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arXiv · 0903.3524

Ambient Isotopic Meshing of Implicit Algebraic Surface with Singularities

Jin-San Cheng·Xiao-Shan Gao·Jia Li
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Abstract

A complete method is proposed to compute a certified, or ambient isotopic, meshing for an implicit algebraic surface with singularities. By certified, we mean a meshing with correct topology and any given geometric precision. We propose a symbolic-numeric method to compute a certified meshing for the surface inside a box containing singularities and use a modified Plantinga-Vegter marching cube method to compute a certified meshing for the surface inside a box without singularities. Nontrivial examples are given to show the effectiveness of the algorithm. To our knowledge, this is the first method to compute a certified meshing for surfaces with singularities.

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Jin-San Cheng, Xiao-Shan Gao, Jia Li. 2009-03-20. Ambient Isotopic Meshing of Implicit Algebraic Surface with Singularities. https://doi.org/10.1007/978-3-642-04103-7_9

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