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Feature-based Surface Decomposition for Correspondence and Morphing between Polyhedra

Feature-based Surface Decomposition for Correspondence and Morphing between Polyhedra Arthur D Gregory Andrei State, Ming C Lin, Dinesh Manocha, Mark A Livingston University of North Carolina at Chapel Hill http://www.cs.unc.edu/~geom/3Dmorphing {gregory,andrei,lin,dm,livingst}@cs.unc.edu

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Feature-based Surface Decomposition for Correspondence and Morphing between Polyhedra

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  1. Feature-based Surface Decomposition for Correspondence and Morphing between Polyhedra Arthur D Gregory Andrei State, Ming C Lin, Dinesh Manocha, Mark A Livingston University of North Carolina at Chapel Hill http://www.cs.unc.edu/~geom/3Dmorphing {gregory,andrei,lin,dm,livingst}@cs.unc.edu

  2. Highlights • Empower animators to create a visually pleasing morph • Simple user interface • General

  3. Previous Work • Kanai et al. [1997] • DeCarlo and Gallier [1996] • Galin and Akkouche [1996] • Lazarus and Verroust [1994] • Kent, Carlson, and Parent [1992] • Kaul and Rossignac [1991] • Wyvill [1990]

  4. Two Input Polyhedra User Specify Correspondence Edit trajectories Compute merged polyhedron Interpolate trajectories Morphing sequence Overview

  5. Correspondence Specification

  6. Correspondence Computation • Feature-Nets decompose input polyhedra into morphing patches • For each corresponding Morphing Patch pair: • map both onto a 2D polygon • merge the vertex-edge graphs • reconstruct the facets

  7. Correspondence Computation A (Igloo) B (House)

  8. Correspondence Computation Patch A Patch B Extremal Vertices

  9. Mapping Patch A Patch B

  10. Mapping Desiderata

  11. Merging Patch A Patch B

  12. Reconstruction

  13. Completed Correspondence

  14. Morphing Trajectory Specification

  15. Analysis Computation time = O(K*[m+n]) K = max{log Q,Q} m = vertices in A n = vertices in B

  16. Implementation • Implemented in C++ • Uses OpenGL and Tcl/Tk libraries for display and user interface. • Interactive user interface on SGI and PC systems

  17. Models Igloo-House Triceratops-Human Human Heads Donut-Cup Triangles 82 40 5,660 17,528 3,426 4,020 4,096 8,452 Output Triangles 214 97,900 32,520 61,701 Morphing Patches 10 86 67 50 User Time ~5min ~6 hours ~3 hours ~4 hours Time to Compute Merged Polyhedron <1sec 2.5min 30 sec 1 min Performance

  18. Ongoing Efforts • Remove restriction that the chains of the feature net must lie on edges of the models • Do not require the user to specify a connected feature net • Provide better control of the model’s shape during the morph

  19. Ongoing Efforts • Remove restriction that models must be homeomorphic • models can change topology during the morph • Extend to include textured objects • currently interpolate only normals and vertex color

  20. System Architecture

  21. Conclusion • Empower animators to create a visually pleasing morph • Simple user interface • Compute correspondence through surface decomposition • General

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