Computer Animation Algorithms and Techniques

1. Computer AnimationAlgorithms 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