Topology modification of hexahedral meshes using atomic dual-based operations

Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.415-423, Sept. 2003

MESHING
RESEARCH
CORNER

12th International Meshing Roundtable
September 14-17, 2003
Santa Fe, New Mexico, U.S.A.

Sandia National Laboratories, Albuquerque, NM., U.S.A.
tjtautg@sandia.gov

University of Wisconsin-Madison, WI., U.S.A.
seknoop@students.wisc.edu

Abstract
Topology modification of hexahedral meshes has been considered difficult due to the propagation of topological modifications non-locally. We address this problem by working in the dual of a hexahedral mesh. We prove several relatively simple combinatorial aspects of hex mesh duals, namely that they are both complexes of simple polytopes as well as simple arrangements of pseudo-hyperplanes. We describe a set of four atomic dual-based hex topology modifications, from which the flipping operations of Bern et. al can be constructed. We also observe several intriguing arrangements and modification operations, which we intend to explore further in the future.

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