1. Computer Animation Algorithms and Techniques
Interpolation-based animation

2. Interpolation based animation
Key-frame systems – in general
Interpolating shapes
Deforming an single shape
3D interpolation between two shapes
Morphing – deforming an image

3. Keyframing – interpolating values

4. Keyframing keys, in-betweens track-based
Avars – articulation variables

5. Keyframing curves

6. Time-Curve interpolation
Implement using surface patch technology

7. Time-Curve interpolation
Establish point correspondence

8. Time-Curve interpolation
Define time – space-curve “patches”
Interpolate in one dimension for curve (spatially)
Interpolate in other dimension temporally

9. Object interpolation Correspondence problem Interpolation problem
1. Modify shape of object interpolate vertices of different shapes
2. Interpolate one object into second object
3. Interpolate one image into second image

10. Object Modification Vertex warping Modify the vertices directly OR
Modify the space the vertices lie in
2D grid-based deforming
Free Form Deformations
Skeletal bending
Global transforms

11. Warping

12. Power functions
For attenuating warping effects

13. 2D grid-based deforming
Assumption
Easier to deform grid points than object vertices

14. 2D grid-based deforming
Inverse bilinear mapping (determine u,v from points)

15. 2D grid-based deforming

16. 2D skeleton-based bending

17. 2D skeleton-based bending

18. 2D skeleton-based bending

19. Global Transformations
Common linear transform of space
In GT, Transform is a function of where you are in space

20. Global Transformations

21. Global Transformations

22. Global Transformations
z above zmin: rotate q
z between zmin ,zmax :
Rotate from 0 to q
z below zmin: no rotation

23. Compound global transformations

24. Free-Form Deformations (FFDs)
2D grid-based deforming
FFDs
2D grid
3D grid
bi-linear interpolation
tri-cubic interpolation

25. Free-Form Deformations
Embed object in rectilinear grid

26. Free-Form Deformations
Register points in grid: cell x,y,z; (s,t,u)

27. Free-Form Deformations
As in Bezier curve interpolation
Continuity controlled by coplanarity of control points

28. FFDs: alternate grid organizations

29. FFDs: bending

30. FFDs
hierarchical

31. FFDs – as tools to design shapes

32. FFDs
Animate by passing over object

33. FFDs
Animate by passing object through FFD

34. FFDs
Facial animation by manipulating FFD

35. FFDs
Exo-muscular system
Skeleton -> changes FFD -> changes skin

36. Interpolate between 2 objects
Correspondence problem: what part of one object to map into what part of the other object
How to handle objects of different genus?
Volumetric approaches with remeshing
Some surface-based approaches
Slice along one dimension; interpolate in other two
Map both to sphere
Recursively divide into panels

37. Object interpolation
For cylinder-like objects

38. Radial mapping
If central axis intersects polygonal slice inside kernel
Then simple radial mapping possible

39. Object interp

40. Object interpolation

41. Object interp

43. Object interpolation
Spherical mapping to establish matching edge-vertex topology
Map to sphere
Intersect arc-edges
Retriangulate
Remap to object shapes
Vertex-to-vertex interpolation

44. Map to sphere

45. Object interpolation

47. Object interpolation – recursive sheets
Continually add vertices to make corresponding boundaries have an equal number

48. Object interpolation

49. Object interp

50. Morphing Image blending Move pixels to corresponding pixels
Blend colors

51. Morphing

52. Morphing

53. Morph

54. Morphing

55. Morphing

56. Morphing

57. Morphing: feature based
Given: corresponding user-defined feature lines in source and destination images

58. Morphing: feature based
Locate each pixel relative to each feature line in source and destination images

59. Morphing: feature based