NDLI: Efficiently Hex-Meshing Things with Topology

Content Provider	Springer Nature Link
Author	Erickson, Jeff
Copyright Year	2014
Abstract	A topological quadrilateral mesh $$Q$$ of a connected surface in $$\mathbb {R}^3$$ can be extended to a topological hexahedral mesh of the interior domain $$\varOmega $$ if and only if $$Q$$ has an even number of quadrilaterals and no odd cycle in $$Q$$ bounds a surface inside $$\varOmega $$ . 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 $$\varOmega $$ that respects $$Q$$ . Finally, if $$Q$$ is given as a polyhedron in $$\mathbb {R}^3$$ 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.
Ending Page	449
Page Count	23
Starting Page	427
File Format	PDF
ISSN	01795376
e-ISSN	14320444
Journal	Discrete & Computational Geometry
Issue Number	3
Volume Number	52
Language	English
Publisher	Springer US
Publisher Date	2014-09-03
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computational Mathematics and Numerical Analysis Computer graphics; computational geometry Mesh generation and refinement Homology Cube complexes General topology of complexes Combinatorics Computational topology Mesh generation
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology

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