the three numbers in the head as a subset, the average is about 0.61, which further partitions the head into the head [1] and the tail [1/2, 1/3] . Thus the dataset has three classes or hierarchical levels, which are termed as the ht-index (Jiang and Yin 2014): [1] , [1/2, 1/3] , [1/4, 1/5, \dots, 1/10] . Alternatively, the data can be considered to be composed of the head of the head of an iterative system: [1] , [1, 1/2, 1/3] , [1, 1/2, 1/3, \dots, 1/10] . On the other hand, the second dataset consists of the 10 numbers [1, 2, 3, \dots, 10] , which is without any inherent hierarchy or violates scaling law. Thus, the first dataset is more living–or more structurally beautiful–than the second dataset. 3. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 4 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #85YSXN 3. A computational approach to the goodness or structural beauty of an image #3UYRFA 3.1 Head/tail breaks for deriving the underlying living structure Matching excerpt #L2FTWA: The average of the three numbers in the head [1, 1/2, 1/3] is 0.61, which further partitions the head into the head [1] and the tail [1/2, 1/3] , so again with far more smalls than larges. Thus, the 10 numbers have three inherent hierarchical levels: [1] , [1/2, 1/3] , and [1/4, 1/5, \dots, 1/10] . The dataset [1, 1/2, 1/3, \dots, 1/10] , because of its inherent hierarchy of 3, is more living than the other dataset [1, 2, 3, \dots, 10] that is without any inherent hierarchy or violates the notion of far more smalls than larges, so called scaling law.) 4. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 12 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #PQFTNG 6. Conclusion Matching excerpt #7Q54HE: Seen from the recursive perspective, an image can be perceived as an iterative system that consists of the figure of the figure of the figure and so on. In this connection, the computational approach resembles very much – in spirit, but not in detail – the head/tail breaks that represents a heavy-tailed dataset as the head of the head of the head and so on. This recursive way of understanding images is probably the most significant contribution of this paper. Based on the computational approach, we (re-)discovered that (1) traditional buildings are more structurally beautiful than their modernist counterparts, (2) Blue Poles is more structurally beautiful than the Mona Lisa , and (3) the weather-beaten face is more structurally beautiful than the posed model. These findings may sound controversial, but they are purely based on the structural point of view without considering cultural, social, racial, and other biophilic factors. Our future work will seek to integrate these other factors into our model. 5. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 3 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #NHF3AU 2. Living structure and its governing laws: a human face image as a working example Matching excerpt #M89VCM: (Jiang 2019). As mentioned earlier, the living structure of the human face image has 779 substructures, which can be put into four hierarchical levels. It becomes less beautiful if the lowest level (all the blue substructures) is removed, because the number of substructures is dramatically reduced, while the level of the hierarchy is decreased from four to three. This rule on beauty constitutes the major criterion for comparing and ranking the goodness of images. The living structure provides an objective measure to quantify structural beauty. This is the foundation of the computational approach to the goodness of an image to be developed in this paper. 6. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 8 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #2JFZU9 4. Experiment and results #F2HCVN 4.2 Blue Poles is more structurally beautiful than the Mona Lisa Matching excerpt #63YM5H: It may not be that hard to understand why Blue Poles is the most beautiful structurally. The painting has many levels of intricate substructures, which are well reflected by the 6 hierarchical levels (the highest among all the studied images). The high ht-index (Jiang and Yin 2014) indicates also that the painting is fractal, which was studied earlier through computing its fractal dimension (Taylor et al. 1999). As a matter of fact, fractals are de fact living structures under the third definition of fractal: a set or pattern is fractal if the notion of far more small things than large ones recurs at least twice (Jiang 2015c). There is little wonder that fractals are in general structurally beautiful. The painting Blue Poles was purchased by the National Gallery of Australia in 1973 and has become one of the most popular exhibits in the gallery. The painting is now worth 350 million Australian dollars – a 300-fold increase on the A$1.3 million when it was first purchased. 7. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 11 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #MHMBEA 5. Implications of the computational approach and future work Matching excerpt #2H3LJ4: The computational approach developed in this paper works very well for measuring structural beauty and further differentiating two images in terms of their goodness or structural beauty. The approach is very much in line with Alexander's vision about the mathematics of beauty or life as cited in the epigraph. To be more specific, the levels of scale property Alexander mentioned is a de facto inherent hierarchy of substructures, or the recurring notion of far more small substructures than large ones. The void property can be viewed as the largest or the most salient substructures, while the inner calm property refers to each level of scale (or hierarchy) in which substructures are more or less similar sized. This section further discusses the computational approach and its implications in a larger context. 8. Source: Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image (#3XSLTA), Bin Jiang, Chris de Rijke, p. 5 Context: #ELWE7N Structural Beauty: A Structure-based Approach to Quantifying the Beauty of an Image #85YSXN 3. A computational approach to the goodness or structural beauty of an image #4BFT5R 3.2 The computational approach to structural beauty Matching excerpt #KQBHQ9: The computational approach aims to capture structural beauty, so it currently works with gray images. A color image must first be transformed into a gray image in order to conduct the computation of the structural beauty or goodness. This transformation is based on the commonly used formula; that is, \text{Gray} = 0.299 * \text{Red} + 0.587 * \text{Green} + 0.114 * \text{Blue} (Poynton 2003). While applying the head/tail breaks to the pixels of an image, we disregard the 40% threshold. Usually according to the black and white percentages, the one with less than 50% is considered as the figure, while the other is considered as the ground (cf. Figure 1 for an example). However, for some images, this rule based on the percentage of dark and light pixels should not be taken for granted. For the human face image shown in Figure 3, the dark percentage is 52%, while the light percentage is 48% (Table 2), but we still take the dark pixels as the figure, which is consistent with human perception of the image. In this paper, we simply used the average cuts to recursively derive the figures or subwholes at different levels of hierarchy. As shown in Figure 3, the gray image is dichotomized into the figure (for dark pixels in the head with pixel values less than the average) and the ground (for light pixels in the tail with pixel values greater than the average). The original gray image is binarized and vectorized into its living structure; the figure and ground are then respectively represented by black and white pixels, and the black pixels are vectorized to constitute a living structure of the image. 9. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 6 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #YEVN37 II. ACTIVE WALKER MODEL OF TRAIL FORMATION Matching excerpt #3YJ2PE: Therefore, the mechanism of trail formation is based on some kind of agglomeration process , which is delocalized due to the directedness of the walkers' motion. Starting with a plain, spatially homogeneous ground, the walkers will move arbitrarily. However, by continuously leaving markings, they produce trails which have an attractive effect on nearby walkers. Thus, the agents begin to use already existing trails after some time. By this, a kind of selection process between trails occurs (cf. [43]): Frequently used trails are reinforced, which makes them even more attractive, whereas rarely used trails may vanish again. The trails begin to bundle, especially where different trails meet or intersect. Therefore, even walkers with different entry points and destinations use and maintain common parts of the trail system. 10. Source: Active walker model for the formation of human and animal trail systems (#B6P8L4), Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár, p. 2 Context: #E9C9Y2 Active Walker Model for the Formation of Human and Animal Trail Systems #TTL9MC I. INTRODUCTION Matching excerpt #KXXUJY: As our experience tells us, trails are adapted to the requirements of their users. In the course of time, frequently used trails become more developed, making them more attractive, whereas rarely used trails vanish again. Trails with large detours become optimized by creating shortcuts. New destinations or entry points are connected to an existing trail system. These dynamical processes occur basically without any common planning or direct communication among the users. Instead, the adaptation process can be understood as a self-organization phenomenon, resulting from the non-linear feedback between the users and the trails [35]. 11. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 8 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #TXBKLJ 4. Case studies: Computing the degrees of life #3NPEFU 4.2 The streets of Manhattan and Sweden Matching excerpt #LUZ5UR: The next two case studies move from the architectural scale to city and country scales. Manhattan as a city was chosen for the case study because its street network is easily perceived as a whole. We generated 1,800 axial lines for Manhattan and converted them into a hierarchical graph in terms of line-to-line intersection. This intersection relationship is based on the simple rule that short lines point to, or support, long ones. The same rule applies to the streets of Sweden. The streets are the complete set, including 166,479 streets for the entire country. The streets are a mix of named and natural streets (Jiang and Claramunt 2004, Jiang, Zhao and Yin 2008). In other words, individual street segments are merged according to the same names, and further merged together to form the natural streets. The street networks are then converted into dual graphs in which the nodes represent the individual streets, and the directed links indicate relationships from short streets (or axial lines) to long ones. Based on the directed graphs, we computed the degrees of life for the individual axial lines and streets, and they were visualized using the spectral colors, with blue as the lowest degree of life, red as the highest degree of life, and the other colors for degrees of life between the lowest and highest. It was surprising that the degrees of life demonstrated very striking power laws (Clauset et al. 2009), with two and three decades of power law fit, and a very high degree of goodness of fit (Table 2). The power law exponent around 2.0+ is consistent with the theoretic rules Salingeros (1998) suggested for scaling hierarchy. 12. Source: Procedural Content Generation via Machine Learning (PCGML) (#CQBDX4), Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass, p. 6 Context: #6EE2TX Procedural Content Generation via Machine Learning (PCGML) #6BC6KQ III. METHODS OF PCGML #QNMYX8 B. Grids #AQ7YV6 1) Frequency Counting Matching excerpt #SKB6TL: A recent approach by Gumin [51] is loosely inspired by quantum mechanics and uses a “super-position” of tiles to generate images and levels from a representative example tile set. This approach is a variant of MRF, except instead of solely sampling, samples are chosen via “collapsing of the wave function” (i.e. probabilistically choosing a tile and propagating constraints that that choice enforces). This in turn can propagate other changes and either deterministically chooses tiles that no longer have any other possible choices or reduces the possible set of other tiles. The probabilities and configurations are determined by finding each N \times N window in the input, and the number of times that window occurs. This approach was initially explored for bitmap generation, but has since been expanded for use with 3-D tile sets as well as for level generation [52], [53]. The source code and examples of the bitmap project can be found online [51]. 13. Source: Procedural Content Generation via Machine Learning (PCGML) (#CQBDX4), Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass, p. 8 Context: #6EE2TX Procedural Content Generation via Machine Learning (PCGML) #6BC6KQ III. METHODS OF PCGML #FFTSJC C. Graphs #G9BY23 2) Frequency Counting Matching excerpt #UBLXCG: PCGML has focused on graphical games, and particularly the levels of graphical games. However, there exists some work in the field of generating interactive fiction, text-based games like choose your own adventure stories. Guzdial et al. adapted Scheherazade [68], a system for automatically learning to generate stories, into Scheherazade-IF [65], which can derive entire interactive fiction games from a dataset of stories. 14. Source: Procedural Content Generation via Machine Learning (PCGML) (#CQBDX4), Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass, p. 11 Context: #6EE2TX Procedural Content Generation via Machine Learning (PCGML) #VAKEPG IV. OPEN PROBLEMS AND OUTLOOK #HKXEPJ F. Style Transfer Matching excerpt #JTJCYL: Style and concept transfer is the idea that information learned from one domain can enhance or supplement knowledge in another domain. Style transfer has most notably been explored for image modeling and generation [95], [96]. For example, in recent work Gatys et al. [97] used neural networks to transfer the style of an artist onto different images. Additionally, Deep Dream [98] trains neural networks on images, and then generates new images that excite particular layers or nodes of the network. This approach could be adapted to learn from game content (e.g., levels, play data, etc.) and generate content that excites layers associated with different elements from the training data. More traditional forms of blending domain knowledge have been applied sparingly to games, such as game creature blending [99] and interactive fiction blending [100]. However, until very recently no one has applied this machine learning-oriented style transfer to procedural content generation. 15. Source: Procedural Content Generation via Machine Learning (PCGML) (#CQBDX4), Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass, p. 0 Context: #6EE2TX Procedural Content Generation via Machine Learning (PCGML) #LVDDDA I. INTRODUCTION Matching excerpt #FRDMQB: Concurrently, there has been an explosion in the use of machine learning to train models based on datasets [4]. In particular, the resurgence of neural networks under the name deep learning has precipitated a massive increase in the capabilities and application of methods for learning models from big data [5], [6]. Deep learning has been used for a variety of tasks in machine learning, including the generation of content. For example, generative adversarial networks have been applied to generating artifacts such as images, music, and speech [7]. But many other machine learning methods can also be utilized in a generative role, including n -grams, Markov models, autoencoders, and others [8], [9], [10]. The basic idea is to train a model on instances sampled from some distribution, and then use this model to produce new samples. 16. Source: Procedural Content Generation via Machine Learning (PCGML) (#CQBDX4), Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass, p. 1 Context: #6EE2TX Procedural Content Generation via Machine Learning (PCGML) #LVDDDA I. INTRODUCTION Matching excerpt #WG8LJK: This paper focuses on game content that is directly related to game mechanics. In other words, we focus on functional rather than cosmetic game content. We define functional content as artifacts that, if they were changed, could alter the in-game effects of a sequence of player actions. The main types of cosmetic game content that we exclude are textures and sound, as those do not directly impact the effects of in-game actions the way levels or rules do in most games, and there is already much research on the generation of such content outside of games [14], [15]. This is not a value judgment, and cosmetic content is extremely important in games; however, it is not the focus of this paper. Togelius et al. [2] previously defined a related categorization with the terms necessary and optional. We note that while there exists some overlap between necessary and functional, it is possible to have optional functional content (e.g., optional levels) and necessary cosmetic content (e.g., the images and sound effects of a player character). 17. Source: Procedural Content Generation via Machine Learning (PCGML) (#CQBDX4), Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass, p. 11 Context: #6EE2TX Procedural Content Generation via Machine Learning (PCGML) #VAKEPG IV. OPEN PROBLEMS AND OUTLOOK #UQ5Q9J D. Learning on Different Levels of Abstraction Matching excerpt #AGCGW3: As described above, one key challenge that sets PCGML for games apart from PCGML for domains such as images or sound is the fact that games are multi-modal dynamic systems. This means that content generated will have interactions: generated rules operate on generated levels which in turn change the consequences of those rules and so on. A useful high-level formal model for understanding games as dynamic systems that create experiences is the Mechanics, Dynamics, Aesthetics (MDA) framework by Hunicke et al. [91]. “Mechanics describes the particular components of the game, at the level of data representation and algorithms. Dynamics describes the run-time behavior of the mechanics acting on player inputs and each other’s outputs over time. Aesthetics describes the desirable emotional responses evoked in the player, when she interacts with the game system.” If the end goal for PCGML for games is to generate content or even complete games with good results at the aesthetic level, the problem is inherently a hierarchical one. It is possible that learning from data will need to happen at all three levels simultaneously in order to successfully generate content for games. 18. Source: Procedural Content Generation via Machine Learning (PCGML) (#CQBDX4), Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass, p. 6 Context: #6EE2TX Procedural Content Generation via Machine Learning (PCGML) #6BC6KQ III. METHODS OF PCGML #QNMYX8 B. Grids #LTJS3M 2) Back Propagation Matching excerpt #X2N698: In [22] Jain et al. show how autoencoders [54] may be trained to reproduce levels from the original Super Mario Bros. game. The autoencoders are trained on series of vertical level windows and compress the typical features of Mario levels into a more general representation. They experimented with the width of the level windows and found that four tiles seems to work best for Mario levels. They proceeded to use these networks to discriminate generated levels from original levels, and to generate new levels as transformation from noise. They also demonstrated how a trained autoencoder may be used to repair unplayable levels, changing tile-level features to make levels playable, by inputting a broken/unplayable level to the autoencoder and receiving a repaired one as output (see Figure 7). 19. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 2 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #3G9YBV 3 Algorithm Overview Matching excerpt #YVP4AW: In the last step, the algorithm gathers information from the previous steps and generates the continuous-terrain model. We propose a novel procedural terrain representation that defines the terrain as a construction tree. The leaves are parameterized primitives that define different terrain features, such as hills, mountains, valleys, and different types of rivers. The inner tree nodes combine the primitives by blending, adding, subtracting, or carving. This approach creates a memory efficient representation of large terrains, comprising numerous levels of details. 20. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 0 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #F9QBNZ Abstract Matching excerpt #7CSK9U: We present a framework that allows quick and intuitive modeling of terrains using concepts inspired by hydrology. The terrain is generated from a simple initial sketch, and its generation is controlled by a few parameters. Our terrain representation is both analytic and continuous and can be rendered by using varying levels of detail. The terrain data are stored in a novel data structure: a construction tree whose internal nodes define a combination of operations, and whose leaves represent terrain features. The framework uses rivers as modeling elements, and it first creates a hierarchical drainage network that is represented as a geometric graph over a given input domain. The network is then analyzed to construct watersheds and to characterize the different types and trajectories of rivers. The terrain is finally generated by combining procedural terrain and river patches with blending and carving operators. 21. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 6 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #UAYDMD 6 Terrain Model Generation #FWT7FF 6.2 Terrain Primitives Generation Matching excerpt #LEWYFM: are generated by semistochastic sampling using Poisson distribution [Lagae and Dutré 2005] that assures aperiodic tiling (Fig. 14 left). Disks' radii are increased until the set of primitives \{T\} covers \Omega . We used 50 samples per cell. Fewer samples give fast and memory inexpensive models but produce less accurate terrain. 22. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 32 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #EEPQMJ 5.7. Trail Layout #XSQ2CN 5.7.3. Maximum Sustainable Linear Grades #DQ4WG4 5.7.3.8. Evaluation of Existing Trails Matching excerpt #S3X7UU: An additional method of determining the maximum sustainable grade of a proposed trail is to evaluate existing trails in the same geographic area. Assuming that the existing trails have the same characteristics identified above as the proposed trail, they can be used as a tool to ground truth the maximum sustainable grade analysis. The key to using existing trails as indicators of maximum sustainable grades is that those trails or portions of those trails must possess the appropriate curvilinear alignment and proper trail construction characteristics. Unfortunately, there are very few trails that possess those qualities. However, you can usually find a segment or segments that meet these criteria. By knowing the use type, levels of use, and seasons of use, and by closely monitoring the linear grade, cross slope, and soil conditions, you can begin to establish the threshold of sustainable linear grade on these trail segments. 23. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 3 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #92S5AZ 5.1. Life of a Trail Matching excerpt #74F9ER: Trails can last for hundreds of years. Many trails in the United States are well over a hundred years old. In Asia, Africa, Europe, and South America there are trails that are several thousand years old. With such a lifespan, trails that are not properly designed, constructed, and maintained can have long lasting adverse impacts on natural and cultural resources, and can be a liability to the land manager's funding and staffing resources. 24. Source: Principles of Trail Layout and Design (#LXV9AT), California State Parks, p. 3 Context: #HE95FY Chapter 5. Principles of Trail Layout and Design #92S5AZ 5.1. Life of a Trail Matching excerpt #MKJB5R: All trails have an impact on the land where they are constructed. This impact can be minor or severe, depending on how well the trail is designed and constructed. In addition, all trails require maintenance. Even the best-designed and constructed trails require cyclical maintenance to perform properly. 25. Source: Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure (#MH5J8D), Bin Jiang, p. 4 Context: #HAZYNL Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty based on the 15 Properties of Living Structure #6XBA45 2. Theoretical Framework #3SBXXB 2.2 Two Surveys about the Mirror-of-the-Self Test (MOST) Matching excerpt #X7VF6W: In 1985, at a conference in New York, Alexander (2002–2005) conducted a similar exercise, asking 100 participants to state which of two objects – a gray steel stool and a blue-painted wooden bench (see Figure 3) – better reflected their sense of self. Only one of the 100 participants chose the steel stool. While he defended his choice as subjective at first, he later changed his mind and opted for the wooden bench. Examples like this underline the profound emotional influence of Alexander’s approach and reveal universal truths regarding how people intuitively relate to designs that reflect their inner sense of life and self. 26. Source: Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure (#MH5J8D), Bin Jiang, p. 7 Context: #HAZYNL Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty based on the 15 Properties of Living Structure #63MN28 4. Case Studies for Verification #HW35C5 4.2 Results and Discussion Matching excerpt #ZHQULC: The results above offer insights into the complexity of human perception when evaluating the concept of living structure or QWAN. Most of the results align with Alexander’s original assessments, where the left images score higher than the right ones. However, there are five exceptional cases where the right images outperform the left. While the reasons for this are uncertain, these cases are rare and may be considered outliers. Nevertheless, we could argue that beauty or life, as perceived in these instances, is not merely the sum of individual properties, but rather the integration and synthesis of various elements working together. Our findings highlight the importance of the 15 properties as a framework for assessing beauty, emphasizing the need to account for the integration of these properties rather than just their individual presence. Beautimeter, while a powerful tool for quantifying human perceptions, requires further refinement to better capture the interplay between these properties. For example, greater weight may need to be given to some properties, such as the levels of scale, echoes, and not separateness, which might be more significant than local properties. As architecture and urban design continue to evolve, tools like Beautimeter can play a vital role in ensuring that the spaces we create resonate with the deep, intuitive sense of beauty and life inherent in our environments. 27. Source: Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure (#MH5J8D), Bin Jiang, p. 8 Context: #HAZYNL Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty based on the 15 Properties of Living Structure #63MN28 4. Case Studies for Verification #HW35C5 4.2 Results and Discussion Matching excerpt #FH8XCN: Beautimeter relies mainly on the 15 properties of living structure to automatically assess and score pairs of images in terms of their livingness thanks to the advance of GPT technology. While Beautimeter is largely relying on the number of the 15 properties, other methods gauge architectural and urban beauty in a more quantitative manner (e.g., Birkhoff 1933, Palmer et al. 2013). An example is based on the formula L = S * H , where L represents the livingness or perceived beauty of a structure, S represents the number of substructures, and H denotes their hierarchical levels. This formula, which is derived from previous work (Jiang and de Rijke 2023) offers an objective and mathematical way of assessing architectural and urban beauty by analyzing the structural and hierarchical properties of spaces. 28. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 4 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #KXUAWS 3. A recursive approach to computing the structural beauty of images #LB8R59 3.1 Head/tail breaks and two laws of living structure Matching excerpt #XUKG48: Head/tail breaks was initially developed as a classification scheme for a dataset with a heavy-tailed distribution. It is a de facto recursive function for deriving the inherent hierarchy of a dataset from the bottom up. That is, the dataset itself determines the inherent hierarchy of classes without any imposed criteria. Let us use the dataset containing 100 numbers [1, 1/2, 1/3, \dots, 1/100] (Figure 3) to illustrate how the dataset can be decomposed into the head for those greater than the average and the tail for those less than the average, and then proceed recursively or iteratively for the head, the head of the head, and so on. All tails and the last head constitute individual classes or hierarchical levels. 29. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 4 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #KXUAWS 3. A recursive approach to computing the structural beauty of images Matching excerpt #2TLGAU: In this section, we introduce a recursive approach to the structural beauty of images by extending the substructures to recursive ones. Before that, we will also illustrate the head/tail breaks (Jiang 2013) as a recursive function for deriving the underlying living structure or the inherent hierarchy of a dataset. The dataset contains 100 numbers as a working example to mimic the rank–size distribution: the largest size is about twice as large as the second largest, approximately three times as large as the third largest, and so on (Zipf 1949). This working example also helps to illustrate the two laws of living structure. 30. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 2 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #7WXQSD 1. Introduction Matching excerpt #XZBXLL: The contribution of this paper lies in the living structure perspective, a holistic and comprehensive approach to measuring the structural beauty of images or the livingness of space in a recursive manner. More specifically, there are four major findings from this study. First, all images are living images that have recursive levels more than four. Second, the centroids of the recursively defined substructures effectively capture the skeleton or saliency of the images, and the number of centroids (or substructures) is far fewer than the number of pixels. Third, among the derived substructures, no more than 2 percent are decomposable. Fourth, not only substructures but also their decomposable subsets can be used to measure the structural beauty of images or the livingness of space. 31. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 5 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #KXUAWS 3. A recursive approach to computing the structural beauty of images #LB8R59 3.1 Head/tail breaks and two laws of living structure Matching excerpt #SEJEBJ: The working example can further illustrate the two laws of living structure (Table 1). The dataset clearly has the recurring notion of far more smalls than larges, so it meets the scaling law. More specifically, the notion of far more smalls than larges recur three times, so with four different levels of scale (or hierarchy). On the other hand, the numbers on each level of the hierarchy (or scale) are more or less similar in size, so the dataset meets Tobler’s law. Among the two laws, the scaling law is available across the hierarchy while Tobler’s law on each level of the hierarchy. More importantly, the scaling law and Tobler’s law imply complex and non-equilibrium character globally, and simple and equilibrium character locally, respectively. 32. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 7 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #563UCF 4. Case studies #TM4DU2 4.1 Verification of the recursive approach Matching excerpt #RZMAD9: The eight pairs are put into two groups: the building group (P1–P4) and the mixed group (P5–P8) (Figure 5). For every pair of images, the left is supposed to be more living or more structurally beautiful than the right, according to the non-recursive approach (Jiang and de Rijke 2021). The new approach can duplicate the same result (Table 3), where both columns (L and V) indicate that the left-hand image has a higher score than the right-hand image. Our primary goal was to differentiate between the two images to see whether the left image's score is higher than that of the right image. This is indeed true; see Columns L (calculated from all substructures) and V (calculated from only decomposable substructures). All the images to the left are more living or more structurally beautiful than those to the right, and all the images are living images, indicated by at least four iterations or four levels of recursion. 33. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 7 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #563UCF 4. Case studies Matching excerpt #D2C54Y: We applied the recursive approach to the eight pairs of images to verify whether the recursive approach is better or more robust than the non-recursive approach. The same set of images had been used to verify the non-recursive approach previously (Jiang and de Rijke 2021), so they were convenient for verification of the recursive approach and for comparing the non-recursive and recursive approaches. The first four pairs had previously been studied by Alexander (2002–2005), who used the 15 properties to examine their livingness, so they are with ground truth on their livingness or structural beauty. In addition to the verification and comparison, we found that (1) the number of the recursively defined substructures of an image is far smaller (3 percent on average) than the number of pixels, and the centroids of these substructures can well capture the skeleton or saliency of the image; (2) all the images have the recursive levels more than four, indicating that they are indeed living images; and (3) no more than 2 percent of the substructures are decomposable, but they can well characterize the structural beauty. 34. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 0 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #K2N49X Abstract Matching excerpt #47VNT4: According to Gestalt theory, any image is perceived subconsciously as a coherent structure (or whole) with two contrast substructures: figure and ground. The figure consists of numerous auto-generated substructures with an inherent hierarchy of far more smalls than larges. Through these substructures, the structural beauty of an image (L), or equivalently the livingness of space, can be computed by the multiplication of the number of substructures (S) and their inherent hierarchy (H). This definition implies that the more substructures something has, the more living or more structurally beautiful it is, and the higher hierarchy of the substructures, the more living or more structurally beautiful. This is the non-recursive approach to the structural beauty of images or the livingness of space. In this paper we develop a recursive approach, which derives all substructures of an image (instead of its figure) and continues the deriving process for those decomposable substructures until none of them are decomposable. All of the substructures derived at different iterations (or recursive levels) together constitute a living structure; hence the notion of living images. We have applied the recursive approach to a set of images that have been previously studied in the literature and found that (1) the number of substructures of an image is far lower (3 percent on average) than the number of pixels and the centroids of the substructures can effectively capture the skeleton or saliency of the image; (2) all the images have the recursive levels more than three, indicating that they are indeed living images; (3) no more than 2 percent of the substructures are decomposable, implying that a vast amount of the substructures are not decomposable; (4) structural beauty can be well measured by the recursively defined substructures, as well as their decomposable subsets. Despite a slightly higher computational cost, the recursive approach is proved to be more robust than the non-recursive approach. The recursive approach and the non-recursive approach both provide a powerful means to study the livingness or vitality of space in cities and communities. 35. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 13 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #AMFSDX 6. Conclusion Matching excerpt #K7EAKA: Any space possesses a certain degree of livingness or structural beauty, although the degree varies from one to another depending on its internal geometry of substructures. Reflected in an image, a substructure is a set of pixels whose pixel values are greater (or less) than the average pixel value. Thus, an image can be viewed as a set of recursively defined substructures, rather than a set of pixels or a set of human recognizable objects as conventionally conceived. The major difference between substructures and objects lies in the fact that substructures are defined by pixels themselves from the bottom up, while objects are defined by human eyes. In this paper, we developed a recursive approach to the structural beauty of images by considering all recursively defined substructures. Through the case studies, we have verified that the recursive approach is better or more robust than the non-recursive approach, although both approaches are based on the same principle: the more substructures the more beautiful, the higher hierarchy of the substructures the more beautiful. We have also verified that the decomposable substructures alone can be used to differentiate two images in terms of their structural beauty, by multiplying the number of decomposable substructures and their levels of recursion. This implies that the more decomposable substructures the more beautiful, and the more levels of recursion the more beautiful. 36. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 11 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #563UCF 4. Case studies #AKW33C 4.3 Decomposable substructures and their centroids Matching excerpt #2R64C6: The case studies above have shown that images are indeed living, although the degree of livingness varies from one image to another. The recursive approach to structural beauty begins with two subwholes – figure and ground – representing either light or dark side of the image. From either the figure or the ground, the structural beauty can then be calculated respectively for differentiating two images. In other words, the recursive approach can be applied to both the figure and ground of images. This implies that living images are living from both the figure and the ground of images. All of the substructures are derived from the images themselves towards the figure of the figure and the ground and so on. The recursive approach can not only effectively differentiate two images in terms of their livingness, but also help reveal the three major findings outlined above. To supplement the case studies, Appendix A further demonstrates that the same approach applies to georeferenced images as well. The recursive approach is therefore better or more robust than the non-recursive one. 37. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 0 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #7WXQSD 1. Introduction Matching excerpt #GCB5VY: All space has some degree of livingness in it, according to its structure and arrangement (Alexander 2002–2005), so the livingness is commonly sensed in our surrounding such as rooms, gardens, buildings, streets, and cities, as well as in tiny ornaments. The livingness sounds like a kind of human experience of space or a sense of place attachment (Tuan 1977, Goodchild and Li 2012), synonymous with the vitality or organized complexity (Jacobs 1961), and the imageability or legibility (Lynch 1960). Unlike these concepts, however, the livingness is defined mathematically through the underlying living structure. The living structure is a mathematical structure with an inherent hierarchy (see Section 2 for an introduction), which can trigger the feeling of livingness in the human mind and heart. The inherent hierarchy of living structure is commonly recognized in a series of urban and geographic theories such as the central place theory (Christaller 1933, 1966), space syntax (Hillier and Hanson 1984, Hillier 1996), and the fractal cities (Batty and Longley 1994). The hierarchy may reflect spatial heterogeneity, one of the two spatial properties, the other being spatial dependence (Goodchild 2004, Anselin 1989, Tobler 1970). As shown later in Section 2, the hierarchy or spatial heterogeneity is better characterized by the recurring notion of far more smalls than larges across different levels of scale. 38. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 14 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #AMFSDX 6. Conclusion Matching excerpt #KNARLX: In addition to the verification of the recursive approach, we have made three major findings. First, the number of substructures of an image is far lower (for example, three percent on average) than the number of pixels, and the centroids of the substructures can capture very well the skeleton or saliency of the image. Second, all the images have the recursive levels more than four, indicating that they are indeed living images. This second finding implies that that any space or matter has a certain degree of livingness or life, according to its internal geometry. Third, no more than 2 percent of the substructures are decomposable, which means that there are far more less-living substructures than more-living ones. To echo the epigraph, we have the following statement about living structure and substructures of an image: in a living structure, every substructure is unique, and the different substructures also cooperate, with no substructures left over, to create a global whole – a whole that can be identified by everyone who is part of it. It is essentially the global whole or wholeness that triggers a sense of livingness in the human mind and heart. The livingness or structural beauty entails that there is a shared notion of livingness among people and even different peoples. It will open a new horizon for research on human experience of space – a sense of places and place attachment – and more importantly on place making. Our future work will concentrate on how the livingness is reflected in the human mind, and whether or how the kind of reflection varies from people to people in terms of their culture, gender, and races. 39. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 4 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #KXUAWS 3. A recursive approach to computing the structural beauty of images #LB8R59 3.1 Head/tail breaks and two laws of living structure Matching excerpt #VP52TJ: To be specific, the average of the 100 numbers is approximately 0.05, and it divides the dataset into two subsets: the head for those greater than the average [1, 1/2, 1/3, \dots, 1/19] and the tail for those less than the average [1/20, 1/5, \dots, 1/100] . For the 19 numbers in the head subset, the average is about 0.19, and it divides the head subset into the head [1, 1/2, 1/3, 1/4, 1/5] and the tail [1/6, 1/7, \dots, 1/19] . For the five numbers in the latest head subset, the average is about 0.46, and it divides the latest head subset into the head [1, 1/2] and the tail [1/3, 1/4, 1/5] . Thus, there are four classes or hierarchical levels for the data: [1, 1/2] , [1/3, 1/4, 1/5] , [1/6, 1/7, \dots, 1/19] , [1/20, 1/21, \dots, 1/100] . The data can be conceived to be composed of the head of the head of the head of an iterative system: [1, 1/2] , [1, 1/2, 1/3, 1/4, 1/5] , [1, 1/2, 1/3, \dots, 1/19] , [1, 1/2, 1/3, \dots, 1/100] . 40. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 9 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Matching excerpt #NEL8YN: Rivers and lakes In Figure 9, we demonstrate how our algorithms can be used on complex large-scale terrains to demarcate lakes and rivers that are registered correctly with existing erosion lines and depressions. On the left in Figure 9, a mountainous region in the Alps transitions into an urbanized flat glacial valley. On the right, a tidal estuary around Mont Saint-Michel, France, leads into the sea. They contain 383,918 and 8,445,644 basins, respectively. In both cases, the elevation data was obtained from the IGN RGE ALTI Digital Elevation 1m dataset [IGN22]. 41. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance Matching excerpt #8VZYXE: For our test dataset, we incorporated a mix of real and synthetic terrains. We began by extracting a set of 10 real terrains from the IGN RGE ALTI Digital Elevation 1m dataset [IGN22] chosen on the basis of topographic variety. These 10 terrains were sampled at cell resolutions of 512 \times 512 , 1024 \times 1024 , 2048 \times 2048 and 4196 \times 4196 to support scaling experiments. 42. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 9 Context: #RNVWWR Water Surface Wavelets #AL43YK 8 RESULTS Matching excerpt #U6MFTD: The resolution of \eta (Equation 20), however, has a direct effect on the visual results. Reducing the number of spatial samples will reduce the highest visible frequency, using only a small number of \theta samples will introduce lattice-like artifacts caused by waves appearing as perfectly aligned, and using only a few k samples will remove visual frequencies from the final wave visualization. 43. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 5 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #6AJDFD 4.1 Discretizing \mathcal{A} Matching excerpt #8LZV63: In practice, we found that we can use surprisingly coarse grids for this discretization. Our simulations use \Theta_{\mathcal{A}} = 16 samples for the wavevector angle, \theta ; finer discretizations did not increase the simulation quality. We use even fewer samples for discretizing the wavenumber, k ; we typically only need K_{\mathcal{A}} = 1 sample to get the effects we desire, though we experiment with up to K_{\mathcal{A}} = 4 samples 44. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 5 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Matching excerpt #FH8NYH: A street network is more correctly conceived of as a set of far more short streets than long ones, or a set of far more less connected streets than well connected ones (Figure 2b). The street network has four levels of scale, indicated by the four colors, far more short streets than long ones across the scales, and more or less similar streets on each of the four scales. A coastline is more correctly represented as a set of far more small bends than large ones (Figure 2d). The coastline has three levels of scale, indicated by three sets of bends: [x_1] , [x_2, x_3] , and [x_4, x_5, x_6, x_7] . The notion – or the recurring notion – of far more smalls than larges should be the major criteria for whether things are the right things that enable us to see a living structure, or whether we have the right perspective and scope for seeing a living structure. As another example, within a large enough scope of time or space, there are far more ordinary weather conditions than extraordinary ones, whereas within a limited scope of time (10 days) or space (a city), weather conditions may be more or less similar. 45. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 5 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Matching excerpt #WAL2ZW: (Note: The 10 numbers [1, 1/2, 1/3, \dots, 1/10] are classified into three classes: [1/4, 1/5, \dots, 1/10] , [1/2, 1/3] , and [1] , which can be said to have three inherent hierarchical levels. The dataset, due to its inherent hierarchy, is therefore more living or more structurally beautiful than another dataset [1, 2, 3, \dots, 10] , which lacks any inherent hierarchy, or violates the scaling law.) 46. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 0 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #GV3UJZ Abstract: Matching excerpt #MFN8JF: Keywords: Scaling law, Tobler's law, differentiation, adaptation, head/tail breaks, natural streets, the third view of space 47. Source: Modelling the Evolution of Human Trail Systems (#UYLTYJ), Dirk Helbing, Joachim Keltsch, Péter Molnár, p. 3 Context: #BSSYS2 Modelling the Evolution of Human Trail Systems Matching excerpt #ST8FZE: At the beginning, pedestrians take the direct ways to their respective destinations. However, after some time they begin to use already existing trails, since this is more comfortable than to clear new ways. By this, a kind of selection process [20,21,16] between trails sets in: Frequently used trails are more attractive than others. For this reason they are chosen very often, and the resulting reinforcement makes them even more attractive. However, the weathering effect destroys rarely used trails and limits the maximum length of the way system which can be supported by a certain rate of trail usage. As a consequence, the trails begin to bundle, especially where different trails meet or intersect. This explains, why pedestrians with different destinations use and produce common parts of the trail system (Figures 2 and 3). 48. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 8 Context: #57PDWB Interactive Procedural Street Modeling #RXG48N References Matching excerpt #WFPYZC: AASHTO. 2004. A Policy on Geometric Design of Highways and Streets , 5th edition. American Association of Highway and Transportation Officials. 49. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 8 Context: #JCB5RE Advected river textures #XSMAUV Future Work Matching excerpt #78AJMB: Further work could explore improvements to Level of Detail rendering for rivers. Our system currently uses only basic geometry LOD on the terrain and no geometric LOD on the river surface itself. Although the river sections are split into LOD patches, this is only for the purpose of changing detail levels within the fluid simulation algorithm. We believe that adding a sophisticated geometry LOD algorithm would allow the simulation and rendering to operate at an even higher frame rate. 50. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 3 Context: #B9LYTR Scalable real-time animation of rivers #S3P9T2 4. Computing flow velocities #89NKTG 4.1. Finding the volumetric flow rate from the hydro geometry Matching excerpt #UE46TV: If our dataset does not include the volumetric flow rate for each channel, we reconstruct plausible values based on the hydrographic network and its geometry. Approximate matches 1. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 7 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results Score: 0.029 Related excerpt #ACDG5B: Figures 1 show different views of an extensive river network, spanning a 3 \times 3 km terrain. The scene has the following statistics: an input digital elevation map with a per-pixel resolution of 100m, a river that extends for approximately 4km, more than 40,000 primitives forming the river surface, and a final terrain and water surface resolution of 10cm. 2. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 5 Context: #JJE8HN Procedural Riverscapes #TFD8TX 5. River Network Amplification #AZ7MGY 5.4. Rosgen Scene Statistics Score: 0.025 Related excerpt #YCESD5: Table 1 reports the parameters and primitives statistics for Figures 14. The generation time of the two construction trees (riverbed and water) is negligible for these scenes (around 15ms). The number of primitives is related to the average density, which has been set in these examples to a sample every 50cm. It is possible to optimize the construction trees by grouping equivalent parameter primitives into a larger one. 3. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 2 Context: #JJE8HN Procedural Riverscapes #FF5JSX 3. Workflow Score: 0.022 Related excerpt #6LFVGV: The workflow is outlined in Figure 2; it begins with a user-supplied heightfield, obtained, for example, as a scanned digital elevation model or generated by a terrain modeling system. Overlay maps for slope, drainage area, and stream power are derived as a first step. 4. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 0 Context: #JJE8HN Procedural Riverscapes #RMH5XA 1. Introduction Score: 0.018 Related excerpt #2JBFEL: Specifically, from the starting point of a bare-earth terrain, either sourced from existing digital elevation models, generated procedurally, or modeled by the user, and with a range of permissible sampling resolutions (1m - 30m per pixel), a plausible river network is derived according to the Rosgen classification used in hydrology, inscribed into the terrain, and populated with a consistent animated water surface. The resulting river structure and dynamics can also 5. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #Z6DVCN 4. River Network Graph Score: 0.014 Related excerpt #TRPJZX: Figure 5). One complication is that the drainage calculation assumes that there are no depressions (local minima) in the digital elevation model, since these have no outlet to neighboring cells. To prevent disconnected river graphs we apply an optimal depression filling algorithm [BLM14], which leaves the surface slightly proud with an available flow channel. 6. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 2 Context: #JJE8HN Procedural Riverscapes #FF5JSX 3. Workflow Score: 0.013 Related excerpt #X3RVN8: Our work uses the Rosgen river classification [Ros94] that defines the detailed characteristics of the geometry of the riverbed ( i.e. the cross section and longitudinal profile, sinuosity, riverbed materials, entrenchment ratio) according to the local slope and flow of the river. From this combined terrain data we generate a river network graph, whose edges correspond to river segments labeled by Rosgen type (see Figure 3). This results in a parameterized river network with per-cell waterflow values for slope, volume, and velocity. From this information the shape of the riverbed can be derived and inscribed into the terrain. 7. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #TFD8TX 5. River Network Amplification Score: 0.013 Related excerpt #EWA69A: The river graph \mathcal{G} has nodes \mathcal{N}_i that correspond to river junctions and edges \mathcal{E}_{ij} that represent the intervening trajectory of the river. The graph nodes store geomorphological data; in particular, the average slope s_i in the local neighborhood of the node and the flow of the river \phi_i . Graph edges, meanwhile, store their Rosgen type t_{ij} (see Figure 3) and encode the river trajectory as a piecewise-cubic curve. 8. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 2 Context: #JJE8HN Procedural Riverscapes #Z6DVCN 4. River Network Graph Score: 0.012 Related excerpt #V4N668: The analysis proceeds as follows: given a terrain \mathcal{T} composed of regular grid cells C_{ij} , we first generate a discretized river network \mathcal{D} , and then convert it into a river network graph \mathcal{G} with nodes and edges labelled with flow data, as a precursor to river network amplification (as described in Section 5). 9. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 8 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results #FYBSSG 7.1. Performance Score: 0.012 Related excerpt #9DU2N2: Table 2 reports timings and statistics for our method for the examples from this paper. Our implementation supports both real-time GPU and high-quality offline photon-traced rendering. The final model has a compact memory footprint: we are able to represent meandering rivers several kilometers in length with complex water effects in less than a few megabytes. Memory consumption is as low as 22 kilobytes for short rivers (of 50m) up to 2.7 megabytes for longer rivers ( \approx 4 km). Even without memory optimization, individual primitives range from 50 bytes to at most 90 bytes. 10. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 3 Context: #JJE8HN Procedural Riverscapes #TFD8TX 5. River Network Amplification #3S2ME8 5.1. Analysis and Trajectory Refinement Score: 0.012 Related excerpt #KN76Q3: For every river segment \mathcal{E}_i in \mathcal{G} , we generate a refined three-dimensional trajectory \tilde{\mathcal{E}}_i , depending on its computed Rosgen type t_i . The horizontal trajectory can be meandering if the local slope s_i is low and the flow \phi_i moderate (type C, E or G), or straight if the slope is steep (type A or A+ ). Afterwards, the longitudinal elevation profile of the trajectory is also refined with a view to creating drops and basins keyed to the Rosgen type (see Figure 7 and 9). This is important since the riverbed slope is one determinant of cascade, wave and turbulence placement. 11. Source: Procedural Riverscapes (#AK7NGE), A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial, p. 7 Context: #JJE8HN Procedural Riverscapes #NHDQDL 7. Implementation and results Score: 0.01 Related excerpt #DJYD3M: For the scenes shown in Figures 9 and 18, we attempted to create a peaceful atmosphere with only a few eddies and small cascades. Note that the steeper river (Figure 9) with Rosgen type A+ has more primitives than its flatter counterpart of type B because our procedural model reduced the radius of water primitives to better capture the more vigorous dynamics. 12. Source: Wholeness as a Hierarchical Graph to Capture the Nature of Space (#BYG3BQ), Bin Jiang, p. 8 Context: #V2MHRV Wholeness as a Hierarchical Graph to Capture the Nature of Space #TXBKLJ 4. Case studies: Computing the degrees of life #3NPEFU 4.2 The streets of Manhattan and Sweden Score: 0.02 Related excerpt #LUZ5UR: The next two case studies move from the architectural scale to city and country scales. Manhattan as a city was chosen for the case study because its street network is easily perceived as a whole. We generated 1,800 axial lines for Manhattan and converted them into a hierarchical graph in terms of line-to-line intersection. This intersection relationship is based on the simple rule that short lines point to, or support, long ones. The same rule applies to the streets of Sweden. The streets are the complete set, including 166,479 streets for the entire country. The streets are a mix of named and natural streets (Jiang and Claramunt 2004, Jiang, Zhao and Yin 2008). In other words, individual street segments are merged according to the same names, and further merged together to form the natural streets. The street networks are then converted into dual graphs in which the nodes represent the individual streets, and the directed links indicate relationships from short streets (or axial lines) to long ones. Based on the directed graphs, we computed the degrees of life for the individual axial lines and streets, and they were visualized using the spectral colors, with blue as the lowest degree of life, red as the highest degree of life, and the other colors for degrees of life between the lowest and highest. It was surprising that the degrees of life demonstrated very striking power laws (Clauset et al. 2009), with two and three decades of power law fit, and a very high degree of goodness of fit (Table 2). The power law exponent around 2.0+ is consistent with the theoretic rules Salingeros (1998) suggested for scaling hierarchy. 13. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification Score: 0.015 Related excerpt #U7AJ7K: The river graph divides the domain \Omega into nonoverlapping cells that allow us to build a set of watersheds and to construct a dual graph that stores crests (Section 5.1). The water flow is extracted from the river graphs, and each water-course is labeled with respect to the Rosgen classification (Section 5.2). 14. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #VE6H2H 5.2 Water-courses Labeling Score: 0.011 Related excerpt #VPDQ33: After the domain is segmented, we classify the water-course presented in every Voronoi cell V_i . Our method relies on the Rosgen classification [Rosgen 1994] that defines nine river categories depending on their slopes and trajectories. Each river class has a trajectory type (A+, A, B, C, D, DA, E, F, or G) and a digging profile of the riverbed (Fig. 9). The classification includes the geological composition of the riverbed (bedrock, rocks, stones, gravel, sand, silt, or clay) in this description. 15. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 5 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #T6FSBF 5 River Classification #VE6H2H 5.2 Water-courses Labeling Score: 0.011 Related excerpt #9QKM5Y: We assign to each river node its classification based on the slope of the river and its proximity to the coast. River nodes that are close to coasts (based on a geodesic distance threshold) are labeled as braided rivers (those consisting of multiple channels separated by bars and defined as D or DA). Similarly, river mouths with a flow greater than a fixed value are marked as deltas. 16. Source: Terrain Generation Using Procedural Models Based on Hydrology (#DMTA8Y), Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin, p. 4 Context: #RULAFW Terrain Generation Using Procedural Models Based on Hydrology #WWSSDJ 4 River Network Generation #DBN56J 4.2 River Network Generation #VTGN6K 4.2.2 Node Expansion Score: 0.011 Related excerpt #5VRAH5: The effect of varying parameters on the generated river network is depicted in Fig. 8. The parameter set ( P_c = 0.2, P_s = 0.7, P_a = 0.1 ) produced highly curved watersheds (left). There are only a few main streams, but many ( > 75\% ) small streams with a Horton-Strahler numbers equal to 1 (Fig. 8 left). In contrast, the parameter set ( P_c = 0.2, P_s = 0.1, P_a = 0.7 ) produced drainage networks with watersheds of comparable sizes (Fig. 8 right). In the second case, the main rivers are longer because their priority indices were statistically kept longer in the queue during the graph generation, and the watersheds are structured around this main river. 17. Source: Mountain Trail Formation and the Active Walker Model (#GY93FG), J. P. Hague, S. J. Gilks, p. 11 Context: #G4BEE9 Mountain trail formation and the active walker model #MKLE5Y 4. A model of mountain walkers #KAWSKG 4.2. Discretization scheme Score: 0.011 Related excerpt #L9CKAZ: As humans tend to walk with different step sizes, we varied the speed of the individual walkers. This variation leads to continuous paths. The width of the area studied was chosen as 10m and the length of the observed area (in the direction of the incline) as 25m. This is probably realistic for this type of trail formation, since we suspect that walkers aim for local goals, rather than the final goal of the peak (which is not necessarily visible from all locations). 18. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 14 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #KNGJAN Data and code availability statement Score: 0.027 Related excerpt #68A5N5: The data used and generated in this study are publicly available at Figshare, which is accessible with the following link https://figshare.com/s/e4a69ee23511de986239 . The file package includes (1) an Excel file with results out of the eight pairs of images' analyses, (2) Shapefiles for all pairs both the decomposable substructures and non-decomposable substructures, and (3) all output results of the living structure algorithm for each individual image. The living structure algorithm is based on Python 2.7 ( https://www.python.org/download/releases/2.7/ ) and uses the following libraries: ArcPy (10.8) and Numpy. (The Python scripts process an input image into recursively defined substructures, and into a tree-like network of decomposable substructures.) The software tools used in the study include ArcGIS 10.8 ( https://www.esri.com/en-us/arcgis/products/arcgis-desktop/overview ) for the processing and analysis of spatial data, Microsoft Excel ( https://www.microsoft.com/en-us/microsoft-365/excel ) for storing and analyzing numerical results, and Gephi 0.9.2 ( https://gephi.org/ ) for network analysis and visualization. 19. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 17 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #2KSWYX Appendix A: Verification of the recursive approach against georeferenced images Score: 0.026 Related excerpt #PCKFDZ: The recursive approach developed in this paper was initially verified by ordinary images that all have the same size and same resolution. Given the same condition, the verification should logically apply to any pair of georeferenced images as well. In this Appendix, we chose two pairs of georeferenced images to demonstrate that how the livingness of space can be well captured (Figure A1). The first pair is about two nighttime images: Belgium, the Netherlands, and Luxburg (Benelux, Panel a1) in contrast to Stockholm region (Panel b1). The central European area including the three countries is much more populated than the Stockholm region, so the former is full of human settlements (far more smalls than larges) therefore more living than the latter; see Panels a2 and b2 or a3 and b3. This fact is clearly reflected in the livingness scores both LR and V. 20. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 17 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #2KSWYX Appendix A: Verification of the recursive approach against georeferenced images Score: 0.026 Related excerpt #DYW867: The second pair is about two satellite images: one from countryside of Sweden (Panel c1) and the other from the center of Stockholm city (Panel d1). Again, the two areas are with the same physical size and their images are with the same resolution. Different from the nighttime images that capture human settlements at night, the satellite images capture geographic features of various kinds. In this case, the natural scene is supposed to be more living than the urban scene (Panels c2 and d2, or c3 and d3). It is indeed true that the natural scene has higher livingness scores than the urban scene. 21. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 6 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #KXUAWS 3. A recursive approach to computing the structural beauty of images #KK923R 3.2 The recursive approach Score: 0.02 Related excerpt #KR5YTL: For the weather-beaten face image, the first decomposable substructure (at the first iteration) is the image itself and it has 768 substructures defined at four hierarchical levels, so LR_1 = 768 \times 4 = 3,072 ; for the last three decomposable substructures (at the sixth iteration), so LR_{61-63} = 7 \times 3 + 10 \times 3 + 9 \times 3 = 78 . In Table 2, we divided the LR score according to individual iterations, so the hierarchy (H) is derived from H = LR/S , which is why H is not integral, except for the first and the last iterations. 22. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 6 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #KXUAWS 3. A recursive approach to computing the structural beauty of images #KK923R 3.2 The recursive approach Score: 0.02 Related excerpt #9LHU4M: As an example, the weather-beaten face image has 63 decomposable substructures derived at the six levels of recursion (Table 2), so V = 63 \times 6 = 378 . 23. Source: Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space (#MJKTBB), Bin Jiang, Chris de Rijke, p. 7 Context: #YXCQD2 Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space #KXUAWS 3. A recursive approach to computing the structural beauty of images #KK923R 3.2 The recursive approach Score: 0.013 Related excerpt #YTCZ4Y: substructures, resulting in 768, 1,856, 1,206, 598, 112, and 26 substructures, respectively, at different levels of the recursion, and their centroids are shown as red dots (c1–c6). Overlapping all the six levels of the 4,566 ( = 768 + 1,856 + 1,206 + 598 + 112 + 26 ) centroids together represents the skeleton of the image (d). Among the 4,566 substructures, only 62 ( = 11 + 20 + 22 + 6 + 3 ) are decomposable substructures and their centroids (e), and the 63 centroids are visualized according to their degree of connectivity (both in- and out-links) by the dot sizes, with colors indicating their levels of recursion (f). 24. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 9 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #HTXQDQ 7.2. Interactive landscape simulation Score: 0.027 Related excerpt #NEL8YN: Rivers and lakes In Figure 9, we demonstrate how our algorithms can be used on complex large-scale terrains to demarcate lakes and rivers that are registered correctly with existing erosion lines and depressions. On the left in Figure 9, a mountainous region in the Alps transitions into an urbanized flat glacial valley. On the right, a tidal estuary around Mont Saint-Michel, France, leads into the sea. They contain 383,918 and 8,445,644 basins, respectively. In both cases, the elevation data was obtained from the IGN RGE ALTI Digital Elevation 1m dataset [IGN22]. 25. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance Score: 0.027 Related excerpt #8VZYXE: For our test dataset, we incorporated a mix of real and synthetic terrains. We began by extracting a set of 10 real terrains from the IGN RGE ALTI Digital Elevation 1m dataset [IGN22] chosen on the basis of topographic variety. These 10 terrains were sampled at cell resolutions of 512 \times 512 , 1024 \times 1024 , 2048 \times 2048 and 4196 \times 4196 to support scaling experiments. 26. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 10 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #M2TBHA 7. Results #ARG9Y4 7.3. Performance Score: 0.019 Related excerpt #PQTH4E: We also included 5 synthetic terrains at the same resolution levels, and each with a controlled proportion of depression coverage (at synth-1% , synth-5% and synth-15% levels). These were generated by erosion simulation (Section 6), followed by layering different amplitudes of uniformly distributed noise. Note that it is common practice to add this type of noise during erosion simulation to mimic natural stochastic processes. 27. Source: FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation (#NV2YRW), Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain, p. 2 Context: #6UY46T FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation #SD69QC 3. Overview Score: 0.014 Related excerpt #GUKBY3: grid of elevations z , often referred to as a Digital Elevation Model (DEM). This is an implementation decision and adaptation of our algorithms to other heightfield structures, such as Triangular Irregular Networks [Ban07], is straightforward. Note, however, that z is a unique mapping h(x, y) = z over the x, y plane and so we do not support true 3D terrains with caves and overhangs [GGP + 19]. 28. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 10 Context: #RNVWWR Water Surface Wavelets #W3R46F 9 DISCUSSION Score: 0.015 Related excerpt #ZB9JR8: Compared to Eulerian height field-based simulations, our method stores 4096^2 (spatial resolution) \times 16 (wave vector resolution) samples for our 4 km by 4 km scene. A height field storing the same number of 29. Source: Water surface wavelets (#PBM2TC), Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan, p. 5 Context: #RNVWWR Water Surface Wavelets #2KAQMF 4 DISCRETIZATION #6AJDFD 4.1 Discretizing \mathcal{A} Score: 0.013 Related excerpt #UG8PZG: in Section 8. As mentioned above, \mathcal{A} varies slowly over space, so we do not require much spatial resolution either. In our implementation we allocate X_{\mathcal{A}} = 4096 grid cells for each spatial dimension, which defines a grid cell spacing of approximately one meter. 30. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 55 Context: #8MPFPH X ECOLOGY OF THE ORDINARY #TFM623 Example 20. The Ecology Of The Ordinary Score: 0.016 Related excerpt #ANS7MY: Cycle 2. latent centers in the site: the bike path, along the south side, Warwick avenue along the west, and Lowell Street in the south east corner. → The computation then identifies a connection and pedestrian precinct generates a curved line, more or less a median through the triangle of the site, but curving slightly and leading to stairs at the east end where there is a 20 foot rise to Lowell street. 31. Source: Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole (#PXG56P), Christopher Alexander, p. 55 Context: #8MPFPH X ECOLOGY OF THE ORDINARY #TFM623 Example 20. The Ecology Of The Ordinary Score: 0.011 Related excerpt #4B4QNJ: Cycle 1. The process starts with a triangular brown-field site in Somerville, 5.5 acres in area, between a railroad line, a bike path, and an existing neighborhood → The computation then identifies latent centers in the site: the bike path, along the south side, Warwick avenue along the west, and Lowell Street in the south east corner. 32. Source: A Layered Particle-Based Fluid Model for Real-Time Rendering of Water (#RBS5K6), Daniel Scherzer, Florian Bagar, Michael Wimmer, p. 5 Context: #5NFAXU A Layered Particle-Based Fluid Model for Real-Time Rendering of Water #T8YYAV 6. Results Score: 0.011 Related excerpt #Z295Y2: We have tested our approach in three scenes (see Figure 8): Corridor has many obstacles and therefore creates a turbulent water flow with a lot of foam and spray. Waterfall is less turbulent, but due to its simplicity, artifacts are easily detected by visual inspection. Here, rendering of foam is essential for realistic results. Bamboo has dynamic elements that interact with the water. The bamboo is slowly filled with water, till the water weights it down and is emptied again. Please see the video for more details. 33. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 5 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Score: 0.022 Related excerpt #FH8NYH: A street network is more correctly conceived of as a set of far more short streets than long ones, or a set of far more less connected streets than well connected ones (Figure 2b). The street network has four levels of scale, indicated by the four colors, far more short streets than long ones across the scales, and more or less similar streets on each of the four scales. A coastline is more correctly represented as a set of far more small bends than large ones (Figure 2d). The coastline has three levels of scale, indicated by three sets of bends: [x_1] , [x_2, x_3] , and [x_4, x_5, x_6, x_7] . The notion – or the recurring notion – of far more smalls than larges should be the major criteria for whether things are the right things that enable us to see a living structure, or whether we have the right perspective and scope for seeing a living structure. As another example, within a large enough scope of time or space, there are far more ordinary weather conditions than extraordinary ones, whereas within a limited scope of time (10 days) or space (a city), weather conditions may be more or less similar. 34. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 6 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Score: 0.015 Related excerpt #AKC5CG: Now let us apply the recursive way of stating a whole or structure into the street network illustrated in Figure 2. Seen from above, the sample street network consists of 50 streets at four hierarchical levels indicated by the four colors: red (r), yellow (y), turquoise (t) and blue (b). Instead of stating the street network as a set or as four classes, we state it as an iterative system consisting of four subwholes or substructures that are recursively defined: [r] , [r, y_1, y_2] , [r, y_1, y_2, t_1, t_2, t_3, t_4, t_5] , and [r, y_1, y_2, t_1, t_2, t_3, t_4, t_5, b_1, b_2, b_3, \dots, b_{42}] . In the same way, it is not difficult to figure out the three recursively defined subwholes for the coastline: [x_1] , [x_1, x_2, x_3] , and [x_1, x_2, x_3, \dots, x_7] . This living structure representation is recursive and holistic, so it differs fundamentally from existing representations that tend to focus on segmented individuals or mechanistic pieces. An advantage of the living structure representation is that the inherent hierarchy of space is obvious. To this point, we have seen clearly how the right things constitute an iterative system, being a living structure consisting of far more smalls than larges. 35. Source: Geography as a Science of the Earth’s Surface Founded on the Third View of Space (#SKRF4C), Bin Jiang, p. 5 Context: #KSQ64X Geography as a Science of the Earth's Surface Founded on the Third View of Space #F4PFN9 3. Living versus nonliving structure: The “things” the two laws refer to Score: 0.011 Related excerpt #WAL2ZW: (Note: The 10 numbers [1, 1/2, 1/3, \dots, 1/10] are classified into three classes: [1/4, 1/5, \dots, 1/10] , [1/2, 1/3] , and [1] , which can be said to have three inherent hierarchical levels. The dataset, due to its inherent hierarchy, is therefore more living or more structurally beautiful than another dataset [1, 2, 3, \dots, 10] , which lacks any inherent hierarchy, or violates the scaling law.) 36. Source: Modelling the Evolution of Human Trail Systems (#UYLTYJ), Dirk Helbing, Joachim Keltsch, Péter Molnár, p. 2 Context: #BSSYS2 Modelling the Evolution of Human Trail Systems Score: 0.016 Related excerpt #PMPCXQ: Our simulations base on a discretization of the considered area in small quadratic elements of equal size, which converts the integral (2) into a sum. Temporal and spatial derivatives are approximated by difference quotients. The presented examples begin with plain, homogeneous ground. All pedestrians have their own destinations and entry points, from which they start at a randomly chosen point in time. In Figure 2 (Figure 3) pedestrians move between all possible pairs of three (four) fixed places. While in Figure 4 the entry points and destinations are distributed over the small ends of the ground. 37. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 1 Context: #57PDWB Interactive Procedural Street Modeling #P35TFV 3 Pipeline Overview Score: 0.03 Related excerpt #QWDWBH: In this section, we give an overview of our modeling pipeline. The input to our system includes four maps loaded as images: 1) a binary valued water map W , 2) a binary valued park and forest map F , 3) a height map H , and 4) a population density map P . Each of these is a discrete function of f: [-X, X] \times [-Y, Y] \rightarrow [0, 1] defined on a grid ( 512 \times 512 in our implementation). Our system employs a three-stage pipeline (Figure 2). 38. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 6 Context: #57PDWB Interactive Procedural Street Modeling #ZN73JY 7 Results Score: 0.021 Related excerpt #2L8GVV: To demonstrate the capabilities of our approach we show a number of street graphs generated using our system. Figure 16 shows a section of downtown Taipei which we have modeled. In Figure 17, a section of the Willamette River in Portland, OR is modeled. A road network for Manhattan is shown in Figure 18. Note that our goal is to generate maps inspired by real world maps, but not to exactly replicate the existing cities. In our experiments, a city with reasonable complexity can be modeled within five minutes, such as the fictional city in Figure 1, and the cities in Figures 16 and 17 took about five minutes for the main layout, but required an additional thirty to sixty minutes to fine tune the details and to experiment with different designs. The final images of three-dimensional geometry were created using RenderMan with ambient occlusion. See Figure 19 for four frames of a fly through shown in the accompanying video. 39. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 1 Context: #57PDWB Interactive Procedural Street Modeling #P35TFV 3 Pipeline Overview Score: 0.02 Related excerpt #BMDPVE: Stage Two is the street graph generation step. Streets are computed as hyperstreamlines (Section 4) of the tensor field. In Section 6 we explain how to generate the street network, edit it, and modify existing street networks using a combination of graph-based and tensor field editing. Street networks are modeled using a hierarchy: major roads and minor roads . Major roads are typically major business roads and local highways, and minor roads are usually residential and back roads. A street network is stored as a graph G = (V, E) where V is a set of nodes and E is a set of edges. Nodes with three or more incident edges are crossings . Road attributes, such as road width, road type, pavement markings, and the type of lanes, are stored at nodes and edges. 40. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 2 Context: #57PDWB Interactive Procedural Street Modeling #P35TFV 3 Pipeline Overview Score: 0.02 Related excerpt #QCYCTQ: (2) that give rise to a major street network (3). Then the user refines the initial major road layout by placing a new tensor field design element inducing a radial structure in the tensor field (4) as well as the street graph (5). Using our segmentation algorithm, the user performs additional local tensor field modifications (6) and generate a minor road network (7). The user uses a rotation noise field to create irregular structures near the top (8) and produces the final result (9). The visualization of tensor fields shown in this paper is based on [van Wijk 2002; Zhang et al. 2007]. 41. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 2 Context: #57PDWB Interactive Procedural Street Modeling #QNKCB5 5 Tensor Field Generation #FCEMBJ 5.1 Generation of Basis Fields Score: 0.019 Related excerpt #6X3MNM: The tensor field is generated based on user constraints (desirable patterns) and topography information (water and park boundaries, terrain height, etc). Near the city center, the user may wish to create a typical North-South and East-West pattern. In contrast, near the coastline, it is often natural to design the road network to follow the coastline. To provide sufficient flexibility in addressing these different and often competing needs, we seek a tensor field design framework that allows both global and local control. 42. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 3 Context: #57PDWB Interactive Procedural Street Modeling #QNKCB5 5 Tensor Field Generation #FCEMBJ 5.1 Generation of Basis Fields Score: 0.018 Related excerpt #UZKZGT: For example, we can extract boundary field from a water map. Since the water map we use is pixel-based, we can extract the boundary [Shapiro and Stockman 2001] of water in the map which can be either open (oceans, or rivers) or closed (lakes). From the boundary curves, we obtain a polyline approximation L , i.e., a curve consisting of a number of connected line segments. 43. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 6 Context: #57PDWB Interactive Procedural Street Modeling #ZPVYV6 6 Street Graph Generation #Y8ER56 6.3 Street Graph Editing Score: 0.014 Related excerpt #EGCNHM: where road networks share some similarities with fracture patterns. One example are major roads in rural Missouri (see Figure 14 left). In this case local topography dominates the road layout. We have some possibility to match these patterns with a tensor field and added noise. Figure 14 (right) shows a map generated using rotation on the graph (i.e. rotating the street segments). The rotation field is generated using Perlin noise discussed in Section 5.3. 44. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 5 Context: #57PDWB Interactive Procedural Street Modeling #ZPVYV6 6 Street Graph Generation #4SLJV9 6.1 Major Street Graph Generation from Tensor Fields Score: 0.012 Related excerpt #J3F7DX: Transitions in Density: At city borders the road density decreases. Transitions in density are a phenomenon of the street graph and not the underlying tensor field. In our system, we use road density maps (or population density maps) to control d_{sep} in the road tracing algorithm described above. Figure 10 provides an illustrative example demonstrating how our system imitates the transition of density. 45. Source: Interactive procedural street modeling (#V4TQYB), Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka, p. 1 Context: #57PDWB Interactive Procedural Street Modeling #P35TFV 3 Pipeline Overview Score: 0.01 Related excerpt #6LJBKK: To give an intuitive feeling for our system, we describe an example editing scenario (see Figure 3). First the user loads a water map (1) and places some tensor field design elements [Zhang et al. 2007] 46. Source: Advected river textures (#WZMZGY), Dirk Arnold, Stephen Brooks, Tim Burrell, p. 8 Context: #JCB5RE Advected river textures #HMVN46 Results Score: 0.016 Related excerpt #PRVSL6: Level of Detail provides notable performance improvements as can be seen in Table 1. Even the modest LOD optimizations we have implemented make a significant difference to the frame rate and to the number of polygons rasterized per second. All screenshots and timings were produced on an off-the-shelf dual-core Athlon XP 3800+ computer with an nVidia 8600GT graphics card and 4GB RAM. However, the code has not been parallelized or GPU optimized, meaning that only one of the two cores on the CPU has been directly used. Most of example river beds used in this paper have been imported from DEM files of real rivers. 47. Source: Procedural Generation of Roads (#XDEFZS), A. Peytavie, E. Galin, E. Guérin, N. Maréchal, p. 6 Context: #UR2SY7 Procedural Generation of Roads #GV6T4B 5. Segment path masks #N4M5TN 5.4. Stochastic sampling Score: 0.016 Related excerpt #WJSTC2: Table 5 reports statistics corresponding to the shortest paths illustrated in Figure 15 and demonstrating the efficiency of the sampling technique. The tunnel and bridge mask areas were set with r_i = 50 m and r_e = 300 m over a 300 \times 300 grid with a sampling grid size of 10 m. The corresponding number of grid points visited at every iteration was equal to \#T = 2728 . In contrast, the number of sample grid points in the stochastic approach was set to \#S = 50 . Timings demonstrate that the speed up is proportional to the ratio \#S/\#T . 48. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 3 Context: #B9LYTR Scalable real-time animation of rivers #S3P9T2 4. Computing flow velocities #89NKTG 4.1. Finding the volumetric flow rate from the hydro geometry Score: 0.015 Related excerpt #UE46TV: If our dataset does not include the volumetric flow rate for each channel, we reconstruct plausible values based on the hydrographic network and its geometry. 49. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 2 Context: #B9LYTR Scalable real-time animation of rivers #XF2N2Y 3. Overview Score: 0.012 Related excerpt #QXYWAJ: Input data. The input data of our algorithm is made of raster data for the terrain elevation and texture, of vector data for the fluid boundaries, and of wave textures (see Figure 2, left). The vector data describes a network of channels connected by junctions , as well as obstacles such as islands. Each channel has two boundary curves, a flow rate and a flow direction. This data could come from a GIS database, be simulated from an erosion model, or be generated interactively or procedurally. The wave textures can come from any source (Perlin noise, FFT waves, etc.). 50. Source: Scalable real‐time animation of rivers (#XDESU9), Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu, p. 2 Context: #B9LYTR Scalable real-time animation of rivers #XF2N2Y 3. Overview Score: 0.011 Related excerpt #J9JNDY: Runtime data. At run-time the terrain data is subdivided in a dynamic quadtree, based on the viewer position and distance. Each quad contains raster data and clipped vector data for its corresponding terrain part (see Figure 2a). This quadtree is computed as described in [BN08]. When a new quad becomes visible we compute on the fly the stream function values at channel boundaries (see Section 4.1). We also create an acceleration structure to quickly compute distances to channel boundaries (see Section 4.4). This data remains in memory as long as the quad is visible. ### 13. Assistant tool calls #### Tool call: `write_note` ```json { "block_ids": [ "ZHQFZP", "MSXUGH", "EKXATA", "MNZNZU", "9VNYCT", "6N825C", "W7JZEK", "E6X4P6", "EQTM8J", "N9TEH4", "LBNKBW", "Z3MXM7", "M53PTE", "YVMH2N", "BDZQP4", "8QGM6W", "NEL8YN", "8ERHN4", "XR7Z7G", "ED94U3", "VG86AP", "HS22AT", "ACDG5B", "YCESD5", "GZJUCV", "9DU2N2", "2KNSHV", "WKY9MT", "UG8PZG", "WV3FXP", "BEDUYL", "23W9S2", "82HGFN", "9AHGRG", "NHQBFC", "RTYCL9", "LUVPJR", "754PPX", "8KBMFE", "JS4LBU", "BMKDJR", "K7SCA8", "EUX776", "43XVF5", "WJSTC2", "JLGV3R", "BPF8Q6", "8AQDAB", "CK2TWF", "3LSFWC", "J2KKMV", "WUZ6YE", "AJSDD6", "HWVUS7", "54E5UT", "GNDKEV", "D33DUB", "SFWHTE", "76SGWC", "247BPE", "8CNUPW", "LUZ5UR", "D2C54Y", "XZBXLL", "MKYDT2", "V5XDSY", "2RHVZB", "KAFWZ7", "A6TZBP" ], "text": "Cross-corpus inventory of notable units, quantities, and parameters.\n\nTerrain/erosion: Large-scale uplift/erosion experiments use 50×50 km terrain, uplift 5×10^-4 m/y, erosion coefficient 5.61×10^-7 y^-1, target summit ≈2000 m, and Δt=2.5×10^5 y (#ZHQFZP); stream-power applicability is 10^5–10^7 y and tens–hundreds km (#MSXUGH), commonly m=0.5,n=1 (#EKXATA), with empirical h_max[km]=2.244u/k (#MNZNZU). Thermal erosion often uses 30° talus (#9VNYCT), or varied 6°–54° limits (#6N825C); mountains form around 50 iterations and stabilize in 100–300 (#W7JZEK). Analytical erosion examples use 512² cells, 50 m spacing, t=4.6 My, 460 simulation steps of 10,000 y versus 43 fixed-point steps (#E6X4P6); shrinking cells 50→25→12 m raises simulation iterations 230→460→980 (#EQTM8J). Examples span 200 ky–1.6 My (#LBNKBW), 100/200/300 ky at 30 m spacing (#Z3MXM7), and a 4.6 My mountain at 5/15/25 km scales (#N9TEH4). FastFlow compares Δt=1,000 y explicit to 20,000 y implicit; a 10 My landscape takes 7.2 s vs 0.5 s (#M53PTE), while 10 iterations/0.1 s represent 700 ky on 512² and 100 iterations take 0.7 s (#YVMH2N). Routing runs under 55 ms to 4096² (#BDZQP4), with 5× flow and 34–52× depression-routing speedups at 1024² (#8QGM6W). Real 1 m DEM examples contain 383,918 and 8,445,644 basins (#NEL8YN).\n\nHydrology/rivers: A recurring empirical relation is discharge φ[m³/s]=0.42A^0.69 for drainage area A[m²] (#VG86AP, #HS22AT). Procedural Riverscapes spans a 3×3 km terrain, ≈4 km river, >40,000 primitives, 100 m input DEM pixels, and 10 cm output detail (#ACDG5B); primitives sampled every 50 cm and construction trees generated in ≈15 ms (#YCESD5), rendering >70 fps at 1920×1080 (#GZJUCV). Storage ranges from 22 kB for 50 m to 2.7 MB for ≈4 km; primitives cost 50–90 bytes (#9DU2N2). Compared offline production used 3 cm precision, 4.5M particles, 200M voxels, 20 s output, and 165 total work/simulation hours (#2KNSHV). Priority-Flood tests include 3 m DEMs of 152M and 318M cells (#8ERHN4); a larger benchmark covered 72,500 km² and ≈8×10^9 cells, averaging 16.8% and maxing 37.2% speedup (#XR7Z7G), with up to 37% improvement and one CPU matching six processors (#ED94U3).\n\nWater/waves/rendering: Surface Wavelets simulates 4×4 km at 60 fps (#WKY9MT), using 4096 cells per spatial axis (≈1 m spacing; #UG8PZG), 16 directions and usually 1–4 wavenumber samples (#WV3FXP). Despite the coarse grid it resolves 2 cm wavelengths; an equivalent direct heightfield would bottom out at 0.5 m under Nyquist (#BEDUYL). Precomputation gives ≈4.7×, 60→280 fps (#23W9S2); a profile-buffer optimization raised evaluation 1.8→275 fps, reported as 233× (#82HGFN). Four wavenumber groups roughly quadruple cost and reduce 70→20 fps (#9AHGRG). Water viscosity is given as 10^-6 m/s in the dissipation model (#NHQBFC; unit as printed should be checked dimensionally). Breaking-wave tests use 160k–200k grid points at 40–75 fps; simulation consumes 80% of runtime (#RTYCL9). Layered particle water uses 20k–64k particles at 1280×720 and 112 bits/pixel of intermediate buffers (#LUVPJR), with runtime split ≈23.12/24.4/27.43/25.05% across depth, thickness, smoothing, and composition over 6k frames (#754PPX). Advected river textures report 60–120 fps, average 85 (#8KBMFE), illustrate 1.3 m/s flow (#JS4LBU), use a 15° flow-hint cutoff (#BMKDJR), and set particle lifetime 1.5 s plus travel limit 5% of river length (#K7SCA8). Scalable river animation tests 25×25 km at 800×600 with 20 px particle/sprite radius (#EUX776). Halftone foam adds <3% load over five-minute tests (#V5XDSY); surveyed historical ocean methods report ≈20–30 fps on GeForce 2 (#2RHVZB) and ≈100 fps on GeForce 3 (#KAFWZ7).\n\nRoads/racing: Procedural road routing discretizes position×orientation as n²×m (#43XVF5); tunnel/bridge masks use 50–300 m lengths on a 300² grid at 10 m spacing, comparing 2728 visited points to 50 stochastic samples (#WJSTC2), and produces paths in <1 s on 100² grids (#JLGV3R). Racing optimization covers a 4.5 km circuit, converges in 4–5 iterations, about 30 s each (#BPF8Q6); experimental laps are 138.6 s versus 139.2 s and a professional 137.7 s, with μ=0.90 and peak 0.9g (#8AQDAB). Each full iteration is 26 s across 1843 timesteps versus hours for nonlinear optimization (#CK2TWF); controller rate is 200 Hz (#3LSFWC).\n\nTrails/movement: Mountain-walker footprints use a 10 cm square footprint (#J2KKMV). Simulations use Gmax=200 m^-1, visibility 10 m, 50 footfalls (versus real-world several hundred), weathering 1000 s (versus days), walker speeds 0.5–1.5 m/s, a 25×10 m slope, and 25,000 walkers (#WUZ6YE). Zigzags appear with forbidden angles 25° uphill/10° downhill, weathering 1500 s, and α≳0.45 (#AJSDD6). Stability tests use Δt 0.5/0.25 s and Δx=Δy 5/2.5 cm (#HWVUS7). Biomechanics: a 10° incline may require 60° hip flexibility vs 30° flat; observed ankle max ≈24° (#54E5UT). Field slopes cited around 1:8 and 1:2 (#GNDKEV). Trail design suggests 8–10% for family/senior users where 12–16% may be structurally sustainable (#D33DUB), hillslope:trail grade ratios around 2:1–3:1 (#SFWHTE), and a worked example adds 500 ft to reduce 200 ft rise over 2000 ft from 10% to 8% (#76SGWC). Sudden changes include 5→10% and 7→20% (#247BPE); paired clinometer readings should agree within 1 percentage point (#8CNUPW).\n\nDomain-specific abstract quantities: Wholeness case studies use 1,800 Manhattan axial lines and 166,479 Swedish streets, finding power-law exponents around 2+ (#LUZ5UR). Living Images reports recursively defined substructures ≈3% of pixels, ≤2% decomposable, and >3–4 recursive levels (#D2C54Y, #XZBXLL). Head/tail breaks continues while the head is ≤40% (#MKYDT2). Platformer physics uses Castlevania ≈3.7 tiles/s, Mario 10 tiles/s, others ≈5.5, and suggests 4–10 tiles/s as playable (#A6TZBP).", "title": "Cross-corpus inventory of units, quantities, and domain-specific numeric parameters" } ``` ### 14. Tool result: write_note NOTE SAVED #4PF6N6 IRI: https://m.sheaf.less.rest/4PF6N6 ### 15. Assistant I gathered the cross-paper inventory into a durable note: #4PF6N6. I prioritized physical units, model parameters, scale limits, resolutions, and performance quantities rather than ordinary counts. ## Most interesting domain-specific quantities ### Terrain, erosion, and geological time - A representative mountain-generation setup uses a $50\times50\ \mathrm{km}^2$ domain, uplift of $5\times10^{-4}\ \mathrm{m\,yr^{-1}}$, erosion coefficient $5.61\times10^{-7}\ \mathrm{yr^{-1}}$, a $2.5\times10^5$-year timestep, and produces peaks around $2000\ \mathrm{m}$ (#ZHQFZP). - The stream-power model is intended for scales of roughly $10^5$–$10^7$ years and tens to hundreds of kilometres (#MSXUGH). - Common stream-power exponents are $m=0.4$–$0.5$ and $n=1$ (#EKXATA, #2DEC4W). - A useful fitted relationship is $$h_{\max}[\mathrm{km}]=2.244\,\frac{u}{k}$$ relating maximum mountain height to uplift and erosion (#MNZNZU). - Thermal erosion commonly uses a $30^\circ$ talus limit; one experiment spatially varies the permitted angle from $6^\circ$ to $54^\circ$ to model rock-strength variation (#9VNYCT, #6N825C). - Mountains become recognizable after about 50 iterations and stop changing appreciably after 100–300 iterations (#W7JZEK). - Analytical erosion examples range from $100$–$300\ \mathrm{ky}$ for gully evolution to $4.6\ \mathrm{My}$ for mature mountains (#Z3MXM7, #E6X4P6). - Reducing terrain spacing from $50$ to $25$ to $12\ \mathrm{m}$ raises conventional simulation iterations from 230 to 460 to 980, illustrating the strong resolution–timestep coupling (#EQTM8J). - FastFlow models $700{,}000$ years in $0.1\ \mathrm{s}$ using ten iterations on a $512^2$ terrain; 100 iterations take $0.7\ \mathrm{s}$ (#YVMH2N). - Its implicit timestep is $20{,}000$ years versus $1{,}000$ years explicitly. A ten-million-year landscape takes $0.5\ \mathrm{s}$ rather than $7.2\ \mathrm{s}$ (#M53PTE). ### Hydrology and rivers - Two papers use the same geomorphological discharge approximation: $$\phi\,[\mathrm{m^3\,s^{-1}}]=0.42A^{0.69},$$ where $A$ is drainage area in $\mathrm{m^2}$ (#VG86AP, #HS22AT). - Procedural Riverscapes demonstrates a $4\ \mathrm{km}$ river across a $3\times3\ \mathrm{km}$ terrain, starting from $100\ \mathrm{m/pixel}$ elevation data but producing terrain and water detail at $10\ \mathrm{cm}$ resolution (#ACDG5B). - That scene contains more than 40,000 river-surface primitives; primitives are sampled every $50\ \mathrm{cm}$ and construction takes about $15\ \mathrm{ms}$ (#ACDG5B, #YCESD5). - Storage ranges from $22\ \mathrm{kB}$ for a $50\ \mathrm{m}$ river to $2.7\ \mathrm{MB}$ for roughly $4\ \mathrm{km}$; individual primitives occupy 50–90 bytes (#9DU2N2). - An offline fluid-production comparison used $3\ \mathrm{cm}$ precision, 4.5 million particles and 200 million voxels. Producing 20 seconds of animation ultimately required 165 hours across 15 authoring cycles (#2KNSHV). - Priority-Flood was tested on $3\ \mathrm{m}$ DEMs containing 152 million and 318 million cells (#8ERHN4). - A larger benchmark covered $72{,}500\ \mathrm{km^2}$ and approximately $8\times10^9$ cells. Speed improvement averaged 16.8% and reached 37.2% (#XR7Z7G). - FastFlow examples identify 383,918 basins in an Alpine landscape and 8,445,644 around Mont Saint-Michel, both from $1\ \mathrm{m}$ elevation data (#NEL8YN). ### Water and wave simulation - Water Surface Wavelets simulates a $4\times4\ \mathrm{km}$ sea at $60\ \mathrm{fps}$ on a GTX 1070 (#WKY9MT). - It uses $4096^2$ spatial cells—about $1\ \mathrm{m}$ spacing—plus 16 directional samples and typically 1–4 wavenumber samples (#UG8PZG, #WV3FXP). - Despite that metre-scale simulation grid, it produces wavelengths down to $2\ \mathrm{cm}$. A direct heightfield with comparable storage would have $25\ \mathrm{cm}$ cells and a Nyquist-limited minimum wavelength of $0.5\ \mathrm{m}$ (#BEDUYL). - Precomputed wave motion increases performance from roughly 60 to 280 fps (#23W9S2). - A profile-buffer optimization increases wave-height evaluation from 1.8 to 275 fps, reported as a $233\times$ speedup (#82HGFN). - Increasing from one to four wavenumber groups roughly quadruples runtime and drops performance from 70 to 20 fps (#9AHGRG). - Breaking-wave simulations use 160,000–200,000 grid points and run at 40–75 fps; fluid simulation accounts for 80% of runtime (#RTYCL9). - Particle-fluid rendering handles 20,000–64,000 particles at $1280\times720$, with intermediate buffers totaling 112 bits per pixel (#LUVPJR). - Advected river textures report 60–120 fps, averaging 85 fps, and use a representative river speed of $1.3\ \mathrm{m\,s^{-1}}$ (#8KBMFE, #JS4LBU). - That model uses a $15^\circ$ directional-deviation threshold and an average advection-particle lifetime of $1.5\ \mathrm{s}$ (#BMKDJR, #K7SCA8). - The wavelet paper prints water viscosity as $10^{-6}\ \mathrm{m/s}$ (#NHQBFC). This should be checked before reuse: kinematic viscosity would normally have units of $\mathrm{m^2/s}$. ### Roads and vehicle motion - Procedural road routing uses tunnel and bridge lengths of $50$–$300\ \mathrm{m}$ on a $300^2$ grid with $10\ \mathrm{m}$ spacing. Stochastic sampling evaluates 50 points instead of 2,728 per iteration (#WJSTC2). - Complete road paths with curvature, tunnels, and bridges are produced in under one second on a $100^2$ grid (#JLGV3R). - The racing-line system covers a $4.5\ \mathrm{km}$ circuit and converges in four or five iterations, each taking about 26–30 seconds (#BPF8Q6, #CK2TWF). - Experimental laps were 138.6 seconds for the new method, 139.2 seconds for nonlinear gradient descent, and 137.7 seconds for a professional driver. The conservative friction coefficient was $\mu=0.90$, permitting peak acceleration of $0.9g$ (#8AQDAB). - The autonomous vehicle controller runs at $200\ \mathrm{Hz}$ (#3LSFWC). ### Trails and human movement - The mountain-walker model represents a footfall as a $10\ \mathrm{cm}\times10\ \mathrm{cm}$ square (#J2KKMV). - Its main experiment uses a $25\times10\ \mathrm{m}$ slope, visibility of $10\ \mathrm{m}$, walker speeds of $0.5$–$1.5\ \mathrm{m\,s^{-1}}$, 25,000 walkers, 50 footfalls for substantial wear, and a $1000\ \mathrm{s}$ weathering timescale (#WUZ6YE). - The authors note that realistic trails would instead require several hundred footfalls and weathering times of days (#WUZ6YE). - Zigzags become substantial around $\alpha\gtrsim0.45$, using forbidden angles of $25^\circ$ uphill and $10^\circ$ downhill (#AJSDD6). - Biomechanical evidence suggests walking on a $10^\circ$ incline requires approximately $60^\circ$ hip flexibility versus $30^\circ$ on level ground; one observed ankle-flexion limit was $24^\circ$ (#54E5UT). - Field examples include slopes around 1:8 and 1:2 (#GNDKEV). - Trail guidance recommends continuous grades of 8–10% for families, seniors, and casual hikers, even where 12–16% might otherwise be sustainable (#D33DUB). - Suggested hillslope-to-trail-grade relationships are roughly 2:1 to 3:1 (#SFWHTE). - In the handbook’s worked example, adding 500 feet to a 2,000-foot alignment with 200 feet of rise lowers its grade from 10% to 8% (#76SGWC). - Paired clinometer measurements during field layout should agree within one percentage point (#8CNUPW). ### Less physical but useful domain-specific quantities - Platformer physics ranges from about 3.7 tiles/s in *Castlevania* to 10 tiles/s in *Super Mario Bros.*; the authors identify roughly 4–10 tiles/s as human-playable (#A6TZBP). - The wholeness study analyzes 1,800 Manhattan axial lines and 166,479 Swedish streets, finding power-law exponents around $2+$ (#LUZ5UR). - The Living Images method finds that recursively extracted substructures average about 3% of pixel count, no more than 2% are further decomposable, and images generally exhibit more than three or four recursive levels (#D2C54Y, #XZBXLL). - Head/tail breaks recursively partitions a dataset while the “head” remains no more than 40% of the observations (#MKYDT2).