Real-Time Rendering Paper Presentation Logarithmic Perspective Shadow Maps

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

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 undersampled aliasing

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

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 low error high error y x Logarithmictransform Perspectiveprojection

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 P - Perspective warping LogP - Logarithmic perspective warping ZP - z-partitioning FP - face partitioning single SM Standard P LogP z-partitioning ZP ZP+P ZP+LogP face-partitioning - FP+P FP+LogP

26. Quantifying aliasing error light

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

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

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

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

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

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 LogPSM LiSPSM Error color mapping LiSPSM LogPSM

36. Partitioning schemes FP+P Standard 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!