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A New Set of Hexahedral Meshes Local Transformations

Hecht, Frederic, Raphael Kuate, and Timothy Tautges

Proceedings, 17th International Meshing Roundtable, Springer-Verlag, pp.451-466, October 12-15 2008


17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 12-15, 2008

Laboratoire Jacques-Louis Lions, Universit¥e Pierre et Marie Curie,
Sandia National Laboratories, Computational Mechanics and Visualization Department

The modification of hexahedral meshes is difficult to perform since their structure does not allow easy local refinement or un-refinement such that the modification does not go through the boundary. In this paper we prove that the set of hex flipping transformations of Bern et. al. [1] is the only possible local modification on a geometrical hex mesh with less than 5 edges per vertex. We propose a new basis of local transformations that can generate an infinite number of transformations on hex meshes with less than 6 edges per vertex. Those results are a continuation of a previous work [9], on topological modification of hexahedral meshes. We prove that one necessary condition for filling the enclosed volume of a surface quad mesh with compatible hexes is that the number of vertices of that quad mesh with 3 edges should be no less than 8. For quad meshes, we show the equivalence between modifying locally the number of quads on a mesh and the number of its internal vertices.

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