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An Approach for Delaunay Tetrahedralization of Bodies with Curved Boundaries

Borovikov, Sergey N., Igor A. Kryukov, and Igor E. Ivanov

Proceedings, 14th International Meshing Roundtable, Springer-Verlag, pp.221-238, September 11-14 2005


14th International Meshing Roundtable
San Diego, CA, USA
September 11-14, 2005

Sergey N. Borovikov and Igor E. Ivanov
Moscow Aviation Institute (State Technical University), Moscow, Russia

Igor A. Kryukov
Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

Problem of tetrahedral meshing of three-dimensional domains whose boundaries are curved surfaces is wide open. Traditional approach consists in an approximation of curved boundaries by piecewise linear boundaries before mesh generation. As the result mesh quality may deteriorate. This paper presents a technique for Delaunay-based tetrahedralization in which a set of constrained facets is formed dynamically during face recovery and mechanisms for mutual retriangulation of the curved faces and the tetrahedralization are suggested. The proposed algorithm is constructed in such a way that a facet that was once added in the set of constrained facets is never split into small triangles. It allows retaining the high quality of surface mesh in the tetrahedralization, because during boundary recovery the surface mesh on the curved faces and the tetrahedralization are refined conjointly.

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