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Computer Animation Algorithms and Techniques

Computer Animation Algorithms and Techniques. Chapter 4 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.

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Computer Animation Algorithms and Techniques

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  1. Computer AnimationAlgorithms and Techniques Chapter 4 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 Sample interface for specifying interpolation of key values and tangents as segment boundaries.

  5. Keyframing curves

  6. Time-Curve interpolation Implement using surface patch technology Two key frames showing a curve to be interpolated.

  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 Skeletal bending Global transforms Free Form Deformations

  11. Warping

  12. Power functions For attenuating warping effects

  13. Space Warping Deform the object by deforming the space it is in • Two main techniques: • Nonlinear Deformation • Free Form Deformation (FFD) Independent of object representation

  14. 2D grid-based deforming Assumption Easier to deform grid points than object vertices

  15. 2D grid-based deforming Inverse bilinear mapping (determine u,v from points)

  16. 2D grid-based deforming

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

  18. Global Transformations

  19. Global Transformations

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

  21. Compound global transformations

  22. Nonlinear Global Deformation Objects are defined in a local object space • Deform this space using a combination of: • Non-uniform Scaling • Tapering • Twisting • Bending

  23. Nonlinear Global Deformation

  24. Nonlinear Global Deformation Good for modeling [Barr 87] Animation is harder

  25. Free Form Deformation (FFD) Deform space by deforming a lattice around an object The deformation is defined by moving the control points Imagine it as if the object were encased in rubber

  26. Free Form Deformation (FFD) The lattice defines a Bezier volume Compute lattice coordinates Alter the control points Compute the deformed points

  27. FFD Example

  28. FFD Example

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

  30. FFDs: alternate grid organizations

  31. FFDs: Bulging & Bending

  32. FFDs:hierarchical

  33. FFDs – as tools to design shapes

  34. FFD Animation Animate a reference and a deformed lattice reference deformed morphed

  35. FFDs Animate by passing over object

  36. FFD Animation Animate the object through the lattice reference deformed morphed

  37. FFDs Animate by passing object through FFD

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

  39. FFD: Examples From “Fast Volume-Preserving Free Form Deformation Using Multi-Level Optimization” appeared in ACM Solid Modelling ‘99

  40. FFD: Examples From “Fast Volume-Preserving Free Form Deformation Using Multi-Level Optimization” appeared in ACM Solid Modelling ‘99

  41. FFD: Examples From “Fast Volume-Preserving Free Form Deformation Using Multi-Level Optimization” appeared in ACM Solid Modelling ‘99

  42. 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

  43. Object interpolation

  44. Object interp.

  45. Object interpolation For cylinder-like objects

  46. Object interpolation Spherical mapping to establish matching edge-vertex topology • Map to sphere • Intersect arc-edges • Re-triangulate • Remap to object shapes • Vertex-to-vertex interpolation

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