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Anisotropic surface meshing

Authors Cheng, S.W. View this author's profile
Dey, T.K.
Ramos, E.A.
Wenger, R.
Issue Date 2006
Source Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms , 2006, p. 202-211
Summary We study the problem of triangulating a smooth closed implicit surface Σ endowed with a 2D metric tensor that varies over Σ. This is commonly known as the anisotropic surface meshing problem. We extend the 2D metric tensor naturally to 3D and employ the 3D anisotropic Voronoi diagram of a set P of samples on Σ to triangulate Σ. We prove that a restricted dual, Mesh P, is a valid triangulation homeomorphic to Σ under appropriate conditions. We also develop an algorithm for constructing P and Mesh P. In addition to being homeomorphic to Σ, each triangle in Mesh P is well-shaped when measured using the 3D metric tensors of its vertices. Users can set upper bounds on the anisotropic edge lengths and the angles between the surface normals at vertices and the normals of incident triangles (measured both isotropically and anisotropically).
ISBN 978-0-89871-605-4
Rights © ACM 2006. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithm, Miami, Florida, 22-24 January 2006, p. 202-211.
Language English
Format Conference paper
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