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Large Mesh Deformation Using the Volumetric Graph Laplacian

Large Mesh Deformation Using the Volumetric Graph Laplacian. Kun Zhou Jin Huang* John Snyder ^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft Research Asia *Zhejiang University ^Microsoft Research. Mesh Deformation. Smooth geometry

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Large Mesh Deformation Using the Volumetric Graph Laplacian

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  1. Large Mesh Deformation Using theVolumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo LiuHujun Bao* Baining Guo Heung-Yeung ShumMicrosoft Research Asia *Zhejiang University^Microsoft Research

  2. Mesh Deformation • Smooth geometry • Freeform deformation [Barr84, Singh98, Bendels03] • Energy minimization [Welch94, Taubin95, Botsch04] • Detailed geometry • Multi-resolution editing [Zorin97, Kobbelt98, Guskov99] • Differential domain methods: • Poisson mesh editing [Yu04] • Laplacian surface editing [Sorkine04, Lipman05]

  3. Large Mesh Deformation • Challenge to existing techniques • Local self-intersection, unnatural volume change Bending Twisting

  4. Large Mesh Deformation • Challenge to existing techniques • Local self-intersection, unnatural volume change Poisson Mesh Editing VGL

  5. Large Mesh Deformation • Challenge to existing techniques • Local self-intersection, unnatural volume change Poisson Mesh Editing VGL

  6. Large Deformation: Why Difficult? • Differential domain methods [Yu04,Sorkine04]  Uniform error distribution using least-squares optimization  Only surface details, volume ignored • Displacement volumes [Botsch03]  Volumetric constraints  Iterative relaxation produces artifacts Solution: Volumetric Constraints & Least-Squares Optimization

  7. F F’ Poisson Mesh Editing Step 1: Specify control curve Step 2: Edit control curve

  8. Poisson Mesh Editing Step 3: Propagate local frame transformations Step 4: Solve Poisson equation

  9. Surface Details & Laplacian

  10. Surface Details & Laplacian

  11. Surface Details & Laplacian

  12. Volumetric Details & Laplacian

  13. Volumetric Details & Laplacian

  14. Quadric Energy Function Surface Details Position Constraints Volumetric Details

  15. Deformation Using VGL • Construct the volumetric graph • Compute Laplacian coordinates • Compute and apply local transformation • Solve the sparse linear system

  16. Volumetric Graph Construction

  17. Volumetric Graph Construction • Construct an inner shell

  18. Volumetric Graph Construction • Embed both the mesh and shell in a lattice

  19. Volumetric Graph Construction • Build edge connections

  20. Volumetric Graph Construction • Simplify and smooth the graph Not Tetrahedral Mesh

  21. Deformation Comparison Laplacian surface [Sorkine04] Poisson mesh [Yu04] VGL

  22. Deformation Comparison Poisson mesh [Yu04] Laplacian surface [Sorkine04] VGL

  23. Deformation Comparison Original model Poisson mesh VGL

  24. Deformation Interface • 3D space manipulation [Yu04] • Tedious and require artistic skill • 2D sketch-based interface • Modeling: Teddy[Igarashi99] • Editing: [Zelinka04, Kho05, Nealen05] “Teddy-like” deformation: intuitive and easy to use

  25. 2D Sketch-based Deformation

  26. Deformation Retargeting

  27. Deformation Retargeting

  28. Results

  29. Results

  30. Results

  31. Results

  32. Results

  33. Conclusion • Volumetric graph Laplacian (VGL) • Volumetric constraints • Least squares minimization • No tetrahedral mesh construction • 2D sketch-based deformation system • “Teddy-like” deformation system • Cartoon deformation retargeting

  34. Future Work • Anchor-based deformation • Dynamic connectivity • Automatic contour tracking

  35. Acknowledgement • Cartoons from Disney Feature Animation and Dongyu Cao • 3D models from Stanford, MIT, Cyberware • Xin Sun, Jianwei Han • Steve Lin, Bo Zhang • NSFC and 973 Program of China

  36. Thank You !

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