The meccano method for automatic volume parametrization of solids

Abstract

In this paper, we present significant advances of the novel meccano technique for simultaneously constructing adaptive tetrahedral meshes of 3-D complex solids and their volume parametrization. Specifically, we will consider a solid whose boundary is a surface of genus zero. In this particular case, the automatic procedure is defined by a surface triangulation of the solid, a simple meccano composed by one cube and a tolerance that fixes the desired approximation of the solid surface. The main idea is based on an automatic mapping from the cube faces to the solid surface, a 3-D local refinement algorithm and a simultaneous mesh untangling and smoothing procedure. Although the initial surface triangulation can be a poor quality mesh, the meccano technique constructs high quality surface and volume adaptive meshes. Several examples show the efficiency of the proposed technique. Future possibilities of the meccano method for meshing a complex solid, whose boundary is a surface of genus greater than zero, are commented.