On Untangled Meshes via Fruchterman Reingold Force Directed Graph Embedding

Abstract

In this paper, we study how to modify a physical, force-directed method based upon the Fruchterman-Reingold (FR) graph layout algorithm so that it can be used for untangling. Specifically, we have chosen Lake_20 Mesh, Lake_35 Mesh and Tri_20258 Mesh for our research work. All these meshes consist of small triangles. The objectives of aesthetic graph layout, such as minimization of edge intersections and near equalization of edge lengths, follow the goals of mesh untangling and generating good quality elements, respectively. We have successfully applied our method to untangle various shapes of triangles i.e. Lake_20, Lake_35 and Tri_20258 finite element meshes.