Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities

摘要

A complete method is proposed to compute an ambient isotopic meshing for an implicit algebraic surface with singularities. By ambient isotopic, we mean a meshing with correct topology and any given precision. We use symbolic computation to guarantee the correctness and use numerical computation whenever possible to enhance the efficiency. Nontrivial examples are given to show the effectiveness of the algorithm.