Name
Abstract | ||
|---|---|---|
We describe how some simple properties of discrete one-forms directly relate to some old and new results concerning the parameterization of 3D mesh data. Our first result is an easy proof of Tutte's celebrated "spring-embedding" theorem for planar graphs, which is widely used for parameterizing meshes with the topology of a disk as a planar embedding with a convex boundary. Our second result generalizes the first, dealing with the case where the mesh contains multiple boundaries, which are free to be non-convex in the embedding. We characterize when it is still possible to achieve an embedding, despite these boundaries being non-convex. The third result is an analogous embedding theorem for meshes with genus 1 (topologically equivalent to the torus). Applications of these results to the parameterization of meshes with disk and toroidal topologies are demonstrated. Extensions to higher genus meshes are discussed. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.cagd.2005.05.002 | Computer Aided Geometric Design |
Keywords | Field | DocType |
one-form,parameterizing mesh,parameterization,computer graphics,planar embedding,embedding,analogous embedding theorem,convex boundary,mesh parameterization,manifold mesh,new result,planar graph,mesh data,discrete one-forms,higher genus mesh,easy proof,one form,computer graphic | Topology,Polygon mesh,Embedding,Volume mesh,Torus,Regular polygon,Planar graph,Mesh generation,Static mesh,Mathematics | Journal |
Volume | Issue | ISSN |
23 | 2 | Computer Aided Geometric Design |
Citations | PageRank | References |
54 | 1.81 | 22 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Steven J. Gortler | 1 | 4205 | 366.17 |
| Craig Gotsman | 2 | 3426 | 183.14 |
| Dylan Thurston | 3 | 82 | 4.69 |