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A characterization of the quadrilateral meshes of a surface which admit a compatible hexahedral mesh of the enclosed volume

  • Scott A. Mitchell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)

Abstract

A popular three-dimensional mesh 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 hexahedra touch the surface in exactly the given quadrilaterals[24]. 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 need 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.

Keywords

Computational Geometry hexahedral mesh generation existence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Scott A. Mitchell
    • 1
  1. 1.Computational Mechanics and Visualization Dept.Sandia National LaboratoriesAlbuquerqueUSA

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