1. Shape Deformation Reporter: Zhang, Lei 5/30/2006

2. Stuff Vector Field Based Shape Deformation (VFSD) Multigrid Alogrithm for Deformation Edit Deforming Surface Animation Subspace Gradient Domain Mesh Deformation J. Huang, X. H. Shi, X. G. Liu, K. Zhou, L. Y. Wei, S. H. Teng, H. J. Bao, B. G. Guo and H. Y. Shum.

3. Vector Field Based Shape Deformations Wolfram von Funck, Holger Theisel, Hans-Peter Seidel MPI Informatik

4. Basic Model Moving vertex along the deformation orbit – defined by the path lines of a vector field v.

5. Path Line of Vector Field X(t 0 ) X(t) Given a time-dependent vector field V(X, t), a Path Line in space is X(t): t0t0 t OR

6. Vector Field Selection Deformation Request: No self-intersection Volume-preserving Details-preserving Smoothness of shape in deformation Divergence-free Vector Field: V=(V 1, V 2, V 3 )

7. Construction of V Divergence-free p, q: two scalar field 2D space: 3D space:

8. Vector Field for Special Deformation Constant Vector Field V : translation Deformation

9. Vector Field for Special Deformation Linear Vector Field V : rotation Deformation

10. Piecewise Field for Deformation Deformation for a selected region Define piecewise continuous field Inner region: V Outer region: zero Intermediate region: blending Region specified by an implicit function And thresholds

11. Piecewise Field for Deformation Inner region Intermediate region Outer region

12. Piecewise Field for Deformation if

13. Deformation Tools Translation: constant vector field

14. Deformation Tool Rotation: linear vector field

15. Path Line Computation Runge-Kutta Integration For each vertex v(x, t i ), integrating vector field above to v(x’, t i+1 )

16. Remeshing Edge Split

17. Examples Demo

18. Examples

19. Performance Benchmark Test AMD 2.6GHz 2 GB RAM GeForce 6800 GT GPU

20. Conclusion Embeded in Vector Field FFD Parallel processing Salient Strength No self-intersection Volume-preserving Details-preserving Smoothness of shape in deformation

21. A Fast Multigrid Algorithm for Mesh Deformation Lin Shi, Yizhou Yu, Nathan Bell, Wei-Wen Feng University of Illinois at Urbana-Champaign

22. Basic Model Two-pass pipeline Local Frame Update Vertex Position Update Multigrid Computation Method R. Zayer, C. Rossl, Z. Karni and H. P. Seidel. Harmonic Guidance for Surface Deformation. EG2005. Y. Lipman, O. Sorkine, D. Levin and D. Cohen-Or. Linear rotation-invariant coordinates for meshes. Siggraph2005.

23. Discrete Form (SIG ’ 05) First Discrete Form

24. Discrete Form (SIG ’ 05) Second Discrete Form

25. Local Frame (SIG ’ 05) Discrete Frame at each vertex forms a right-hand orthonormal basis.

26. First Pass (EG ’ 05) Harmonic guidance for local frame Boundary conditions: 1: edited vertex 0: fixed vertex Scaling Rotation 1 0

27. Second Pass (SIG ’ 05) Solving vertex position

28. Second Pass Solving vertex position “Normal Equation”

29. Some Results

30. Computation First Pass Second Pass Multigrid Method

31. defect equation coarsest level

32. Performance

34. Conclusion Computation Method for large mesh

35. Editing Arbitrary Deforming Surface Animations S. Kircher, M. Garland University of Illinois at Urbana-Champaign

36. Problem Deforming Surface Editing Surface

38. Pyramid Scheme Quadric Error Metric M. Garland and P. S. Heckbert. Surface simplification using quadric error metrics. SIGGRAPH’97.

39. Pyramid Scheme CoarseFine 2nd-order divided difference Detail vector Construct by and adding detail vectors for level k. Sig’99

40. Adaptive Transform

41. is generated from by improving its error with respect to Adaptive Transform Multilevel Meshes (Sig ’ 05) Reclustering Swap

42. Basis Smoothing Blockification Vertex Teleportation PRE-processing: Time-varying multiresolution transform for a given animation sequence.

43. Editing Tool Direct Manipulation level k level 0

44. Editing Tool Direct Manipulation

45. Editing Tool Direct Manipulation

46. Multiresolution Embossing Multiresolution set of Edit

48. Conclusion Multiresolution Edit

49. The End