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

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Presentation on theme: "Large Mesh Deformation Using the Volumetric Graph Laplacian Kun Zhou Jin Huang* John Snyder^ Xinguo Liu Hujun Bao* Baining Guo Heung-Yeung Shum Microsoft."— Presentation transcript:

1 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

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 BendingTwisting

4 Large Mesh Deformation Challenge to existing techniques – Local self-intersection, unnatural volume change Poisson Mesh EditingVGL

5 Large Mesh Deformation Challenge to existing techniques – Local self-intersection, unnatural volume change Poisson Mesh EditingVGL

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 Poisson Mesh Editing Step 1: Specify control curveStep 2: Edit control curve F F

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

9 Surface Details & Laplacian

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12 Volumetric Details & Laplacian

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14 Quadric Energy Function Surface DetailsVolumetric DetailsPosition Constraints

15 1. Construct the volumetric graph 2. Compute Laplacian coordinates 3. Compute and apply local transformation 4. Solve the sparse linear system Deformation Using VGL

16 Volumetric Graph Construction

17 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 Poisson mesh [Yu04] Laplacian surface [Sorkine04] Deformation Comparison VGL

23 Deformation Comparison Original modelPoisson meshVGL

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

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28 Results

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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 !

37 Poisson Mesh Editing Mesh GeometryGuidance FieldBoundary Condition

38 Quadric Energy Function Surface DetailsVolumetric DetailsPosition Constraints : unknown positions : control points : mesh Laplacian : new mesh Laplacian coords : volumetric graph Laplacian : new graph Laplacian coords : control parameters

39 Geodesic distance fields-based blending – Compute the local transform for each control point – Blend the transforms of all control points – Blend the transform with the identity Compute Local Transformation


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