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Computer Animation Algorithms and Techniques

Computer Animation Algorithms and Techniques. Interpolation-based animation. Interpolation based animation. Key-frame systems – in general Interpolating shapes Deforming an single shape 3D interpolation between two shapes Morphing – deforming an image. Keyframing – interpolating values.

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Computer Animation Algorithms and Techniques

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  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

  42. 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

  43. Map to sphere

  44. Object interpolation

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

  46. Object interpolation

  47. Object interp

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

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