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Boundary recovery after 3D Delaunay tetrahedralization without adding extra nodes
Author(s) -
Liu Jianfei,
Chen Bin,
Chen Yongqiang
Publication year - 2007
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.2044
Subject(s) - boundary (topology) , delaunay triangulation , computer science , packing problems , transformation (genetics) , sizing , mathematical optimization , constrained delaunay triangulation , polyhedron , algorithm , topology (electrical circuits) , mathematics , geometry , combinatorics , mathematical analysis , art , biochemistry , chemistry , visual arts , gene
In this paper, we investigate boundary recovery, the problem that has troubled researchers ever since Delaunay‐based methods were applied to generate mesh. There are a number of algorithms for boundary recovery already and most of them depend heavily on adding extra nodes. In this paper, we make an effort to seek a method to recover boundaries without using extra nodes. It was noted that some previous algorithms imposed artificial boundary constraints on a meshing problem at the recovering stage; we first try to discard these artificial constraints and thus make things easier. Then a new method is proposed by which the boundaries can be recovered by means of two operations: (1) creating a segment in the mesh and (2) removing a segment from the mesh. Both operations are special cases of a general local transformation called small polyhedron reconnection operation. The method works well when coupled with the sphere‐packing method proposed by the first author. If the mesh sizing function is suitable, a good configuration of nodes will be created accordingly by the sphere‐packing method and the boundary can be recovered by the local transformation presented here without inserting extra nodes. Copyright © 2007 John Wiley & Sons, Ltd.