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Aspects of three‐dimensional constrained Delaunay meshing
Author(s) -
Wright Julian P.,
Jack Alan G.
Publication year - 1994
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.1620371105
Subject(s) - delaunay triangulation , node (physics) , polyhedron , chew's second algorithm , tetrahedron , constrained delaunay triangulation , ruppert's algorithm , computer science , mesh generation , polygon mesh , algorithm , topology (electrical circuits) , regular polygon , bowyer–watson algorithm , finite element method , mathematics , combinatorics , geometry , structural engineering , engineering , computer graphics (images)
Presented in this paper are the theoretical aspects of node addition to a non‐convex, multiboundary mesh of tetrahedral elements as used in finite element modelling. The method used is derived from Watson 1 and Shenton and Cendes 2 and is extended to deal with node addition on inter‐material boundaries. Several situations are identified that result in an illegal insertion polyhedron (IP), these could be caused by the ‘constrained’ nature of the mesh, adjacent objects with different material properties, or degenerate node configurations. A new Delaunay algorithm is described that checks for illegal cases of the IP and then corrects them, this checking relies on the consistent ordering of the element nodes. It is shown that a particular type of illegal IP can easily be identified and corrected using this technique. The Delaunay algorithm is then applied to automatic mesh generation, and modification to the basic Delaunay algorithm is described so that previously meshed edges and faces of the current object being meshed are not deleted during the addition of subsequent nodes. This ‘protection’ method only becomes viable by recognizing the node ordering sense of the IP faces.