1. Applications of Computer Graphics

2. Business applications Maps Industrial applications Consumer applications Entertainment Education

3. Weather maps: Temperature, heat flow, rainfall

4. architecture

5. CAD

6. Mechanical engineering

7. Electric circuit design

8. simulators

9. Chemical plants

10. Consumer products

11. Medical applications

12. Molecular Biology

13. movies

14. Video games

15. Computer art

16. Hierarchical modeling

17. 2. Transformations

18. 3. Clipping

19. 4. Creating Curved surfaces

20. 3D Graphics 5. 3D Transformations

21. 6. Parallel projections

22. 7. Perspective views

23. Hidden Surface elimination

24. 8. Hidden Surface elimination

25. Z – buffer algorithm

26. Painter’s algorithm Depth sorting

27. Steps in painter’s algorithm

28. Generation of surfaces

29. Surfaces Bilinear Interpolation v u b 00 b 10 b 11 b 01 u v Bilinear interpolation fits the simplest surface for the four corner points Shape Representation

30. Surfaces Bilinear Interpolation Two Stage Process b 11 b 01 Shape Representation

31. Surfaces Coon’s Patch Given Four Boundaries C 1 (u),C 2 (u),D 1 (v),D 2 (v) v u C2C2 C1C1 D1D1 D2D2 Shape Representation

32. Surfaces Coon’s Patch C1C1 C2C2 rCrC Ruled surface between C 1 (u),C 2 (u) D1D1 D2D2 rDrD Ruled surface between D 1 (v),D 2 (v) Shape Representation

33. 9. Bezier surface

34. Bezier surface patch

35. Bezier surface patches

36. Bspline surface patch

37. Rendering Illumination and shading models

38. 10. Shading

39. Diffused lightingSpecular Phong model

40. Diffuse lighting model

42. Phong specular model

45. Powers of cos Ə

46. n=1 5 10 large n: metals small n: paper Specular Reflection Background Illumination Rendering

47. Transparent & translucent objects

48. Transparent objects

51. Polygon Shading Flat Shading Computationally fast Not smooth Mach Band effect Shading Rendering

52. Flat shading & Gourad shading

53. Flat polygon shading

54. Gouraud Shading Interpolation IaIa IbIb I2I2 I3I3 I4I4 IsIs Scan line Polygon Shading I1I1 (x 1, y 1 ) (x 2, y 2 ) (x 3, y 3 ) (x 4, y 4 ) Scan conversion! Shading Rendering

55. Phong Shading Polygon Shading NaNa NbNb N2N2 N3N3 N4N4 NsNs Scan line N1N1 (x 1, y 1 ) (x 2, y 2 ) (x 3, y 3 ) (x 4, y 4 ) N s I s Illumination using N s Shading Rendering

56. Generation of solids

57. 11. Generation of solids

58. Surfaces Sweep Surfaces Translation sweep of a circle generates a cylinder Translation sweep of a circle accompanied by scaling generates cone Shape Representation

59. Sweep solids

61. 9b. Constructive solid geometry

62. CSG

63. AUAU

64. Fractals

65. 12. Fractals

67. Generating a dragon fractal

69. Fractal dimension

70. Computer Animation

71. Conventional Animation Process Story board Sequence of drawings with descriptions Key frames A few important frames as drawings Inbetweens Draw the rest of the frames Painting Redraw onto acetate Cels, color them

72. Computer Animation Conventional Animation Stretch and Squash Exaggeration with believability

73. Computer Animation Real Time vs. Image by Image a) Real Time: Compute - Draw b) Image by Image: Compute – Store - Draw c) Display rate: 30 fps or 25 fps Animation characteristics Spatial (position, orientation, form ) Temporal (velocity, acceleration ) Visual (color, texture )

74. Computer Animation Key Framing Selected (key) frames are specified Interpolation of intermediate frames Simple and popular approach May give incorrect (inconsistent) results

75. Computer Animation Key Framing Interpolation Spline

76. Computer Animation Characteristic parameters for motion are specified and interpolated. Less data is required e.g for motion of an arm, the parameter could be rotation angle.  Parametric

77. Computer Animation Laws of motion: physical or procedural animation t ylinear actual Algorithmic Simulation

78. Computer Animation Example

79. Computer Animation Transformation of object shapes from one form to another Each form may be considered as a key frame Establish common topology for the two key frames Interpolate the intermediate frames t added point Intermediate form Morphing

80. Computer Animation Transformation of one image (source) to another image (target) Normalization of both images Feature correspondence Warping of the two images (spatial deformation) Color blending Image Morphing

81. Computer Animation Without feature correspondence (cross dissolving) SourceDestination Image Morphing

82. Computer Animation Image Morphing Correspondence

83. Computer Animation Image Morphing Correspondence

84. Computer Animation Triangle Method Feature points are marked on source and target. These feature are given the correspondence. Triangulate the points. Interpolate triangulation for intermediate frames. Warp the images, and blend colors. SourceTarget Image Morphing

85. Computer Animation Particle Systems An object is represented as cloud of particles Particles are not static; particle system evolves Non deterministic Particles are simple (computationally efficient) but can model complex amorphous objects and behaviors Dust, Water fall, Rain, Fire, Cloud, Stars, Grass, Fur, etc

86. Computer Animation Particle Systems Generate new particles with initial attributes Particles have lifespan: Kill-off dead particles Modify particle attributes: color, position Render particles In a typical particle system

87. Computer Animation Particle Systems Particle Termination For each new frame, particle’s life time is decremented by one When life time = zero, the particle is removed

88. Computer Animation Particle Systems Particle Animation Particle dynamics From force find acceleration velocity position Other attributes (color, opacity, etc.) may also change with time

89. Computer Animation Particle Systems Examples

90. Computer Animation Particle Systems More Examples Smoke and Fire

91. Computer Animation Particle Systems A grass clump is a particle system A particle is a blade of grass Draw parabolic streak over entire life time

92. Obvious approach for any camera moving shot The camera-character relationship is very fundamental to animation View dependent animation – animation that automatically changes in response to changes in view point View Dependent Character Animation

95. Camera Recovery View Dependent Character Animation

96. Deformation View Dependent Character Animation

98. Cloth Modeling

99. Suggested Readings Computer graphics by Hearn and Baker, Pearson Publications Computer graphics by Foley, Van Dam, and others, Pearson Publications Computer graphics by Hanmandlu, BPB publications Procedural elements of Computer Graphics by Rogers, McGraw Hill