17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 1215, 2008
Laboratoire JacquesLouis Lions, UniversitĀ„e Pierre et Marie Curie
hecht@ann.jussieu.fr,kuate@ann.jussieu.fr
Sandia National Laboratories, Computational Mechanics and Visualization Department
tautges@mcs.anl.gov
Abstract
The modification of hexahedral meshes is difficult to perform since their
structure does not allow easy local refinement or unrefinement 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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