The document discusses various algorithms for rendering hard and soft shadows in interactive computer graphics applications. It begins by explaining the motivation for realistic shadows and the difference between hard and soft shadows. It then summarizes several important algorithms for rendering hard shadows, including projected geometry, shadow volumes, shadow maps, and a hybrid approach. Next, it discusses approaches for sampling light sources to produce soft shadows. Finally, it introduces soft shadow maps as an efficient method for producing soft penumbra regions for linear light sources using a shadow map approach.

1. Advanced Lighting for Interactive Applications Shadow Algorithms Stefan Brabec Max-Planck-Institut für Informatik Saarbrücken, Germany

2. Overview Motivation Algorithms for hard shadows Algorithms for soft shadows Conclusion

3. Motivation Shadows do significantly contribute to the realism of rendered images Global effect which is expensive to compute Lot of work done in this area Which algorithms are suitable for interactive applications ?

4. Motivation Hard shadows vs. Soft shadows Hard shadow edges - unreal (like geometry) + computation easier Soft shadow boundaries + realistic - expensive

5. Algorithms for Hard Shadows Approximated shadows Projected geometry [Blinn88] Shadow volumes [Crow77] Shadow maps [Williams78] Hybrid approach [McCool00] Extended light maps [Brabec00]

6. Approximated Shadows Hand-Drawn Geometry Images from TombRaider. ©Eidos Interactive.

7. Approximated Shadows Polygons / Texture Maps: Precomputed shape that moves with object Rotation / Translation / Scale Blurred (more realistic, soft) Pros: Fast & simple: no global computation Cons: Quality not very realistic

8. Projected Geometry [Blinn88] Me and my fake shadow Shadows for selected large receiver polygons Ground plane Walls

9. Projected Geometry Example: xz plane at y=0

10. Projected Geometry Transformation as 4 by 4 matrix

11. Projected Geometry General case: receiver polygon in plane E 4x4 matrix (see Blinn)

12. Projected Geometry Basic algorithm Render scene (full lighting) For each receiver polygon Compute projection matrix M Mult with actual transformation (modelview) Render selected (occluder) geometry Darken/Black

13. Projected Geometry Problems Z-Fighting Use bias when rendering shadow polygons Use stencil buffer (no depth test) Bounded receiver polygon ? Use stencil buffer (restrict drawing to receiver area) Shadow polygon overlap ? Use stencil count (only the first pixel gets through)

14. Projected Geometry Stencil buffer algorithm (1bit stencil) 1. Render scene without receiver polygon 2. Clear stencil buffer 3. Render receiver polygon - stencil operation ‘set’ (visible pixels) 4. Render shadow polygons - without depth test - stencil test ‘is set?’ - stencil operation ‘clear’ - blending e.g. ‘dest = dest * 0.2’ (darken)

15. Projected Geometry Wrong Shadows & Anti-Shadows Objects behind light source Objects behind receiver Solution Clipping Use 3D-3D transformation e.g. [Heckbert97] for valid z coordinates

16. Projected Geometry Summary Only practical for very few, large receivers Easy to implement Use stencil buffer (z fighting, overlap, receiver) Efficiency can be improved by rendering shadow polygons to texture maps Occluders and receiver ‘static’ for some time

17. Shadow Volumes [Crow77] Shadow algorithms for computer graphics Compute regions of shadow in 3D Object-space algorithm Cast shadows onto arbitrary receiver geometry (polygons)

18. Shadow Volumes Extend occluder polygons to form semi-infinite volumes Light source is center-of-projection Everything behind occluder is in shadow Test if point is in at least one volume ! Extend to reach outside of view frustum Light Source Shadow Region Occluder

19. Shadow Volumes Shadow volume generation Trivial way One volume for each polygon Better Silhouette-based approach Goal: one shadow volume Selected occluders only By objects (shared edges)

20. Shadow Volumes Shadow test: in-out counter Counter == 0: lit Counter >=0: shadowed

21. Shadow Volumes Use stencil buffer as counter 1. Render scene (ambient color) 2. Render front-facing parts of shadow volumes with stencil operation increment (enter) 3. Render back-facing parts of shadow volumes with stencil operation decrement (exit) 4. Render scene (fully lit) with stencil test equal zero

22. Shadow Volumes Implementation Generate volumes in software (object space) Counting can be done in hardware (image space) Images from Mark Kilgard’s shadow volume demo (NVIDIA).

23. Shadow Volumes Counting problems Viewer in shadow (correct counter initialization) Correct ownership of adjacent polygons (no double hits)

24. Shadow Volumes Counting problems Stencil depth 8 bits for intersecting volumes Stencil wrap mode Missing shadows for ‘counter mod 2^n == 0’ Stencil clamp Missing shadows (missing some ‘enter’ events) 1 bit enough for non-intersecting volumes Generate volumes from silhouette Toggle stencil bit

25. Shadow Volumes Summary Shadow volumes in object precision CPU intensive, requires polygon representation Shadow test in image precision Stencil buffer count Hardware-accelerated Many, large shadow polygons Fill rate, geometry processing

26. Shadow Maps [Williams78] Casting curved shadows on curved surfaces Image-space algorithm Well suited for hardware implementation

27. Shadow Maps Basic Algorithm Render scene as seen from light source Save back depth buffer (2D shadow map) Render scene from viewer’s position Transform pixel coordinates to light source space Compare z with z value stored in shadow map Pixel is in shadow if z(light) < z(viewer)

28. Shadow Maps Shadow map Final scene

29. Shadow Maps Hardware implementation Render scene to z-buffer (light source view) Depthbuffer-to-texture copy Render-to-texture / pbuffer

30. Shadow Maps Hardware implementation Project shadow map into the scene Brabec/Heidrich ‘Marilyn'. Image taken from OpenGL Programming Guide. Projective texturing: Slide projector

31. Shadow Maps How to perform shadow test in hardware ? Dedicated shadow mapping hardware SGI Onyx/Reality (OpenGL extension) Compare fragment’s depth with depth in shadow map Use homogenous texture coordinates (s,t,r,q) Compare r/q with texture value at (s/q,r/q) Output 1 for lit and 0 for shadow Blend fragment color with shadow test result High-precision depth texture format

32. Shadow Maps Shadow mapping using standard OpenGL [Heidrich99] Encode depth values as alpha values Shadow test using alpha test or programmable texture units (multi texturing)

33. Shadow Maps Distance to light source in alpha channel: Use 1D ramp texture and automatic texture coordinate generation Use fog factor as linear distance function [Brabec00]

34. Shadow Maps Algorithm using multi texturing 1. Render scene from light source view - 1D ramp texture or linear fog 2. Copy frame buffer (alpha channel) to texture 3. Render scene shadowed (ambient light only) 4. Render scene fully lit with alpha as - Tex #1: 2D shadow map (projective texture) - Tex #2: 1D linear ramp (distance to light) - Alpha test: clamp(Tex#2 - Tex#1) == 0 5. Add up illumination (blending)

35. Shadow Maps Linear sample distribution Better than 1/z (depth buffer read) Color resolution problematic 8bits in alpha: 256 depth samples 16bits possible Use 2D texture map S-coordinate for lower 8bit (texture coordinate repeat) T-coordinate for higher 8bit (texture coordinate clamp) Needs two channels and programmable texture unit

36. Shadow Maps Problems Needs high-resolution texture maps to sample fine details Offscreen buffers, render-to-texture Filtering ? Numerical problems (light leaks, surface acne) Bias needed [Reeves87]

37. Hybrid Approach [McCool00] Shadow volume reconstruction from depth maps Combine the pros from shadow maps and shadow volumes Shadow volumes generated from depth maps Reduced number of shadow volumes for very complex scenes Does not need special hardware features (standard shadow text using stencil buffer)

38. Hybrid Approach Algorithm overview 1. Render scene from light source view (depth only) 2. Read back depth buffer 3. Reconstruct shadow volumes - Edge detection (Canny) - Surface reconstruction (Template matching) 4. Render shadow volume with stencil operation 5. Render final scene (stencil test)

39. Hybrid Approach

40. Hybrid Approach Summary Better than normal shadow volumes for very complex scenes Volume for silhouette Only one stencil bit (in-out toggle) Needs CPU and memory transfer Use CPU’s special instruction set OpenGL imaging extensions (convolution)

41. Extended Light Maps [Brabec00] Extended Light Maps Additional calculations during shadow map generation Utilize special hardware features Pre-compute light-relative ‘static’ things Use as much hardware resources as available !

42. Extended Light Maps Shadow map generation is expensive ! Additional geometry pass Needs frame buffer reconfiguration Idea Do as much work as possible during shadow map generation

43. Extended Light Maps Light Maps store pre-computed illumination Extended Light Map Light Channel (RGB) Normal light map Shadow Channel (Alpha) Alpha-encoded depth values

44. Extended Light Maps Use RGB channel for arbitrary calculations e.g. OpenGL lighting Object textures Realistic spotlights Special effects Reflection mapping Bump mapping

45. Extended Light Maps Example: Pre-computed reflection mapping

46. Extended Light Maps First pass: Use color channel for environment cube map Use alpha channel for z-distance

47. Extended Light Maps How to perform cube mapping in light source space ? Need correct reflection vector Calculate in camera space: Viewing Matrix Projection Matrix

48. Extended Light Maps Two final passes Render normal scene (textures & lighting) Apply extended light map (shadows & reflections)

49. Algorithms for Soft Shadows Sampling the Light Source Soft Shadow Maps [Heidrich00]

50. Sampling the Light Source Use arbitrary hard shadow algorithm Select point sample on area light source Render hard shadows Sum up weighted result (e.g. accumulation buffer)

51. Sampling the Light Source Ground plane shadow texture 1. Initialize FB (white) 2. For each sample point do 2a. Render scene 2b. Subtract 1/N from FB only once for each pixel (stencil) ! Image from ATI Developer’s Site

52. Sampling the Light Source Result Image from ATI Developer’s Site

53. Sampling the Light Source Number of samples == number of passes Problematic for complex scenes N samples == (N+1) levels of shadow Fully lit, fully shadowed (N-1) levels of penumbra How much samples ?

54. Sampling the Light Source Similar technique in [Heckbert97] Simulating soft shadows with graphics hardware Shadow texture for each receiver Perspective transformation Pyramid to box Z value for clipping (behind light, behind receiver) Runs at interactive frame rates (reasonable number of receivers)

55. Soft Shadow Maps [Heidrich00] Soft shadow maps for linear lights

56. Soft Shadow Maps [Heidrich00] Soft penumbra regions for linear light sources Based on “traditional” shadow map algorithm Suitable for hardware and software rendering Very small number of light source samples Soft shadows at real-time / interactive frame rates

57. Soft Shadow Maps Visibility of light source 100% to 0% for [p1,p2] 0% for [p2,q2] 0% to 100% for [q2,q1] Idea Normal shadow maps for umbra and completely lit regions Linear interpolation of visibility for penumbra regions

58. Soft Shadow Maps Linear interpolation of visibility Rational function: Approximation: valid because large penumbra regions when Receiver Light Source Occluder

59. Soft Shadow Maps Visibility map: Additional shadow map channel (percentage visibility) Two-channel shadow map for each sample point

60. Soft Shadow Maps Generating the visibility map Triangulate depth discontinuities (shadow map) Warp resulting skin polygons to other view

61. Soft Shadow Maps Generating the visibility map Render skin polygons to visibility map Gouraud-shading (linear interpolation) “ White” for vertices on receiver “ Black” for vertices on occluder Completely lit regions Default visibility 0.5 Completely shadowed regions First shadow map channel

62. Soft Shadow Maps Edge Detection (on shadow map) Laplacian-of-Gaussian left sample point right sample point camera view

63. Soft Shadow Maps Triangulate and warp

64. Soft Shadow Maps Render using Gouraud shading

65. Soft Shadow Maps Visibility maps left sample point right sample point

66. Soft Shadow Maps New shadow map algorithm shade(p) { if( depth 1 (p) > S 1 [p] ) l 1 = 0; else l 1 = V 1 [p] * illum(p,L 1 ); if( depth 2 (p) > S 2 [p] ) l 2 = 0; else l 2 = V 2 [p] * illum(p,L 2 ); return l 1 +l 2 ; }

67. Soft Shadow Maps Shadow & visibility maps only need to be re-computed if light and/or scene changes Minimal overhead for “static walkthroughs”

68. Soft Shadow Maps

69. Soft Shadow Maps

70. Conclusion Without shadows there is no realism Good looking shadows are expensive Global effect Choice of algorithm depends on application Use CPU resources ? Use hardware resources ? Scene complexity Shadow quality

71. Thank you !