1. Games, Movies and Virtual Worlds – An Introduction to Computer Graphics Ayellet Tal Department of Electrical Engineering Technion

2. When you think about graphics, you envision

5. Applications  Science  Art  Engineering  Medicine  Entertainment  Advertising  Education

6. Applications  Science  Art  Engineering  Medicine  Entertainment  Advertising  Education

7. Applications  Science  Art  Engineering  Medicine  Entertainment  Advertising  Education

8. Applications  Science  Art  Engineering  Medicine  Entertainment  Advertising  Education

9. Applications  Science  Art  Engineering  Medicine  Entertainment  Advertising  Education

10. Applications  Science  Art  Engineering  Medicine  Entertainment  Advertising  Education

11. Applications  Science  Art  Engineering  Medicine  Entertainment  Advertising  Education

12. Applications  Science  Art  Engineering  Medicine  Entertainment  Advertising  Education Outside-In http://www.geom.uiuc.edu/docs/outreach/oi/moregraphics.html http://www.physics.orst.edu/~bulatov/vrml/index.html

13. Why interesting? The world complex dynamic multi-dimensional continuous The screen simple static two-dimensional discrete

14. Beauty  Science – math and physics  Engineering – software and hardware  Artistic and aesthetic issues  Fun!

15. Issues in computer graphics  Geometric modeling  Rendering  Animation  Scientific visualization “The purpose of computing is insight, not numbers” Hamming  Virtual reality  Human-computer interaction

16. Geometric modeling How do we represent objects?

17. Wish list 1. Large domain 2. Unambiguous 3. Unique 4. Accurate 5. Impossible to create invalid representations 6. Easy to create and maintain 7. Closure under certain operations 8. Compact 9. Efficient

18. Geometric modeling How do we represent objects? Voxels

19. Geometric modeling How do we represent objects? Splines

20. Geometric modeling How do we represent objects? Polyhedra

21. Rendering 1. What pixels? 2. What ’ s in the pixel? 3. Which color?

22. What pixels = scan conversion  Given: A mathematical description of a two or a three dimensional “scene”  Find: A value for each pixel in the frame buffer

23. What pixels = scan conversion  Given: A mathematical description of a two or a three dimensional “scene”  Find: A value for each pixel in the frame buffer

24. What ’ s in the pixel - visibility Goal: Hidden surface removal  In object space or in image space?  In software or in hardware?

25. What color?  Illumination and shading  Transparency, reflection

26. Issues - recap  Modeling:  Construct / represent objects  Transform to construct scene  Rendering:  Project  Scan convert  Remove hidden surface  Assign colors

27. Animation How to define / represent complex time-dependent behavior of objects?

29. Animation topics  Automatic in-between  Transformations  Collision  Motion  Facial animation  Morphing  Physically-based simulation

30. Animation topics  Automatic in-between  Transformations  Collision  Motion  Facial animation  Morphing  Physically-based simulation

31. Animation topics  Automatic in-between  Transformations  Collision  Motion  Facial animation  Morphing  Physically-based simulation

32. Animation topics  Automatic in-between  Transformations  Collision  Motion  Facial animation  Morphing  Physically-based simulation

33. Animation topics  Automatic in-between  Transformations  Collision  Motion  Facial animation  Morphing  Physically-based simulation

34. Animation topics  Automatic in-between  Transformations  Collision  Motion  Facial animation  Morphing  Physically-based simulation 72 Frames - 5 Full Frames

35. Animation topics  Automatic in-between  Transformations  Collision  Motion  Facial animation  Morphing  Physically-based simulation

36. Animation topics  Automatic in-between  Transformations  Collision  Motion  Facial animation  Morphing  Physically-based simulation 1993, Apple Computer, Inc.

37. Case study – Teaching dinos to dance

38. Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

39. Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

40. Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

41. Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

42. Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

43. Research topic: decomposition Let S be an orientable mesh. Goal: decompose S into connected sub-meshes S 1, S 2 … S k that are face-wise disjoint, and whose union gives S. S S1S1 S2S2 SkSk

44. Key idea: two-phase algorithm 1. Find major components with fuzzy boundaries 2. Find exact boundaries

45. Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

46. Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

47. Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

48. Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

49. Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

50. Problem: finding boundaries  Given:  G=(V,E) the dual graph of the mesh  A,B,Fuzzy  Goal: Partition V into V A ’ and V B ’ s.t. A A B B Fuzzy

51. Algorithm for finding boundaries 1. Assign capacities 2. Construct a flow network on Fuzzy 3. Find the minimum cut

52. The algorithm has 1. Geometry 2. Probability 3. Clustering 4. Graph theory

53. Shuttle

54. Dove

55. Alien

56. Camel

57. Heart

58. Venus

59. Skeleton hand

60. Skeleton extraction

64. Help the dove fly

65. So, Games, movies and virtual world?

66. So, Games, movies and virtual world? Or Modeling, rendering, animations

67. So, Games, movies and virtual world? Or Modeling, rendering, animations Math, physics, data structures, algorithms, software, hardware

68. So, Games, movies and virtual world? Or Modeling, rendering, animations Math, physics, data structures, algorithms, software, hardware Science, education, medicine, engineering..

69. THE END