English

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

R2 v1 2026-06-21T12:42:43.259Z