CS 148, Summer 2012 Introduction to Computer Graphics and Imaging Justin Solomon

Transcription

1 CS 148, Summer 2012 Introduction to Computer Graphics and Imaging Justin Solomon

2

3

4

5 Light source

6 Light interacts with objects in scene

7 Image plane

8 ?? Most light doesn t reach the camera

9 ?? Most light doesn t reach the camera

10 Many lighting effects are reversible

11 Trace rays from light to camera

12 Trace rays from light to camera

13 Draw viewing ray through each pixel

14 Intersect with geometry

15 Compute light ray

16 Evaluate shading µ

17 Take closest one

18 µ µ Redirect ray

19 µ µ Redirect ray

20 Rasterization for (each object in scene) drawobject();

21 Rasterization for (each object in scene) drawobject(); Ray Tracing for (each pixel in image) sendray();

22 Rasterization for (each object in scene) drawobject(); Ray Tracing for (each pixel in image) sendray();

23 for each pixel do compute viewing ray if (ray hits an object with t>0) then Compute normal Evaluate shading model else Set pixel color to background color Textbook page 85

24 ~d = direction ~o = origin Ray

25 ~d = direction Does not have to be unit length! ~o = origin Ray

26 t 1 t 2 (0; 1) ~o + t ~ d Point on Ray

27 ~o + t ~ d t < 0 Point on Ray

28 ~o + t ~ d t < 0 Point on Ray

29 No perspective transformation needed! ~j ~p 0 ~p = ~p 0 + u~i + v~j u 2 [0; w]; v 2 [0; h] ~i Generating rays

30 k~x ~ck 2 = R 2 ~o + t ~ d Ray-object intersection

31 ~o + t ~ d k~x ~ck 2 = R 2 Ray-object intersection

32 ~o + t ~ d k~x ~ck 2 = R 2 k~o + t ~ d ~ck 2 = R 2 Ray-object intersection

33 ~o + t ~ d k~x ~ck 2 = R 2 k~o + t ~ d ~ck 2 = R 2 (~o + t ~ d ~c) (~o + t ~ d ~c) = R 2 Ray-object intersection

34 ~o + t d ~ k~x ~ck 2 = R 2 k~o + t d ~ ~ck 2 = R 2 (~o + t d ~ ~c) (~o + t d ~ ~c) = R 2 k dk ~ 2 t 2 + 2((~o ~c) d)t ~ + k~o ~ck 2 = R 2 Ray-object intersection

35 Ray-object intersection CS 148, fall 2011

36 ~x ~c ~ N = ~x ~c k k Normals

37 ~v 3 ~N = (~v 2 ~v 1 ) (~v 3 ~v 1 ) k(~v 2 ~v 1 ) (~v 3 ~v 1 )k ~v 3 ~v 1 ~v 1 ~v 2 ~v 2 ~v 1 Normals

38 ~ l2 ~x ~ l1 ~x ~x Light rays

39

40 Intersect light ray with scene

41 abstract class surface virtual hit-record hit(ray, t0, t1) virtual box bounding-box() struct hit-record vector3d position, normal surface hit-surface abstract class material color evaluate(in-ray, normal, pos)

42 color ray-trace(ray r) hit-record record = intersect(r); if (record.hit-surface.is-reflective) ray reflected-ray = reflect(r,record.normal); color reflected-color = ray-trace(reflected-ray); compute-spectral-component( reflected-color);

43 Lots of bounces Fewer bounces CS 148, fall 2011 Save time; avoid infinite recursion

44 Deal with repeated objects

45 Store object once, use often Deal with repeated objects

46 Each instance stores a transformation matrix M (can stretch, rotate, etc!) Deal with repeated objects

47 M 2 R 3 3 Object coordinates World coordinates Deal with repeated objects

48 M 2 R 3 3 ~o + t ~ d Deal with repeated objects

49 Do intersection here! M 2 R 3 3 M 1 ~o + tm 1 ~ d ~o + t ~ d Deal with repeated objects

50 M 2 R 3 3 M 1 ~o + tm 1 ~ d Same t! ~o + t ~ d Deal with repeated objects

51 M 2 R 3 3 ~N ~ M ~ N Deal with repeated objects

52 Binary operations for shape

53 A B A [ B A B A \ B Binary operations for shape

54 A B A [ B A B A \ B Binary operations for shape

55 A B in(a) = [1; 3] in(b) = [2; 6] in(a \ B) = [2; 3] in(a [ B) = [1; 6] in(a B) = [1; 2) Store inside intervals

56 A B in(a) = [1; 3] in(b) = [2; 6] in(a \ B) = [2; 3] in(a [ B) = [1; 6] in(a B) = [1; 2) Store inside intervals

57 A B in(a) = [1; 3] in(b) = [2; 6] in(a \ B) = [2; 3] in(a [ B) = [1; 6] in(a B) = [1; 2) Store inside intervals

58 A B in(a) = [1; 3] in(b) = [2; 6] in(a \ B) = [2; 3] in(a [ B) = [1; 6] in(a B) = [1; 2) Store inside intervals

59

60

61 Scatter rays to make ray tracing less crisp.

62 Multiple rays per pixel

63 Moiré pattern Multiple rays per pixel

64 Remove Moiré patterns

65 ???

66

67

68 Hard shadows Soft shadows

69 Lights aren t all point sources

70 Randomly sample light rays

71 Shadow computed per ray

72 Shadow computed per ray

73 Shadow computed per ray

74

75 Square lens Focus plane Randomly sample eye positions

76 Randomly sample reflected rays

77 Randomly sample positions

78 Diffuse Ambient Brightness depends on nearby geometry

79 Account for indirect lighting

80 Diffuse inter-reflection Account for indirect lighting

81 Caustics Account for indirect lighting

82 Value p b m Variable Pixels on screen Objects in scene Average pixels/object Rasterization: O(bm) Ray tracing: O(bp) Accelerated ray tracing: O(p log b) CS 148, fall 2011

83 Bounding Volume Hierarchy (BVH)

84 Binary Space Partitioning (BSP) trees

85 Uniform subdivision grid

86 [NVIDIA, SIGGRAPH 2008] Embarrassingly parallel, but not SIMD?

87 CS 148, Summer 2012 Introduction to Computer Graphics and Imaging Justin Solomon