Shadow and Shadow Maps

1. Shadow and Shadow Maps [5]

2. What kind of visual cues does shadow give? • Object without shadow seem floating above the scene • Shadow gives the depth information • Shadow gives the information of the relative position of lights and objects in the scene [1]

3. What kind of visual cues does shadow give? • Shadow increases scene realism • Shadow makes the scene conceivable

4. Some Shadow Algorithms • Shodow Polygon (Blinn) • Basically project polygon vertices to a flat plane • Shadow Polygon Scanline (Appel; Bouknight, Kelly) • Shadow Volume (F. C. Crow) [1]

5. Some Shadow Algorithms • Shodow Polygon (Blinn) • Shadow Polygon Scanline (Appel; Bouknight, Kelly) • Figure out all the polygons involved in shadowing. • Pair each polygon that cast shadow with each polygon that it casts shadow upon • Process shadow at each scanline for those polygons • Shadow Volume (F. C. Crow)

6. Some Shadow Algorithms • Shodow Polygon (Blinn) • Shadow Polygon Scanline (Appel; Bouknight, Kelly) • Shadow Volume (F. C. Crow) • Create a volume polygon for the intersection of view frustum and semi-infinite shadow volume • Collision test for the shadow volume and polygons [2]

7. Shadow Algorithms • Pros: • Precision • Good for production / static scenes • Cons: • Requires non-trivial data structures • Requires large amount of memory • Lack hardware support • Too slow for interactive rendering

8. Shadow Map (L. Williams 1978) • Render from the view point of the light source. • Use the depth buffer as shadow map [5]

9. Shadow Map (L. Williams 1978) • Render from camera view point • Project to light source and compare with shadow map • If the depth are the same, it’s not under shadow (1) • If the point is behind shadow map, it’s under shadow (2) 1 2 [5]

10. Shadow Map Aliasing • It’s all because of undersampling [5]

11. Shadow Map Aliasing • dsrs/ri becomes large  perspective aliasing • cos/cos becomes large  projection aliasing [5]

12. Shadow Map Aliasing • dsrs/ri becomes large  perspective aliasing • cos/cos becomes large  projection aliasing [5]

13. Shadow Map • Pros: • Performance not constrained by number of polygons • Shadow map = z-buffer. • Supported in today’s graphic cards due to its simplicity • Cons: • Aliasing!

14. Adaptive Shadow Map (R. Fernando, S. Fernandez, K. Bala, D.P. Greenberg 2001) • Transform as usual • Analyze shadow map base on depth. Try to reduce dsrs/ri and cos/cos [4]

15. Adaptive Shadow Map • Refined shadow map by building an hierarchical refinement map [4]

16. Adaptive Shadow Map • Pros: • Much better quality than uniform shadow map • No manual intervention involved • Uses mip-map feature on hardware • Cons: • Still a software solution (analyzer, data structure etc) • Interactive drawbacks – need to refine a lot of data during interaction

17. Perspective Shadow Map – The Idea (Marc Stamminger, Gorge Drettakis 2002) • Apply perspective transformation to the scene • View frustum is now a cube instead of a pyramided [5]

18. Perspective Shadow Map – The Idea • Now the size in this new scene is proportional to the final image • We take the shadow map of the new scene instead • The result is a shadow map with resolution same as the final image [5]

19. Uniform Shadow Map Shadow map has lower resolution than image plane [5] Perspective Shadow Map Shadow map has exactly same resolution than image plane

20. Is it really that easy? • No! The light sources need perspective transformation too • No! All objects casting shadow into view frustum must be included – need an optimization plan for bounding box

21. Perspective Shadow Map – Light Sources • Light sources need to be relocated before shadow map is taken • Directional light in world space becomes point lights in post perspective space on infinity plane [5]

22. Perspective Shadow Map – Light Sources • Point lights are still point lights but not on the infinity plane • Point lights on infinity plane in world space becomes directional light [5]

23. Perspective Shadow Map – Objects • What happens if a shadow in view frustum is cast by an object outside of view frustum? • In post-perspective space, the objects that needs to cast shadow appear beyond infinity plane. • Transformed objects beyond infinity plane appears inverted [5]

24. Perspective Shadow Map – Objects • Need to include more than just view frustum for perspective transformation • M is all rays from light source to view frustum boundary • The new world space to transform, H, is intersection of M, S(world space boundary) and light frustum • Now we have a little more than just view frustum [5]

25. Perspective Shadow Map – Objects • What about the inverted trees beyond infinity plane? • Move the camera back in post perspective space so everything looks upright • This solves the problem but we lose some resolution for taking a bigger picture [5]

26. Perspective Shadow Map • Pros: • Everything uniform shadow map does, this can do much better • Way faster than adaptive shadow map • Takes full advantage of hardware supported shadow map • Cons: • Transformations are not so trivial • Slight computational overhead • Occasional degradation when shadows are cast by objects behind camera (but always better than shadow map)

27. Perspective Shadow Map – Pictures [5]

28. Perspective Shadow Map – Pictures [5]

29. Perspective Shadow Map – Pictures cs2.machineroom.org/ media/doom3-2.jpg

30. References • J. Teng. Institute of automation. Chinese Academy of Science liama.ia.ac.cn/meeting/Archives/shadow.ppt 2002 • F.C. Crow Shadow algorithms for computer graphics. ACM Press. 1977. • L. Williams. Casting curved shadows on curved surface. Computer Graphics SIGGRAPH 1978 • R. Fernando, S. Fernndez, K. Bala, D.P. Greenberg. Adaptive shadow maps. SIGGRAPH 2001 • M. Stamminger, G. Drettakis. Perspective shadow maps. SIGGRAPH 2002

31. http://www-sop.inria.fr/reves/publications/data/2002/SD02/psm_divx.avi.gzhttp://www-sop.inria.fr/reves/publications/data/2002/SD02/psm_divx.avi.gz