1. Der, Sumner, and Popović Inverse Kinematics for Reduced Deformable Models Kevin G. Der Robert W. Sumner 1 Jovan Popović Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology 1 ETH Zürich

2. Der, Sumner, and Popović Our Goal: Interaction mesh manipulation direct, intuitive control speed

3. Der, Sumner, and Popović Related Work mesh editing [Zorin et al. 1997, Kobbelt et al. 1998, Sorkine 2005] Mesh-based inverse kinematics [Sumner et al. 2005] Skinning mesh animations [ James and Twigg 2005]

4. Der, Sumner, and Popović Our Method Reduced Deformable Model Mesh Examples Inverse Kinematics decouple deformation complexity from geometric complexity! - completely automated animation pipeline

5. Der, Sumner, and Popović Reduced Deformable Model expresses deformations compactly automatically constructed Control parameters: Examples Reduced Deformable Model [James and Twigg 2005] non-rigid no hierarchy Skinning weights: (Using mean-shift clustering)

6. Der, Sumner, and Popović RDM: Mesh Reconstruction Control parameters: Skinning weights: 20 to 50huge number different values estimate each example x: before deformation v: after deformation

7. Der, Sumner, and Popović Inverse Kinematics obtain natural poses by blending examples blend in which domain? –vertex positions ? –control parameters ? find a semantically proper shape Desired Blending function.

8. Der, Sumner, and Popović Deformation Gradients simple 3x3 transformation matrices describe deformation of each example Skinning equation. Vertex deformation gradient. deformation function

9. Der, Sumner, and Popović Deformation Gradients flattened deformation gradients of vertices constant matrix flattened control matrices for each example: have t → get f

10. Der, Sumner, and Popović Shape Blending combine example deformation gradients Blending function. recover the control parameters given deformation gradients Has closed form solution. solving for reduced basis! but still slow

11. Der, Sumner, and Popović Proxy Vertices evaluating deformation gradients at every vertex is undesirable summarize using a few vertices same deformation gradient! controlsvertex groups weighted centroid of the group’s vertices

12. Der, Sumner, and Popović Inverse Kinematics “Find best natural pose that meets user constraints” When there’s only a few constraints:

13. Der, Sumner, and Popović Results seconds Solving time for interaction

14. Der, Sumner, and Popović Results Solving time for interaction MeshVerticesExampleCtPxyTotalSolveMIKEfull(Eproxy) Horse843112331950.0190.0070.4243.01(3.00) Human1250010424710.0310.0130.6756.01(5.95) Mouse1318826482780.0370.0191.3511.63(1.73) Dragon155607723800.0460.0230.5900.96(0.97) Gorilla2543627281980.0450.0132.9624.38(4.33) Elephant4232111232100.0580.0081.9285.38(5.46)

15. Der, Sumner, and Popović Conclusion interactive control of reduced deformable models future work –error correction for new poses –model transfer between meshes –other reduced deformable models