Discrete One-forms on Meshes and Applications to 3D mesh Parameterization
| Title: | Discrete One-forms on Meshes and Applications to 3D mesh Parameterization |
| Author: |
Thurston, Dylan; Gortler, Steven; Gotsman, Craig
Note: Order does not necessarily reflect citation order of authors. |
| Citation: | Gortler, Steven. J., Craig Gotsman, and Dylan Thurston. 2006. Discrete one-forms on meshes and applications to 3D mesh parameterization. Computer Aided Geometric Design 23(2): 83-112. |
| Full Text & Related Files: |
Gortler_DiscreteOneForms.pdf (960.6Kb; PDF) 
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| 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. |
| Published Version: | http://dx.doi.org/10.1016/j.cagd.2005.05.002 |
| Terms of Use: | This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA |
| Citable link to this page: | http://nrs.harvard.edu/urn-3:HUL.InstRepos:2634288 |
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