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Conclusions

In the present paper, an approach for the discretization of 3D domains info fully conforming tetrahedral mesh was proposed. It is based on building first the constrained Delaunay triangulation of the boundary points. The conformity of the mesh with constraining facets is achieved by the a priori boundary recovery process, which should ensure that each constraining facet appears in the intermediate constrained Delaunay triangulation immediately after all its vertices are inserted. The case, when the facet may not appear but can be recovered without delay by a simple topological transformation, is considered too. The boundary points are inserted using the modified Watson's algorithm which prevents constraining facet already present in the intermediate constrained Delaunay triangulation to be removed. A simple criterion, based on empty-sphere property applied to the smallest sphere circumscribed to the facet, is adopted to decide whether a constraining facet appears in the Delaunay triangulation. The actual appearance of inserted boundary facets in the triangulation is achieved by proper ordering of point insertion. This ordering is deduced from the oriented dependency graph which represents the violation of empty-circumsphere property of individual facets and from which all the cyclic dependencies are eliminated using perturbations, safe violations, and insertion of a new tetrahedron using the AFT. The initial boundary conforming constrained Delaunay triangulation is then enriched by inserting additional points in the interior of the domain, while keeping the boundary constraints, to make the size and shape of the tetrahedra compliant with user specifications. The final mesh, from which the tetrahedra outside the computational domain are discarded, is then smoothed using the Laplacian smoothing combined with topological transformations to remove the potential slivers and to improve the overall mesh quality.



Next: Acknowledgments Up: Top Previous: Future Work

Daniel Rypl
2005-11-06