A simple unstructured tetrahedral mesh generation algorithm for complex geometries

This paper describes the logic of a dynamic algorithm for a general 3D tetrahedrization of an arbitrarily prescribed geometry. The algorithm requires the minimal surface information. The solid modelling of the 3D objects needs not to be given in full explicit connectivity definitions of the surface triangles. The generated tetrahedrons have empty circumspheres which are the indication of the Delaunay property. A new automatic node replacement scheme reflecting the initial surface nodal spacings is developed. The successive refinement scheme results in such a point distribution that the algorithm does not require any surface conforming checks to avoid penetrated surface boundaries and overlapped tetrahedrons. The surface triangles become a direct consequence of interior tetrahedrization. The rules of the generation algorithm are simple to understand and to program. Some of the existing methods in the literature and the effectiveness of the geometric searching strategies are discussed in the context.