Generation of All-Quadrilateral Meshes Using a Triangular Mesh Generator

Abstract

This paper deals with discretization of 3D surfaces into all-quadrilateral meshes. The focus is laid on using an existing triangular mesh generator based on the Advancing Front Technique subjected to some minor modifications instead of developing a complex strategy for a new quadrilateral mesh generator. The actual discretization is split into three phases. In the first phase, a mixed mesh is created using the augmented triangular mesh generator. This initial mesh could generally contain a large percentage of triangular elements. In the second phase, the initial mesh is subjected to optimization in terms of Laplacian smoothing and topological cleanup. After the second phase, only very low percentage of the triangular elements is present in the mesh. In the third phase, the remaining triangles are eliminated by a one-level refinement applied to the optimized initial mesh. The final mesh is then once more optimized using the Laplacian smoothing. The proposed strategy is capable to produce uniform and graded all-quadrilateral meshes of high quality. The performance of the adopted approach is demonstrated on several examples.