A Local/Global Approach to Mesh Parameterization
By Ligang Liu, Lei Zhang, Yin Xu, Craig Gotsman, Steven J. Gortler. Computer graphics forum (Print), 2008
463 citations recorded by the source corpus.
We present a novel approach to parameterize a mesh with disk topology to the plane in a shape‐preserving manner. Our key contribution is a local/global algorithm, which combines a local mapping of each 3D triangle to the plane, using transformations taken from a restricted set, with a global “stitch” operation of all triangles, involving a sparse linear system. The local transformations can be taken from a variety of families, e.g. similarities or rotations, generating different types of parameterizations. In the first case, the parameterization tries to force each 2D triangle to be an as‐similar‐as‐possible version of its 3D counterpart. This is shown to yield results identical to those of the LSCM algorithm. In the second case, the parameterization tries to force each 2D triangle to be an as‐rigid‐as‐possible version of its 3D counterpart. This approach preserves shape as much as possible. It is simple, effective, and fast, due to pre‐factoring of the linear system involved in the global phase. Experimental results show that our approach provides almost isometric parameterizations and obtains more shape‐preserving results than other state‐of‐the‐art approaches.
Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design
View Paper: https://www.semanticscholar.org/paper/51f39f8e5087432e6af65f490ac55c05e0568232
How researchers see this paper
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In Computational Mechanics
- Meirav Galun
- Shahar Ziv Kovalsky
- Yaron Lipman
- M. Ovsjanikov
- Olga Sorkine-Hornung
- Daniel Cohen-Or
- Leonidas J. Guibas
- Michael M. Bronstein
In Computer Graphics and Computer-Aided Design
- Shahar Ziv Kovalsky
- Meirav Galun
- Yaron Lipman
- Emanuele Rodolà
- Thomas A. Funkhouser
- Michael M. Bronstein
- Leonidas J. Guibas
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