TY - GEN

T1 - A practical delaunay meshing algorithm for a large class of domains

AU - Cheng, Siu Wing

AU - Dey, Tamal K.

AU - Levine, Joshua A.

PY - 2008

Y1 - 2008

N2 - Recently a Delaunay refinement algorithm has been proposed that can mesh domains as general as piecewise smooth complexes [7]. This class includes polyhedra, smooth and piecewise smooth surfaces, volumes enclosed by them, and above all non-manifolds. In contrast to previous approaches, the algorithm does not impose any restriction on the input angles. Although this algorithm has a provable guarantee about topology, certain steps are too expensive to make it practical. In this paper we introduce a novel modification of the algorithm to make it im-plementable in practice. In particular, we replace four tests of the original algorithm with only a single test that is easy to implement. The algorithm has the following guarantees. The output mesh restricted to each manifold element in the complex is a manifold with proper incidence relations. More importantly, with increasing level of refinement which can be controlled by an input parameter, the output mesh becomes homeomorphic to the input while preserving all input features. Implementation results on a disparate array of input domains are presented to corroborate our claims.

AB - Recently a Delaunay refinement algorithm has been proposed that can mesh domains as general as piecewise smooth complexes [7]. This class includes polyhedra, smooth and piecewise smooth surfaces, volumes enclosed by them, and above all non-manifolds. In contrast to previous approaches, the algorithm does not impose any restriction on the input angles. Although this algorithm has a provable guarantee about topology, certain steps are too expensive to make it practical. In this paper we introduce a novel modification of the algorithm to make it im-plementable in practice. In particular, we replace four tests of the original algorithm with only a single test that is easy to implement. The algorithm has the following guarantees. The output mesh restricted to each manifold element in the complex is a manifold with proper incidence relations. More importantly, with increasing level of refinement which can be controlled by an input parameter, the output mesh becomes homeomorphic to the input while preserving all input features. Implementation results on a disparate array of input domains are presented to corroborate our claims.

UR - http://www.scopus.com/inward/record.url?scp=84878201130&partnerID=8YFLogxK

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U2 - 10.1007/978-3-540-75103-8_27

DO - 10.1007/978-3-540-75103-8_27

M3 - Conference contribution

AN - SCOPUS:84878201130

SN - 9783540751021

T3 - Proceedings of the 16th International Meshing Roundtable, IMR 2007

SP - 477

EP - 494

BT - Proceedings of the 16th International Meshing Roundtable, IMR 2007

T2 - 16th International Meshing Roundtable, IMR 2007

Y2 - 14 October 2007 through 17 October 2007

ER -