1. Efficient Image-Based Methods for Rendering Soft Shadows Maneesh Agrawala Ravi Ramamoorthi Alan Heirich Laurent Moll Pixar Animation Studios Stanford University Compaq Computer Corporation Bo Gao

2. Hard vs. Soft Shadows Hard ShadowsSoft Shadows

3. Area Lights Spot LightArea Lights

4. Cornell Box

5. Code Time //for each light: for (int i=0; i<lightNum; i++){ double ly=lights[i].getPosition().y; double lx=lights[i].getPosition().x; double lz=lights[i].getPosition().z; Vector3d lp=new Vector3d(lx, ly, lz); RT_color lColor=lights[i].getColor(); lColor=lColor.scale(1.0/lightNum); …… } // Light segments; 4 // x0 y0 z0 x1 y1 z1 r g b 400.0 0.0 465.0 450.0 0.0 515.0 1.0 1.0 1.0

6. 3 X 3 Lights8 X 8 Lights Regular Light Samples

7. Revised Code // Light segments; 4 // x0 y0 z0 x1 y1 z1 r g b 400.0 0.0 465.0 450.0 0.0 515.0 1.0 1.0 1.0 //for each light: for (int i=0; i<lightNum; i++){ ly=lights[i].getPosition().y; lx=lights[i].getPosition().x+lightdx*Math.ran dom(); lz=lights[i].getPosition().z+lightdz*Math.ran dom(); Vector3d lp=new Vector3d(lx, ly, lz); RT_color lColor=lights[i].getColor(); lColor=lColor.scale(1.0/lightNum); …… } //for each light: for (int i=0; i<lightNum; i++){ ly=lights[i].getPosition().y; lx=lights[i].getPosition().x+lightdx*Math.ran dom(); lz=lights[i].getPosition().z+lightdz*Math.ran dom(); Vector3d lp=new Vector3d(lx, ly, lz); RT_color lColor=lights[i].getColor(); lColor=lColor.scale(1.0/lightNum); …… }

8. 3 X 3 Lights8 X 8 Lights Randomly Light Samples

9. Shadow maps The above is the Object-based soft shadows Image-based hard shadows [Williams 78] Time, memory depend on image size, not geometric scene complexity Disadvantage: bias and aliasing artifacts The above is the Object-based soft shadows Image-based hard shadows [Williams 78] Time, memory depend on image size, not geometric scene complexity Disadvantage: bias and aliasing artifacts

10. The Shadow Mapping Algorithm procedure SHADOWMAPPING Render depth buffer (Z-buffer) from lights point of view, resulting in a shadow map or depth map Now, render scene from the eye’s point of view for all rasterized fragments do Determine fragment’s xyz position relative to the light That is transform each fragment’s xyz into the light’s coordinate system A = depth map(x,y) B = z-value of fragment’s xyz light position if A < B then fragment is shadowed else fragment is lit end if end for © 2003-2004 DevMaster.net procedure SHADOWMAPPING Render depth buffer (Z-buffer) from lights point of view, resulting in a shadow map or depth map Now, render scene from the eye’s point of view for all rasterized fragments do Determine fragment’s xyz position relative to the light That is transform each fragment’s xyz into the light’s coordinate system A = depth map(x,y) B = z-value of fragment’s xyz light position if A < B then fragment is shadowed else fragment is lit end if end for © 2003-2004 DevMaster.net

11. Williams’ Shadow Mapping 1 | 2 3 | 1 View from observer 2 View from light 3 Final view

12. ContributionsContributions Extend shadow maps to soft shadows Image-based rendering especially suitable Two novel image-based algorithms: Layered attenuation maps (LAM) Coherence-based raytracing (CBRT) Extend shadow maps to soft shadows Image-based rendering especially suitable Two novel image-based algorithms: Layered attenuation maps (LAM) Coherence-based raytracing (CBRT)

13. LAM Display: 5-10 fps Some aliasing artifacts Interactive applications Games Previewing CBRT Render: 19.83 min Production quality images

14. Refresher: LDIs Layered depth images Geometry Camera

15. Refresher: LDIs Layered depth images LDI

16. Refresher: LDIs Layered depth images LDI (Depth, Color)

17. PrecomputationPrecomputation Render views from points on light (hardware) Create layered attenuation map (software) Warp views into LDI Store (depth, attenuation) Objects in LAM visible in at least 1 view Render views from points on light (hardware) Create layered attenuation map (software) Warp views into LDI Store (depth, attenuation) Objects in LAM visible in at least 1 view

18. PrecomputationPrecomputation 1 st viewpoint

19. PrecomputationPrecomputation 2 nd viewpoint Attenuation = 1/2 Attenuation = 2/2

20. PrecomputationPrecomputation Warped 2 nd viewpoint Attenuation = 1/2 Attenuation = 2/2 Not present

21. DisplayDisplay Render scene without shadows (hardware) Project into LAM (software) Read off attenuation Attenuation modulates shadowless rendering Render scene without shadows (hardware) Project into LAM (software) Read off attenuation Attenuation modulates shadowless rendering

22. DisplayDisplay LAM (center of light) Eye

23. DisplayDisplay LAM (center of light) Eye Attenuation = 2/2 Color = Color * 2/2

24. DisplayDisplay LAM (center of light) Eye

25. DisplayDisplay LAM (center of light) Eye Not in LAM Attenuation = 0 Color = Color * 0

26. LAM size: 512 x 512 Precomp: 7.7 sec (64 views) 29.4 sec (256 views) Display: 5-10 fps

27. LAM size: 512 x 512 Precomp: 6.0 sec (64 views) 22.4 sec (256 views) Display: 5-10 fps

28. Layered attenuation maps – fast, aliases Coherence-based raytracing – slow, noise Layered attenuation maps – fast, aliases Coherence-based raytracing – slow, noise LAMCBRT

29. Coherence-based raytracing Hierarchical raytracing through depth images Time, memory decoupled from geometric scene complexity Coherence-based sampling Light source visibility changes slowly Reduce number shadow rays traced Also usable with geometric raytracer Hierarchical raytracing through depth images Time, memory decoupled from geometric scene complexity Coherence-based sampling Light source visibility changes slowly Reduce number shadow rays traced Also usable with geometric raytracer

30. Light Image-based raytracing 1 st shadow map

31. Light Image-based raytracing 2 nd shadow map 1 st shadow map

32. Trace shadow ray through shadow maps Light Image-based raytracing 2 nd shadow map 1 st shadow map

33. Light source visibility image Light Visibility image s1s1

34. Light source visibility image s1s1 s2s2 Vis image for s 1 Light Visibility image

35. Coherence-based sampling Compute visibility image at first point s 1 Loop over following surface points s i Predict visibility image at s i from s i-1 Trace rays where prediction confidence low Compute visibility image at first point s 1 Loop over following surface points s i Predict visibility image at s i from s i-1 Trace rays where prediction confidence low

36. Predicting visibility Blocker pts s1s1 s1s1 s2s2 Prediction

37. Predicting visibility Blocker pts s1s1 s1s1 s2s2 Prediction

38. Low confidence Light source edges Blocked/unblocked edges Prediction confidence Predicted visibility Trace rays in all X’ed cells High confidence:5 Low confidence:31 Total cells:36 Ratio:5/36 = 0.14

39. Low confidence Light source edges Blocked/unblocked edges Prediction confidence Predicted visibility Trace rays in all X’ed cells High confidence:56 Low confidence:88 Total cells:144 Ratio:56/144 = 0.40

40. Propagating low confidence If traced ray = prediction trace neighbor cells Prediction correct

41. Propagating low confidence If traced ray = prediction trace neighbor cells Prediction incorrect

42. Light cells: 16 x 16 (256) Four 1024 x 1024 maps Precomp: 2.33 min Render:19.83 min Rays:79.86 Speedup:12.96x 2.27x due to image-based raytracing accelerations 5.71x due to coherence-based sampling

43. Light cells: 16 x 16 (256) Four 1024 x 1024 maps Precomp: 3.93 min Render:65.13 min Rays:88.74 Speedup:8.52x 2.16x due to image-based raytracing accelerations 3.94x due to coherence-based sampling

44. LAMCBRT

45. Render from light Ray tracing from lightShadow depth

46. Simulating Z-buffer Vector3d lp=lights[l].getPosition(); P.setLocation(i, j); Vector3d rdir=new Vector3d(P.getX()-lp.x,P.getY()-lp.y, 0.0-lp.z); RT_ray sRay=new RT_ray(lights[l].getPosition(), rdir); intersects=computeIntersection(sRay, objects); double ft=Define.maxt; Vector3d intersectionP=new Vector3d(); Enumeration anenum=intersects.elements(); //computer smallest t; while(anenum.hasMoreElements()){ Intersection sis=(Intersection)anenum.nextElement(); if (ft>sis.getT()){ ft=sis.getT();// smallest t; closestObject=sis.getObject();// closest intersected sphere; intersectionP=sis.getPoint();// intersection point; }} if(intersects.size()>0) zBuffer[l][i][j]=intersectionP.z; else zBuffer[l][i][j]=0.0; Vector3d lp=lights[l].getPosition(); P.setLocation(i, j); Vector3d rdir=new Vector3d(P.getX()-lp.x,P.getY()-lp.y, 0.0-lp.z); RT_ray sRay=new RT_ray(lights[l].getPosition(), rdir); intersects=computeIntersection(sRay, objects); double ft=Define.maxt; Vector3d intersectionP=new Vector3d(); Enumeration anenum=intersects.elements(); //computer smallest t; while(anenum.hasMoreElements()){ Intersection sis=(Intersection)anenum.nextElement(); if (ft>sis.getT()){ ft=sis.getT();// smallest t; closestObject=sis.getObject();// closest intersected sphere; intersectionP=sis.getPoint();// intersection point; }} if(intersects.size()>0) zBuffer[l][i][j]=intersectionP.z; else zBuffer[l][i][j]=0.0;

47. Shadow Mapping Ray tracing shadowShadow mapping

48. 1560 triangles, 16 lights, 800X800 resolution, about 23 mins TeapotTeapot

49. ReferencesReferences [1] L. Williams. Casting curved shadows on curved surfaces. In SIGGRAPH 78 proceedings, pages 270–274, 1978. [2] Shadow mapping From Wikipedia, the free encyclopedia [3] Shadow Mapping: Casting curved shadows on curved surfaces http://www.paulsprojects.net/tutorials/smt/smt.html [4] L. McMillan. An Image–Based Approach to Three–Dimensional Computer Graphics. Phd thesis, Department of Computer Science, University of North Carolina, 1997. [5] Shadow Mapping and Shadow Volumes http://www.devmaster.net/articles/shadow_techniques/ [6] Raytracing: Theory & Implementation Part 5, Soft Shadows http://www.devmaster.net/articles/raytracing_series/part5.php [7] F. C. Crow. Shadow algorithms for computer graphics. In SIGGRAPH 77 proceedings, pages 242–248, 1977. [8] Efficient Image-Based Methods for Rendering Soft Shadowshttp://graphics.stanford.edu/papers/shadows/ [1] L. Williams. Casting curved shadows on curved surfaces. In SIGGRAPH 78 proceedings, pages 270–274, 1978. [2] Shadow mapping From Wikipedia, the free encyclopedia [3] Shadow Mapping: Casting curved shadows on curved surfaces http://www.paulsprojects.net/tutorials/smt/smt.html [4] L. McMillan. An Image–Based Approach to Three–Dimensional Computer Graphics. Phd thesis, Department of Computer Science, University of North Carolina, 1997. [5] Shadow Mapping and Shadow Volumes http://www.devmaster.net/articles/shadow_techniques/ [6] Raytracing: Theory & Implementation Part 5, Soft Shadows http://www.devmaster.net/articles/raytracing_series/part5.php [7] F. C. Crow. Shadow algorithms for computer graphics. In SIGGRAPH 77 proceedings, pages 242–248, 1977. [8] Efficient Image-Based Methods for Rendering Soft Shadowshttp://graphics.stanford.edu/papers/shadows/