1. Deformation using interpolation CSE 3541 Matt Boggus

2. Interpolation based animation Keyframe systems – in general Interpolating shapes Deforming an single shape 3D interpolation between two shapes Image morphing

3. Keyframing

4. Time-Curve interpolation Conditions: P(0) maps to Q(0) P(1) maps to Q(1) All of P maps to all of Q One to one – no two P(u) map to same Q(v) Onto – every Q(v) has a P -1 (u) value

5. Time-Curve interpolation Solutions: If P and Q use the same curve formation and # control points, then generate intermediate curves by interpolating the control points Supersample: Generate same number of points on P and Q, then interpolate between matching points

6. Object interpolation topics 1. Modify shape of one object 2. Interpolate one object into second object 3. Interpolate one image into second image

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

8. Warping Vertices closer to seed are displaced more

9. Power functions For attenuating warping k determines how quickly increase in distance decreases warping

10. 2D grid-based deforming Assumption: easier to deform grid points than object vertices A (global coordinates): (25.6,14.7) A (local coordinates): (5.6, 2.7) A’s Grid cell (5, 2) A’s position in cell (0.6, 0.7)

11. 2D grid-based deforming Inverse bilinear mapping P values at corners known from grid deformation u and v are known from point’s position in original grid cell

12. 2D grid-based deforming

13. 2D skeleton-based bending

14. For each vertex, determine which line segment (or bone) it is closest to: L 2 distance to it: d relative position on the line segment: r = d 2 /d 1

15. 2D skeleton-based bending For new vertex position on repositioned (and possibly rescaled) line segment, Interpolate r along line segment Place d units away from the line segment

16. Examples of artist driven deformation Point based, skeleton based, cage based From Bounded Biharmonic Weights for Real-Time Deformation by Alec Jacobson, Ilya Baran, Jovan Popovic and Olga Sorkine, appearing at SIGGRAPH 2011 http://www.youtube.com/watch?v=P9fqm8vgdB 8&feature=related http://www.youtube.com/watch?v=P9fqm8vgdB 8&feature=related

17. Free-Form Deformations (FFDs) 2D grid-based deformingFFDs 2D grid 3D grid tri-cubic interpolationbi-linear interpolation

18. FFDs Animate by passing object through FFD

19. Interpolate between 2 objects Correspondence problem: what part of one object to maps into what part of the other object

20. Interpolate between 2 objects – difficulties How to handle objects of different genus? (roughly speaking: number of holes in the model)  map to

21. Morphing Image blending Move pixels to corresponding pixels Example from http://www.mukimuki.fr/flashblog/2009/05/10/morphing/

22. Morphing

24. Using feature lines instead of grid points