1

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

2

Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

3

Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

4

Standard Shadow Map

aliasing undersampled

5

Perspective Warping

aliasing

6

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

7

Logarithmic Perspective Warping

8

Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

9

Single shadow map warping

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

10

Single shadow map warping

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

Trapezoidal shadow maps [Martin and Tan 2004]

11

Face partitioning

Perspective warped cube maps[Kozlov 2004]

12

z-partitioning

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

Separating-plane shadow maps[Mikkelsen 2007]

z

13

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]

14

Irregular z-buffer

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

Hardware architecture[Johnson et al. 2005]

15

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

16

Sampling modified methods

Scene-dependent Methods

Adaptive Irregular

Benefit Lower error

Drawback Higher, variable cost

17

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]

18

Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

19

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

20

Logarithmic + perspective warping

Starts with perspective projection similar to PSMs

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

21

Logarithmic + perspective warping

Perspectiveprojection

Logarithmictransform

high

err

or

low

err

or

y

x

22

Logarithmic + perspective warping

Causes planar primitives to become curved

→ need a specialized rasterization to render

23

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

24

Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

25

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

26

Quantifying aliasing error

light

27

Quantifying aliasing error

light

light imageplane

shadow map

eye imageplane

28

Quantifying aliasing error

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

light

29

Scene-independent maximum error

Standard FP+P ZP5+P FP+LogP

30

Near optimal, scene-independent warping

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

31

Maximum error over all light positions

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

Uniform

Perspective

Log+Persp.

Near optimal

32

Error distribution along a face

0 0.5 10

5

10

15

20

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

33

Maximum error for varying light directions with z-partitioning

view direction

direction to light

34

Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

35

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

36

Partitioning schemes

Standard FP+P ZP5+P FP+LogP

37

Point lights

38

Demo video

39

Outlines

Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion

40

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

41

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

42

Thanks For Your Participation!