An Iterative Mesh Untangling Algorithm Using Edge Flip

Jibum Kim

doi:10.1155/2017/2953736

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, optimization-based 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.

Highlights

Geometric domains are often discretized by meshes for partial differential equation- (PDE-) based applications
We propose an iterative mesh untangling and smoothing method using mesh modification methods when inverted elements are produced during mesh generation or mesh deformations
We propose an iterative mesh untangling algorithm using edge flip for highly tangled meshes

Summary

Introduction

Geometric domains are often discretized by meshes for partial differential equation- (PDE-) based applications. Poor quality and inverted elements often occur during mesh generation [1], mesh optimization [2], and mesh deformation [3]. For many scientific applications such as Arbitrary-Lagrangian-Eulerian (ALE) simulations and biomedical applications, geometric domains (i.e., domain boundaries) deform as time varies When these geometric domains deform, the meshes should be updated appropriately such that the deformed meshes have good element qualities with no inverted elements. When huge deformations occur, many poor-quality elements and inverted elements are produced. We perform an optimization-based mesh untangling method to eliminate inverted elements in the mesh. Numerical experiments show that the proposed mesh untangling and smoothing method efficiently eliminates inverted elements in the mesh while maintaining good element qualities in the mesh with huge boundary deformations

Previous Work

Mesh Deformation and Inverted Elements

Proposed Mesh Untangling and Smoothing Method

Numerical Experiments

Findings

Conclusions