An Iterative Mesh Untangling Algorithm Using Edge Flip

Abstract

Existing mesh untangling algorithms are unable to untangle highly tangled meshes. In this study, we address this problem by proposing an iterative mesh untangling algorithm using edge flip. Our goal is to produce meshes with no inverted elements and good element qualities when inverted elements with poor element qualities are produced during mesh generation or mesh deformation process. Our proposed algorithm is composed of three steps: first, we iteratively perform edge flip; subsequently, optimizationbased mesh untangling is conducted until all inverted elements are eliminated; finally, we perform mesh smoothing for generating high-quality meshes. Numerical results show that the proposed algorithm is able to successfully generate high-quality meshes with no inverted elements for highly tangled meshes.

Simultaneous Smoothing and Untangling of 2D Meshes Based on Explicit Element Geometric Transformation and Element Stitching

“…Inverted elements should be eliminated before carrying out numerical simulations, since they usually produce invalid solutions [14]. There are many methods for eliminating inverted elements, including remeshing [15], local mesh modification [16], topological transformations [17] and mesh smoothing. Remeshing may not be automatic, especially for models with complex geometries.…”