Fast Global-Illumination on Dynamic Height Fields

Derek Nowrouzezahrai University of Toronto Fast Global-Illumination on Dynamic Height Fields John Snyder Microsoft Research

Related Work • static geometry [Sloan02; Ng04; …] • dynamic geometry [Bunnell05, Ren06, Sloan07, Ritschel08]

[Sloan&Cohen00] Related Work • screen-space shading [Shanmugam07;Ritschel09…] • ignores view-occluded blockers • horizon mapping [Max88; …] • precomputation for hard shadows on static geometry [Dimitrov08]

Related Work • fast soft-shadowing on dynamic height fields [SN08]

Goals • all of [SN08]as well as • dynamic indirect illumination • glossy effects (direct and indirect)

Goals [SN08] Our results

Goals • unified formulation for direct- and indirect-illumination • diffuse and glossy bounces • environmental + directional lighting • dynamic geometry (not precomputed) • real-time performance • simple implementation • limitation: geometry is a height field • applications: • terrain rendering (flight simulators, games, mapping/navigation) • data visualization

Summary of Main Ideas • create height and shading pyramids • sample from pyramid levels • pre-filter data • approximate visibility & incident radiance w/ multi-resolution • compute visibility and radiance at discrete azimuthal directions • determine final spherical visibility and incident radiance

Azimuthal Swaths [SN08] • for smaller area (key) light sources: • restrict azimuthal extent and use m = 3 • get sharper shadows • acts as a geometric mask • only sample where necessary • env lights and incident radiance: • complete swath and use m = 32

Definitions and Notation blocking angle: (t) angle p makes at t along  incident radiance: u(t) incident radiance at t towards p along  u(t) (t) Sample and u at all points talong direction .

Calculating the Max Blocking Angle max

Calculating the Max Blocking Angle t

Calculating the Max Blocking Angle max t

Calculating the Incident Radiance  Which points on the height field contribute indirect radiance?

Calculating the Incident Radiance  Which points on the height field contribute indirect radiance?

Calculating the Incident Radiance  Which points on the height field contribute indirect radiance? The set of points with monotonically increasing blocking angles. We call this the casting set.

Brute Force Sampling – Pitfall… Problem: aliasing – need many samples in t. Solution: prefilter data, apply multi-scale sampling.

Multi-Resolution Height Sampling height pyramid level i sampling distance for level i τ τ τ τ i-1 i-2 i-3 i Sample coarser levels further from x. fi fi-1 fi-2 fi-3

Multi-Resolution Radiance Sampling multi-scale incident radiance samples τ τ τ τ radiance pyramid (for the previous bounce) i-2 i-1 i-3 i blocking angle at Sample coarser levels further from x. ui ui-1 ui-2 ui-3

Summary of Main Ideas • approximate visibility & incident radiance w/ multi-resolution • compute visibility and radiance at discrete azimuthal directions • determine final spherical visibility and incident radiance • analytic visibility and incident radiance • use normalized Legendre polynomials (NLPs)

Analytic Occlusion Elevation Function σ • we start with the binary occlusion function: 0 1 • and represent it analytically in the Normalized Legendre Polynomial (NLP) basis:

Analytic Visibility and IR • can represent visibility and incident radiance in NLP with = max + + v() 1 max 1 - • visibility  binary function with 1 transition from 0 to 1 @ max as increases 1 = 0 u() • incident radiance piece-wise constant, RGB function of elevation

Summary of Main Ideas • approximate visibility & incident radiance w/ multi-resolution • compute visibility and radiance at discrete azimuthal directions • determine final spherical visibility and incident radiance • NLPSH blending & projection • fast shading pipeline

From Sampled NLP to Full SH • given (2 x m) NLP vectors • need full spherical functions (represented in SH) • interpolate between azimuthal samples + • project resulting spherical function into SH • requires only 1 pre-computed matrix! • matrix acts on NLP coefficients at edges of each swath • rotate & sum across swaths for final SH • All operations performed in a single GPGPU shader. See • supplemental material for full source code.

N x f f ( ( N R ) ) x x Global Illumination Shading with SH • at each shading point: compute m azimuthal visibility + incident radiance NLP vectors interpolate & project into SH. Rotate & sum across directions R or x BRDF: clamped cosine and/or Phong lobe or external lighting environment

Global Illumination Shading with SH Direct Illumination: BRDF x Visibility SH Product and take inner product with lighting Indirect Illumination: BRDF take inner product with Incident Radiance

Comparison to Ground Truth m = 32 ground truth

Memory Usage • we typically sub-sample visibility & IR • shade with full-resolution geometry & normals

Measured Performance

Results

Conclusions • multi-resolution sampling of: • visibility • incident radiance • compact, analytic representation of: • elevation-only functions • SH interpolation and projection operators • simple GPU implementation • real-time up to 512x512 dynamic HFs • can sub-sample visibility and incident radiance • performance independent of geometric content

Future Work • combine with dynamic shadow casters • via [Ren06;Sloan07] (sphere set blocker approximation) • apply to image-space global illumination frameworks • generalize geometry • local height field displacements • tiled height field representations

Thanks! Any questions? We acknowledge the helpful suggestions of the anonymous reviewers.

Fast Global-Illumination on Dynamic Height Fields