A new unstructured surface mesh generation scheme for arbitrary three-dimensional domains

摘要

The generation of an unstructured grid on a surface, prior to a volume grid (i.e., tetrahedral mesh), is one of the most difficult and yet important aspects of mesh generation in three dimensions. The approach usually followed to generate grids on surfaces consists of representing the geometry in parametric coordinates. This is of particular importance, since the mesh generation on a surface involves the same techniques developed for two-dimensional problems. The present paper proposes an algorithm for constructing Constrained Delaunay triangulations of three-dimensional domains in this usual way. The geometry description is based on a set of planar polygons of an arbitrary orientation in space. The shared sides of these polygons are carefully manipulated to satisfy the periodicity constraints. The appropriate choice of the discretization sequence of these polygons requires special attention. A smoothing technique for ensuring good geometrical quality in the final mesh is also applied. The presented results show that the algorithm is a simple and powerful method to generate unstructured surface meshes with a very low computational cost.