1. Advanced topics Advanced Multimedia Technology: Computer Graphics Yung-Yu Chuang 2006/01/04 with slides by Brian Curless, Zoran Popovic, Mario Costa Sousa and Robin Chen

2. Outline Mapping techniques –Texture mapping –Displacement mapping –Bump mapping Shadows Ray tracing

3. Texture maps How is texture mapped to the surface? –Dimensionality: 1D, 2D, 3D –Texture coordinates (s,t) Surface parameters (u,v) Projection: spherical, cylindrical, planar Reparameterization What does texture control? –Surface color and transparency –Illumination: environment maps, shadow maps –Reflection function: reflectance maps –Geometry: displacement and bump maps

4. Texture

5. History 1974 basic idea (Catmull/Williams) 1976 reflection maps (Blinn/Newell) 1978 bump mapping (Blinn) 1983 mipmap (Williams) 1984 illumination (Miller/Hoffman) 1985 solid texture (Perlin)

6. Texture maps

7. Reflection maps

8. Environment maps

9. Bump/displacement maps

10. Illumination maps

11. Solid textures

12. Texture mapping

14. (u,v) sphericalcylindricalplanar

15. Spherical mapping

16. Cylindrical mapping

17. Planar mapping

18. Spherical mapping

19. Cylindrical mapping

20. Planar mapping

21. Aliasing

22. Antialiasing

23. Mip maps A mipmap takes at most 1/3 more memory

24. Sum area table

25. Antialiasing

26. Displacement mapping

28. Bump mapping

31. Bump v.s. displacement mapping

32. Shadow buffer

33. Forward ray tracing

34. Precursors to ray tracing local illumination cast one ray, then shade according to light ray casting (Appel 1968) cast one eye ray + one ray to light

35. Whitted ray tracing algorithm

37. Ray tree

38. Shading

39. Outer loop

40. traceRay

41. Reflection

42. Refraction

44. Ray-sphere intersection

46. Ray-plane intersection

47. Ray-triangle intersection

48. Acceleration techniques Object subdivision: hierarchical bounding volume Space subdivision: –Uniform: uniform grid –Adaptive: kd-tree, octree…

49. Bounding volume hierarchy

50. 1)Find bounding box of objects Bounding volume hierarchy

51. 1)Find bounding box of objects 2)Split objects into two groups Bounding volume hierarchy

52. 1)Find bounding box of objects 2)Split objects into two groups 3)Recurse Bounding volume hierarchy

53. 1)Find bounding box of objects 2)Split objects into two groups 3)Recurse Bounding volume hierarchy

54. 1)Find bounding box of objects 2)Split objects into two groups 3)Recurse Bounding volume hierarchy

55. 1)Find bounding box of objects 2)Split objects into two groups 3)Recurse Bounding volume hierarchy

56. At midpoint Sort, and put half of the objects on each side Use modeling hierarchy Where to split?

57. BVH traversal If hit parent, then check all children (from the closer to the further?)

58. BVH traversal Don't return intersection immediately because the other subvolumes may have a closer intersection

59. Bounding volume hierarchy

61. Space subdivision approaches KD tree Unifrom grid

62. Space subdivision approaches BSP tree Quadtree (2D) Octree (3D)

63. Uniform grid

64. Preprocess scene 1.Find bounding box

65. Uniform grid Preprocess scene 1.Find bounding box 2.Determine grid resolution

66. Uniform grid Preprocess scene 1.Find bounding box 2.Determine grid resolution 3.Place object in cell if its bounding box overlaps the cell

67. Uniform grid Preprocess scene 1.Find bounding box 2.Determine grid resolution 3.Place object in cell if its bounding box overlaps the cell 4.Check that object overlaps cell (expensive!)

68. Uniform grid traversal Preprocess scene Traverse grid 3D line = 3D-DDA

69. A A Leaf nodes correspond to unique regions in space K-d tree

70. A A Leaf nodes correspond to unique regions in space B K-d tree

71. A B A B Leaf nodes correspond to unique regions in space K-d tree

72. A B A B C

73. A B C A B C

74. A B C A B C D

75. A B C D A B C D

76. A B C D A B C D Leaf nodes correspond to unique regions in space K-d tree

77. A B C D A B C D Leaf nodes correspond to unique regions in space K-d tree traversal

78. Antialiasing with supersampling

79. Result

80. Advanced ray tracing