Ambient Isotopic Meshing of Implicit Algebraic Surface with Singularities
Computational Geometry
2015-05-13 v1 Graphics
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.
Keywords
Cite
@article{arxiv.0903.3524,
title = {Ambient Isotopic Meshing of Implicit Algebraic Surface with Singularities},
author = {Jin-San Cheng and Xiao-Shan Gao and Jia Li},
journal= {arXiv preprint arXiv:0903.3524},
year = {2015}
}
Comments
34 pages, 17 Postscript figures