The Automatic Meccano Method to Mesh Complex Solids

In this paper, we present significant advances of the novel meccano technique to construct adaptive tetrahedral meshes of 3-D complex solids. Specifically, we will consider a solid whose boundary is a surface of genus 0, i.e. a surface that is homeomorphic to the surface of a sphere. 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. A crucial consequence of the new mesh generation technique is the resulting discrete parametrization of a complex volume (solid) to a simple cube (meccano). 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.