Chapter 8. Summed-Area Variance Shadow Maps — Andrew Lauritzen · GPU Gems 1–3（精选章节摘录）

Source: https://developer.nvidia.com/gpugems/gpugems3/part-ii-light-and-shadows/chapter-8-summed-area-variance-shadow-maps
Volume: GPU Gems 3
Note: add-only excerpt for wiki ingest; images omitted; prose and key listings kept.

Summary of full chapter read

Shadow mapping (Williams 1978) has magnification/minification artifacts. Hardware filtering averages depths then does one binary compare — wrong. PCF (Reeves 1987) filters comparison results instead. VSMs (Donnelly & Lauritzen 2006) store depth and depth² so moments can be linearly filtered (mipmaps, anisotropic, SAT, MSAA).

VSM core

Moments M1, M2 → mean μ and variance σ². Chebyshev one-tailed upper bound: p_max = σ² / (σ² + (t−μ)²) when t > μ; else 1. Exact for single planar occluder/receiver. Clamp min variance for numeric stability and acne.

Bias via second moment

Use ddx/ddy of depth so M2 = Depth² + 0.25*(dx²+dy²) represents planar distribution over pixel — elegant bias without Peter Panning. Clamp derivative contribution when nearly parallel to light.

Light bleeding

Pathological multi-occluder cases cannot be exact without sampling all. Approximation: linstep(Amount, 1, p_max) removes low-intensity false penumbrae; Amount is scene-scale-independent artist parameter.

Numeric / depth metric

Prefer linear distance-to-light (or light-plane distance for directional) over post-projection z. Use 32-bit float textures.

Implementation outline

Render moments with linear metric + optional MSAA; optional separable blur; mipmaps; one filtered lookup; Chebyshev; optional bleeding reduction. Do NOT render only casters (receivers must be in distribution). Compatible with warping/partitioning (CSM/PSSM).

SAVSM

Summed-area tables (Crow 1984) give constant-time average over arbitrary rectangles — enables per-pixel filter width for soft shadows. SAT generation: line-by-line or recursive doubling. Precision burns log(W×H) bits; mitigations: bias −0.5, distribute moments into 4 components, origin-centered SAT, 32-bit int wraparound with known max filter, or doubles.

PCSS + SAVSM

Fernando 2005 PCSS: blocker search → penumbra estimate from similar triangles → filter. SAVSM replaces sparse PCF in filter step; blocker search still reintroduces depth-test bias.

Guidance

Constant filter width → blurred VSM + bleeding reduction is best. Dynamic width → SAVSM. Min filter width ≥4 often needed to hide aliasing.