Abstract
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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Hecht, F., Kuate, R., Tautges, T. (2008). A New Set of Hexahedral Meshes Local Transformations. In: Garimella, R.V. (eds) Proceedings of the 17th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87921-3_27
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DOI: https://doi.org/10.1007/978-3-540-87921-3_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87920-6
Online ISBN: 978-3-540-87921-3
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