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

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

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]

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

Correspondence Specification

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

Correspondence Computation A (Igloo) B (House)

Correspondence Computation Patch A Patch B Extremal Vertices

Mapping Patch A Patch B

Mapping Desiderata

Merging Patch A Patch B

Reconstruction

Completed Correspondence

Morphing Trajectory Specification

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

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

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

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

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

System Architecture

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