1. Real-Time Rendering Paper Presentation Logarithmic Perspective Shadow Maps Brandon Lloyd Naga Govindaraju Cory Quammen Steve Molnar Dinesh Manocha Slides refer to Brandon Lloyd’s Presented by Bo-Yin Yao 2010.3.11 1

2. Outlines Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion 2

3. Outlines Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion 3

4. Standard Shadow Map aliasing undersampled 4

5. Perspective Warping aliasing 5

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 6

7. Logarithmic Perspective Warping 7

8. Outlines Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion 8

9. Single shadow map warping Perspective shadow maps (PSMs) [Stamminger and Drettakis 2002] 9

10. Single shadow map warping Light-space perspective shadow maps (LiSPSMs) [Wimmer et al. 2004] Trapezoidal shadow maps [Martin and Tan 2004] 10

11. Face partitioning Perspective warped cube maps [Kozlov 2004] 11

12. z-partitioning Cascaded shadow maps [Engel 2007] Parallel split shadow maps [Zhang et al. 2006] Separating-plane shadow maps [Mikkelsen 2007] z 12

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] 13

14. Irregular z-buffer GPU implementations [Arvo 2006; Sintorn et al. 2008] Hardware architecture [Johnson et al. 2005] 14

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 15

16. Sampling modified methods Scene-dependent Methods Adaptive Irregular Benefit Lower error Drawback Higher, variable cost 16

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] 17

18. Outlines Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion 18

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 x PSM LiSPSM high error low error moderate error y x 19

20. Logarithmic + perspective warping Starts with perspective projection similar to PSMs Then applies a logarithmic transformation to correct for the high error in y 20

21. Logarithmic + perspective warping Perspective projection Logarithmic transform high error low error y x 21

22. Logarithmic + perspective warping Causes planar primitives to become curved → need a specialized rasterization to render 22

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 23

24. Outlines Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion 24

25. Combinations of algorithms single SM Standard P LogP z-partitioning ZP ZP+P ZP+LogP P - Perspective warping LogP- Logarithmic perspective warping ZP- z-partitioning FP- face partitioning face-partitioning - FP+P FP+LogP 25

26. Quantifying aliasing error light 26

27. Quantifying aliasing error light light image plane shadow map eye image plane 27

28. Quantifying aliasing error Maximum error: over a light ray over the frustum over all light positions light 28

29. Scene-independent maximum error Standard FP+P ZP5+P FP+LogP 29

30. Near optimal, scene-independent warping Minimizes maximum error over a face Too complicated for practical use Used as a baseline 30

31. Maximum error over all light positions Param.End faceSide face - sSide face - t Side face - combined Uniform Perspective Log+Persp. Near optimal 31

32. Error distribution along a face max error in s max error in t near far Uniform LiSPSM PSM LogPSM Uniform LiSPSMPSMLogPSM 32

33. Maximum error for varying light directions with z-partitioning view direction direction to light 33

34. Outlines Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion 34

35. Single shadow map LogPSM LogPSMs have lower maximum error more uniform error LiSPSM LogPSM LiSPSM LogPSM Error color mapping 35

36. Partitioning schemes Standard FP+P ZP5+PFP+LogP 36

37. Point lights 37

38. Demo video 38

39. Outlines Introduction Related work Logarithmic perspective warping Error analysis Results Conclusion 39

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 40

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 41

42. Thanks For Your Participation! 42