Research note

Foliage/grass continuous LOD as unbiased statistical estimation

Synthesis: continuous LOD for foliage/grass as statistical estimation. Core claim: a coarse LOD should be an unbiased estimator of the fine LOD’s expected appearance (coverage, radiance, motion), not a simplified mesh.

  1. Conserve coverage across mips: HZD coverage-preserving alpha mip chain rescales each mip so post-threshold coverage matches the source #WZDZZW Hashed alpha testing achieves the same invariant stochastically: random threshold makes the alpha test an unbiased coverage estimator #N6QLYJ #S4F32B

  2. Far representation = statistics of near representation: Bruneton–Neyret shader-maps encode expected forest radiance incl. view-light correlations #7R6ZNJ seamless transition forces near-model radiances to converge to statistical averages before cross-fading #D4D5AP #W8VWLB #X9PHPN #DPJ27C Blends only work after expectations agree.

  3. Continuity via continuous parameter spaces: Tsushima Bézier blades sampled at 15 vs 7 verts #DJSHKW #4TS8SV #AYX9GT Jahrmann analytic blades + hardware tessellation #26R36D GPU tree generation makes LOD a frame-time feedback controller over continuous quality parameters with rate-limited change #2WBRVG

  4. Stochastic density reduction: Jahrmann per-blade hashed distance culling, up to 75% culled without visible density loss; distance projected onto ground plane because perspective density rises toward horizon #KDYKVC #EEZRRW #LSJVNS

  5. LOD the motion too: HZD scales wind animation to zero and pushes vertices down with distance #8VWZJV #UUL95W #FH7HUR physics ladder from per-blade forces #EEZRRW to statistical wind.

  6. Variance budgeted by solid angle: quadratic noise fade-in b(x)=(x/n)^2 and anisotropy scaling in hashed alpha #8TDNZZ #XTSQCM #H65LSZ

One-liner: analytic ground truth ⇒ detail is a sampling rate; coarse levels are unbiased estimators; drops in count are dithered; transitions converge expectations before blending; noise metered by solid angle.