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Efficiently Hex-Meshing Things with Topology

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...

Optimally Cutting a Surface into a Disk

]. See http://www.cs.uiuc.edu/ jeffe/pubs/schema.html for the most recent version of this paper. Jeff Erickson was partially supported by a Sloan Fellowship, NSF CAREER Award CCR-0093348, and NSF ITR Grant