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

Fast Global-Illumination on Dynamic Height Fields

John Snyder

Microsoft Research

Derek Nowrouzezahrai

University of Toronto

Related Work

• static geometry [Sloan02; Ng04; …]

• dynamic geometry [Bunnell05, Ren06, Sloan07, Ritschel08]

3

Related Work

• screen-space shading [Shanmugam07;Ritschel09…]

– ignores view-occluded blockers

[Dimitrov08]

• horizon mapping [Max88; …]

– precomputation for hard shadows on static geometry

[Sloan&Cohen00]4

Related Work

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

5

Goals

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

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Goals

[SN08] Our results7

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

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1. approximate visibility & incident radiance w/ multi-resolution

2. compute visibility and radiance at discrete azimuthal directions

3. determine final spherical visibility and incident radiance

Summary of Main Ideas

- create height and shading pyramids

- sample from pyramid levels

- pre-filter data

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Azimuthal Swaths [SN08]

• for smaller area (key) light sources:– restrict azimuthal extent and use m = 3

– env lights and incident radiance:– complete swath and use m = 32

get sharper shadowsacts as a geometric maskonly sample where necessary

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Definitions and Notation

blocking angle: (t) angle p makes at t along

Sample and u at all points t along direction .

incident radiance: u(t) incident radiance at t towards p along

u(t)(t)

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Calculating the Max Blocking Angle

max

12

t


t


t


t


16

t


t


t


t


t

max


21

Calculating the Incident Radiance

Which points on the height field contribute indirect radiance?

22





















The set of points with monotonically increasing blocking angles.We call this the casting set.

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Brute Force Sampling

Problem: aliasing – need many samples in t.Solution: prefilter data, apply multi-scale sampling.

– Pitfall…

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Multi-Resolution Height Sampling

sampling distance for level i

if height pyramid level i

Sample coarser levels further from x.

fi fi-1 fi-2 fi-3

τiτi-1

τi-2τi-3

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Multi-Resolution Radiance Sampling

multi-scale incident radiance samples)()( iii uu radiance pyramid (for the previous bounce)

Sample coarser levels further from x.

ui ui-1 ui-2 ui-3

τiτi-1

τi-2τi-3

iu

blocking angle at i i

35





- analytic visibility and incident radiance

- use normalized Legendre polynomials (NLPs)

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Analytic Occlusion Elevation Function

• we start with the binary occlusion function:

otherwise

if ,0

,1);(

v

and represent it analytically in the Normalized Legendre Polynomial (NLP) basis:

σ

1

0)(v

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Analytic Visibility and IR

• can represent visibility and incident radiance in NLP with

v () max

0

1• visibility binary function with 1 transition

from 0 to 1 @ max as increases

• incident radiance piece-wise constant, RGB function of elevation

u ()

)( 0tu

)( 1tu)( 2tu

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1

)2/(v

1

)( maxv max

- =

v

))(()( 00 tvtu ))(())(()( 122 tvtvtu ))(())(()( 011 tvtvtu

+ + =





- NLPSH blending & projection

- fast shading pipeline

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From Sampled NLP to Full SH

• matrix acts on NLP coefficients at edges of each swath• rotate & sum across swaths for final SH

• given (2 x m) NLP vectors• need full spherical spherical functions (represented in SH)

All operations performed in a single GPGPU shader. See

supplemental material for full source code.

• interpolate between azimuthal samples +

project resulting spherical function into SH• requires only 1 pre-computed matrix!

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Global Illumination Shading with SH

uv & compute m azimuthal visibility + incident radiance NLP vectors

L external lighting environment

• at each shading point:

UV & interpolate & project into SH. Rotate & sum across directions

BRDF: clamped cosine and/or Phong lobe

)( xf N

)( xf Ror

xN xRor

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xVxT

Direct Illumination:

BRDF x Visibility SH Product

and take inner product with lightingLTx ,

Global Illumination Shading with SH

Indirect Illumination:

BRDF take inner product with Incident Radiance

UN ),( xf

)( xf N

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Comparison to Ground Truth

m = 32 ground truth

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HF resolution pyramid levels memory requirements

no sub-sampling 2x sub-sampling

256 x 256(130k triangles)

33 17.4 MB 4.5 MB


37 76 MB 20 MB

1024 x 1024(2.1M triangles)

41 336 MB 88 MB


45 1.4 GB 360 MB

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Memory Usage

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

Measured Performance

HF resolutionFPS (nVidia GTX 285)

no ss 2x ss 4x ss


50 125 229


12 36 73


3 8 19

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Results

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Results

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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

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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

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Thanks! Any questions?

We acknowledge the helpful suggestions of the anonymous reviewers.

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

Documents

indirect radiance

ut incident radiance

max blocking angle slide

points t

t max calculating

height field applications

t angle p

dynamic height fields