The meccano technique is a very efficient adaptive tetrahedral mesh generator for solids whose boundary is a surface of genus zero. We remark that the method requires minimum user intervention and has a low computational cost. The proce-dure is fully automatic and it is only defined by a surface triangulation of the solid, a cube and a tolerance that fixes the desired approximation of the solid surface.
A crucial consequence of the new mesh generation technique is the resulting discrete parametrization of a complex volume (solid) to a simple cube (meccano).
a
c d
b
Fig. 3 Cross sections of the cube (a) and the Bone tetrahedral mesh before (b) and after (c) the application of the mesh optimization procedure. (d) Resulting tetrahedral mesh of the Bone obtained by the meccano method
13 The Meccano Method for Automatic Volume Parametrization of Solids 165
We have introduced an automatic partition of the given solid surface triangula-tion for fixing an admissible mapping between the cube faces and the solid surface patches, such that each cube face is the parametric space of its corresponding patch.
The mesh generation technique is based on sub-processes (subdivision, mapping, optimization) which are not in themselves new, but the overall integration using a simple shape as starting point is an original contribution of the method and has some obvious performance advantages. Another interesting property of the new mesh generation strategy is that it automatically achieves a good mesh adaption to the geometrical characteristics of the domain. In addition, the quality of the resulting meshes is high.
The main ideas presented in this paper can be applied for constructing tetrahe-dral or hexahetetrahe-dral meshes of complex solids. In future works, the meccano tech-nique can be extended for meshing a complex solid whose boundary is a surface of genus greater than zero. In this case, the meccano can be a polycube or constructed by polyhedral pieces with compatible connections. At present, the user has to define the meccano associated to the solid, but we are implementing a special CAD package for more general input solid.
Acknowledgements This work has been partially supported by the Spanish Government, “Secre-tarı´a de Estado de Universidades e Investigacio´n”, “Ministerio de Ciencia e Innovacio´n”, and FEDER, grant contract: CGL2008-06003-C03.
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