Research note

moppe forest.metal as an implementation of LOD-as-statistics

Analysis of moppe’s forest shader (moppe/shaders/metal/forest.metal, with docs/forest-lod.md and docs/forest-density-and-aggregates.md): it implements the LOD-as-statistics credo #CYDXJ2 #USARUR end to end.

Mapping to the framework:

  • Continuous parameter space: fractional bough count as float ramp of projected pixels (21..63), boughs grow in from nothing over size-scaled windows; Kuth-style per-frame generation, no stored meshes #EDURTK #2WBRVG

  • Dithered LOD front: per-individual hashed threshold (0.88..1.12) staggers construction boundaries across a stand — Jahrmann’s hashed culling #KDYKVC promoted to transition timing.

  • Conservation of coverage: “conservation of foliage” — survivor widening sqrt(63/count) area ratio, bundle tufts widen sqrt(13/3); geometric analogue of HZD coverage-preserving mips #WZDZZW exact by construction, converges to 1 near.

  • Solid-angle budget: bough ramp saturates at 90 projected px (~1/10 frame height); size-invariant completion distance via forest_bough_measure boost clamp(22.5/h,1,4.5) — echoes quadratic noise fade reasoning #8TDNZZ

  • Geometry→material renormalization in shading: resolvable factor collapses per-blade backlight lobe to its ensemble mean (0.30) as tufts fall subpixel, and modulates temporal-history rejection. This is the microfacet-statistics move executed in the fragment shader.

  • Perceptual arrival order: first 9 ranks sketch silhouette (one bough/whorl bottom-up), then even densification top-first with opposed azimuths; silhouette sacred, interior negotiable.

  • Physically based leaf shading: Beer–Lambert via exposure-as-optical-depth, chlorophyll transmittance spectrum, tint on sqrt(base) (half pigment path), diffuse yields energy to transmission.

  • Missing/next: Bruneton–Neyret-style far-field canopy material #7R6ZNJ — density-and-aggregates doc argues closed canopy at distance is statistically uniform and should render as one surface; ranked lever list includes a Kuth-style rate-limited auto-LOD governor.

  • Methodological point for the thesis: docs record that still frames cannot verify temporal behaviour — dolly atlas at constant apparent size, video ride captures, and perceived-unit arithmetic are the valid judges of continuous-LOD quality.