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The boundary recovery and sliver elimination algorithms of three‐dimensional constrained Delaunay triangulation
Author(s) -
Guan Zhenqun,
Song Chao,
Gu Yuanxian
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1707
Subject(s) - delaunay triangulation , constrained delaunay triangulation , boundary (topology) , algorithm , ruppert's algorithm , bowyer–watson algorithm , triangulation , smoothing , pitteway triangulation , topology (electrical circuits) , chew's second algorithm , mesh generation , mathematics , laplacian smoothing , finite element method , computer science , mathematical optimization , geometry , computer vision , engineering , combinatorics , mathematical analysis , structural engineering
A boundary recovery and sliver elimination algorithm of the three‐dimensional constrained Delaunay triangulation is proposed for finite element mesh generation. The boundary recovery algorithm includes two main procedures: geometrical recovery procedure and topological recovery procedure. Combining the advantages of the edges/faces swappings algorithm and edges/faces splittings algorithm presented respectively by George and Weatherill, the geometrical recovery procedure can recover the missing boundaries and guarantee the geometry conformity by introducing fewer Steiner points. The topological recovery procedure includes two phases: ‘dressing wound’ and smoothing, which will overcome topology inconsistency between 3D domain boundary triangles and the volume mesh. In order to solve the problem of sliver elements in the three‐dimensional Delaunay triangulation, a method named sliver decomposition is proposed. By extending the algorithm proposed by Canvendish, the presented method deals with sliver elements by using local decomposition or mergence operation. In this way, sliver elements could be eliminated thoroughly and the mesh quality could be improved in great deal. Copyright © 2006 John Wiley & Sons, Ltd.