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

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 Extremal Vertices Patch APatch B

9. Mapping Patch APatch B

10. Mapping Desiderata

11. Merging Patch APatch 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. Performance 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 Morphing Patches User Time Time to Compute Merged Polyhedron 214 97,900 32,520 61,701 10 86 67 50 ~5min ~6 hours ~3 hours ~4 hours <1sec 2.5min 30 sec 1 min

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