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Efficiently Hex-Meshing Things with Topology
Jeff Erickson
Department of Computer Science
3 Submitted to Discrete & Computational Geometry
4 Revised and resubmitted
5 Abstract
6 A topological quadrilateral mesh Q of a connected surface in R3 can be extended to a
7 topological hexahedral mesh of the interior domain Ω if and only if Q has an even number
8 of quadrilaterals and no odd cycle in Q bounds a surface inside Ω. Moreover, if such a mesh
9 exists, the required number of hexahedra is within a constant factor of the minimum number
10 of tetrahedra in a triangulation of Ω that respects Q. Finally, if Q is given as a polyhedron
11 in R3 with quadrilateral facets, a topological hexahedral mesh of the polyhedron can be
12 constructed in polynomial time if such a mesh exists. All our results extend to domains with
13 disconnected boundaries. Our results naturally generalize results of Thurston, Mitchell, and
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