the university of north carolina at chapel hill practical logarithmic rasterization for low error...

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Practical logarithmic rasterization for low error shadow maps

Brandon LloydUNC-CHNaga GovindarajuMicrosoftSteve Molnar NVIDIADinesh Manocha UNC-CH

2


Shadows

Shadows are important aid spatial reasoningenhance realismcan be used for dramatic effect

High quality shadows for real-time applicationsremains a challenge

3


Shadow approaches

Raytracing [Whitted 1980] not yet real-time for complex, dynamic scenes at high resolutions

Shadow volumes [Crow 1977] can exhibit poor performance on complex scenes

4


LightEye

Shadow maps [Williams 1978]

5


Logarithmic perspective shadow maps (LogPSMs) [Lloyd et al. 2007]

Standard shadow map LogPSM

6


Logarithmic perspective shadow maps (LogPSMs) [Lloyd et al. 2007]

Standard shadow map LogPSM

7


Goal

linear rasterization logarithmic rasterization

Perform logarithmic rasterization at rates comparableto linear rasterization

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Outline

BackgroundHandling aliasing errorLogPSMs

Hardware enhancementsConclusion and Future work

9


High resolution shadow maps

Requires more bandwidth

Decreases shadow map rendering performance

Requires more storage

Increased contention for limited GPU memory

Decreased cache coherence

Decreases image rendering performance

Poor shadowmap querylocality

10


Sample at shadow map query positions

No aliasing

Uses irregular data structures

requires fundamental changes to graphics hardware [Johnson et al. 2005]

Irregular z-buffer[Aila and Laine 2004;Johnson et al. 2004]

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Adaptive partitioning

Adaptive shadow maps [Fernando et al. 2001]

Queried virtual shadow maps[Geigl and Wimmer 2007]

Fitted virtual shadow maps [Geigl and Wimmer 2007]

Resolution matched shadow maps [Lefohn et al. 2007]

Multiple shadow frusta [Forsyth 2006]

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Adaptive partitioning

Requires scene analysisUses many rendering passes

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Scene-independent schemes

Match spacing between eye samplesFaster than adaptive partitioning

no scene analysis few render passes eye sample spacing

14


Cascaded shadow maps [Engel 2007] Parallel split shadow maps [Zhang et al. 2006]

Cascade shadow maps

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Projective warping

Perspective shadow maps (PSMs) [Stamminger and Drettakis 2002]

Light-space perspective shadow maps (LiSPSMs) [Wimmer et al. 2004]

Trapezoidal shadow maps (TSMs)[Martin and Tan 2004]

Lixel for every pixel [Chong and Gortler 2004]

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Projective warping

Not necessarily the best spacing distribution

PSM LiSPSM

hig

h e

rror

low error

mod

era

te e

rror

moderate error

y

x

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Logarithmic+perspective parameterization

Perspectiveprojection

Logarithmictransform

Resolutionredistribution

18


Size of the shadow map* required to remove aliasing

error(ignoring surface orientation)

Uniform

Perspective

Logarithmic + perspective

Bandwidth/storage savings

- near and far plane distances of view frustum

*shadow map texels / image pixels

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Single shadow map LogPSM

LogPSMs havelower maximum errormore uniform error

Image resolution: 5122

Shadow map resolution: 10242

f/n = 300Grid lines for every 10 shadow map texels Color coding for maximum texel extent in image

LiSPSM

LogPSMLiSPSM

LogPSM

>107.753.2511113.257.7510< >107.753.2511113.257.7510<

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Comparisons

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More details

Logarithmic perspectiveshadow maps

UNC TR07-005

http://gamma.cs.unc.edu/logpsm

22


Outline

BackgroundHardware enhancements

rasterization to nonuniform gridgeneralized polygon offsetdepth compression

Conclusion and Future work

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Graphics pipeline

fragment processor

vertex processor

rasterizer

alpha, stencil, & depth tests

blending

clipping

memoryinterface

depthcompression

colorcompression

setup

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Rasterization

Coverage determinationcoarse stage – compute covered tiles fine stage – compute covered pixels

Attribute interpolationinterpolate from verticesdepth, color, texture coordinates, etc.

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Signs used to compute coverageWater-tight rasterization

Use fixed-point fixed-point “snaps” sample locations to an underlying uniform grid

Edge equations

+++ -+++-+

++-

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Attribute interpolation

Same form as edge equations:

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Logarithmic rasterization

light space linear shadow mapspace

warped shadow mapspace

Linear rasterization with nonuniform grid locations.

y

x

y'

x

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Edge and interpolation equations

Monotonicexisting tile traversal algorithms still workoptimizations like z-min/z-max culling still work

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Coverage determinationfor a tile

Full parallel implementation

Full evaluation

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Per-triangle constants

Coverage determination for a tile

Incremental in x

Full evaluationIncremental x

1 2

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Generalized polygon offset

texelwidth

- depth slope

- smallest representable depth difference

constant

light

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texelwidth

- depth slope

- smallest representable depth difference

constant

not constant

light

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Do max per pixelSplit polygonInterpolate max at end points

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Depth compression

Important for reducing memory bandwidth requirementsExploits planarity of depth valuesDepth compression survey [Hasselgren and Möller 2006]

depthcompressor

tile

tile table

store compressed

yes

store uncompressedno

fits in bitbudget?

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Depth compression - Standard

compresseduntouchedclamped

Linear depth compressionOur depth compression

Resolution:512x512

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Depth compression - LiSPSM



Resolution:512x512

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Depth compression - LogPSM



Resolution:512x512

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Depth compression – LogPSM Higher resolution



low curvature

Resolution:1024x1024

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ΔxΔxΔx

ΔxΔxΔx

ΔxΔxΔx

ΔxΔxΔx

Δy

Δy

Δy

z0

dd

dda0

a1dd

ddz0

Δy Δy

Δy

Δy

Δx

24 3 6 3

10 3 16 3

18 3 10 3

10 3 9 3

Differentialencoding

Anchor encoding 128-bit allocationtable

Our compression scheme

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Test scenes

Town model• 58K triangles

Robots model• 95K triangles

Power plant• 13M triangles • 2M rendered

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Compression methods tested

Anchor encoding[Van Dyke and Margeson 2005]

Differential differential pulse code modulation (DDPCM)[DeRoo et al. 2002]

Plane and offset[Ornstein et al. 2005]

Hasselgren and Möller [2006]

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Compression results

256 512 1024 20480

20

40

60

80

100

Com

pres

sed

size

(%

)

Resolution

Linear Rasterization

Our algorithm

Anchor [VM05]

DDPCM [DMFW02]

Plane & depth offset [OPS*05]

Hasselgren and Möller [HA06]

256 512 1024 20480

20

40

60

80

100 Logarithmic Rasterization

Com

pres

sed

size

(%

)

Resolution

Our algorithm

Anchor [VM05]

DDPCM [DMFW02]



Average compression over paths through all modelsVarying light and view direction

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256 512 1024 20480

20

40

60

80

100

Com

pres

sed

size

(%

)

Resolution

Linear Rasterization

Our algorithm

Anchor [VM05]

DDPCM [DMFW02]



256 512 1024 20480

20

40

60

80

100 Logarithmic Rasterization

Com

pres

sed

size

(%

)

Resolution

Our algorithm

Anchor [VM05]

DDPCM [DMFW02]



Compression results

Anchor encoding best linear method

higher tolerance for curvature

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Summary of hardware enhancements

Apply F(y) to vertices in setuplog and multiply-add operations

Evaluators for G(y’)exponential and multiply-add operations

Possible increase in bit width for rasterizer Generalized polygon offsetNew depth compression unit

can be used for both linear and logarithmic rasterization

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Feasibility

Leverages existing designsTrades computation for bandwidthAligns well with current hardware trends

computation cheapbandwidth expensive

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Conclusion

Shadow mapsHandling errors requires high resolution

Logarithmic rasterization significant savings in bandwidth and storage

Incremental hardware enhancements

Rasterization to nonuniform gridGeneralized polygon offsetDepth compression

Feasibleleverages existing designsaligns well with hardware trends

47


Future work

Prototype and more detailed analysis Greater generalization for the rasterizer

reflections, refraction, caustics,multi-perspective rendering [Hou et al. 2006; Liu et al. 2007]

paraboloid shadow maps for omnidirectional light sources [Brabec et al. 2002]

programmable rasterizer?

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Acknowledgements

Jon Hasselgren and Thomas Akenine-Möller for depth compression codeCorey Quammen for help with videoBen Cloward for robots modelAaron Lefohn and Taylor Halliday for town model

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Acknowledgements

Funding agenciesNVIDIA University FellowshipNSF Graduate FellowshipARO Contracts DAAD19-02-1-0390 and W911NF-04-1-0088NSF awards 0400134, 0429583 and 0404088DARPA/RDECOM Contract N61339-04-C-0043Disruptive Technology Office.

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Questions

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Precisiondepends on resolution in y and

Inputs limited to 24 bits of precision(floating point mantissa)

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fFor flythroughs in our test scenes:

Split situation occured for 1% of polygonsAverage was .001

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Incremental in y

Full evaluationIncremental xIncremental y

1

32Per-frame constants

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Look up table

Full evaluationIncremental xIncremental yLUT

21Per-frameconstants

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Look up table

Full evaluationIncremental xIncremental yLUT

32

1

Per-frameconstants

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Comparisons

Standard FP+Perspective ZP5+Perspective FP+Log+Perspective

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Equal error

29002 (4096x2053) 5122 (210x1248)

LiSPSM LogSPSM

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Simulating logarithmic rasterization

Apply F(y) in vertex programrequires fine tesselation to avoid errorincreases vertex transformation load

Brute-force rasterization with a fragment program

disables optimizations due to depth writes

the university of north carolina at chapel hill practical logarithmic rasterization for low error...

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