The Meccano Method for Automatic Tetrahedral Mesh Generation of Complex Genus-Zero Solids

In this paper we introduce an automatic tetrahedral mesh generator for complex genus-zero solids, based on the novel meccano technique. Our method only demands a surface triangulation of the solid, and a coarse approximation of the solid, called meccano, that is just a cube in this case. The procedure builds a 3-D triangulation of the solid as a deformation of an appropriate tetrahedral mesh of the meccano. For this purpose, the method combines several procedures: an automatic mapping from the meccano boundary to the solid surface, a 3-D local refinement algorithm and a simultaneous mesh untangling and smoothing. A volume parametrization of the genus-zero solid to a cube (meccano) is a direct consequence. The efficiency of the proposed technique is shown with several applications.