Real-Time Rendering Paper Presentation Logarithmic Perspective Shadow Maps

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Real-Time Rendering Paper Presentation

Logarithmic Perspective Shadow Maps

Brandon LloydNaga Govindaraju

Cory QuammenSteve Molnar

Dinesh Manocha

Slides refer to Brandon Lloyd’s

Presented by Bo-Yin Yao

2010.3.11

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Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

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Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

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Standard Shadow Map

aliasing undersampled

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Perspective Warping

aliasing

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Logarithmic perspective shadow maps (LogPSMs)

Warp the shadow map using a perspective transformation with an additional logarithmic warping

Reduce maximum error to levels that are nearly optimal for scene-independent algorithms

Similar performance to PSM with less error

Similar error to PSM with less texture resolution

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Logarithmic Perspective Warping

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Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

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Single shadow map warping

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

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Single shadow map warping

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

Trapezoidal shadow maps [Martin and Tan 2004]

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Face partitioning

Perspective warped cube maps[Kozlov 2004]

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z-partitioning

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

Separating-plane shadow maps[Mikkelsen 2007]

z

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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] Tiled shadow maps

[Arvo 2004] Multiple shadow frusta

[Forsyth 2006]

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Irregular z-buffer

GPU implementations [Arvo 2006; Sintorn et al. 2008]

Hardware architecture[Johnson et al. 2005]

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Sampling modified methods

Scene-independent Methods

Single SM warping Face partitioning z-partitioning

Benefit Lower, nearly constant cost

Drawback Higher error

Scene-dependent Adaptive Irregular

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Sampling modified methods

Scene-dependent Methods

Adaptive Irregular

Benefit Lower error

Drawback Higher, variable cost

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Filtering methods

Percentage closer filtering[Reeves et al. 1987]

Variance shadow maps[Donnely and Lauritzen 2006; Lauritzen and McCool 2008]

Convolution shadow maps[Annen et al. 2007]

Exponential shadow maps[Salvi 2008; Annen et al. 2008]

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Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

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Perspective warping

PSM Tight fit to the view frustum Low error in x, but high error along y

LiSPSMs Relax the warping to reduce the error in y, but this

increases the error in xPSM LiSPSM

high

err

or

low error

mod

erat

e er

ror

moderate error

y

x

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Logarithmic + perspective warping

Starts with perspective projection similar to PSMs

Then applies a logarithmic transformation to correct for the high error in y

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Logarithmic + perspective warping

Perspectiveprojection

Logarithmictransform

high

err

or

low

err

or

y

x

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Logarithmic + perspective warping

Causes planar primitives to become curved

→ need a specialized rasterization to render

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Logarithmic rasterization

Brute-force rasterization Use a fragment program Slower than standard rasterization

disables optimizations z-culling double-speed z-only rendering

breaks linear depth compression schemes

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Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

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Combinations of algorithms

single SMStandardPLogP

z-partitioningZPZP+PZP+LogP

P - Perspective warpingLogP - Logarithmic perspective warpingZP - z-partitioning FP - face partitioning

face-partitioning-FP+PFP+LogP

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Quantifying aliasing error

light

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Quantifying aliasing error

light

light imageplane

shadow map

eye imageplane

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Quantifying aliasing error

Maximum error: over a light ray over the frustum over all light positions

light

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Scene-independent maximum error

Standard FP+P ZP5+P FP+LogP

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Near optimal, scene-independent warping

Minimizes maximum error over a face Too complicated for practical use Used as a baseline

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Maximum error over all light positions

Param. End face Side face - s Side face - t Side face - combined

Uniform

Perspective

Log+Persp.

Near optimal

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Error distribution along a face

0 0.5 10

5

10

15

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v

e Mp;s

0 0.5 10

5

10

15

20

ve M

p;t

max

err

or in

s

max

err

or in

tnear near farfar

UniformLiSPSMPSMLogPSM

Uniform LiSPSM PSM LogPSM

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Maximum error for varying light directions with z-partitioning

view direction

direction to light

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Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

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Single shadow map LogPSM

LogPSMs have lower maximum error more uniform error

LiSPSM

LogPSMLiSPSM

LogPSM

>107.753.2511113.257.7510< >107.753.2511113.257.7510<

Error color mapping

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Partitioning schemes

Standard FP+P ZP5+P FP+LogP

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Point lights

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Demo video

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Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

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Benefits of LogPSMs

LogPSMs are close to optimal for scene-independent algorithms

LogPSMs achieve low error with few shadow maps

Can replace perspective warping in scene-independent directly single shadow map z-partitioning face partitioning

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Limitations of LogPSMs

Not currently supported in hardware

Share problems as other warping algorithms: Do not handle aliasing error due to surface orientation Face partitioning needed for most benefit

Not as simple as z-partitioning Can exhibit shearing artifacts

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