Abstract
A topological quadrilateral mesh Q of a connected surface in (Formula Prseented.) can be extended to a topological hexahedral mesh of the interior domain (Formula Prseented.) if and only if Q has an even number of quadrilaterals and no odd cycle in Q bounds a surface inside (Formula Prseented.). Moreover, if such a mesh exists, the required number of hexahedra is within a constant factor of the minimum number of tetrahedra in a triangulation of (Formula Prseented.) that respects Q. Finally, if Q is given as a polyhedron in (Formula Prseented.) with quadrilateral facets, a topological hexahedral mesh of the polyhedron can be constructed in polynomial time if such a mesh exists. All our results extend to domains with disconnected boundaries. Our results naturally generalize results of Thurston, Mitchell, and Eppstein for genus-zero and bipartite meshes, for which the odd-cycle criterion is trivial.
Original language | English (US) |
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Pages (from-to) | 427-449 |
Number of pages | 23 |
Journal | Discrete and Computational Geometry |
Volume | 52 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1 2014 |
Keywords
- Computational topology
- Cube complexes
- Homology
- Mesh generation
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics