A Characterization of the Quadrilateral Meshes of a Surface Which Admit a Compatible Hexahedral Mesh of the Enclosed Volume
Mitchell, Scott
, 1996
A popular three-dimensional generation scheme is to start with a quadrilateral mesh of the surface of a volume, and then attempt to fill the interior of the volume with hexahedra, so that the hexaherda touch the surface in exactly the given quadrilaterals. Folklore has maintained that there are many quadrilateral meshes for which no such compatible hexahedral mesh exists. In this paper we give an existence proof which contradicts this folklore. A quadrilateral mesh needs only satisfy some very weak conditions for there to exist a compatible hexahedral mesh. For a volume that is topologically a ball, any quadrilateral mesh composed of an even number of quadrilaterals admits a compatible hexahedral mesh. We extend this to certain non-ball volumes: there is a construction to reduce to the ball case, and we give a necessary condition as well.
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