3D boundary recovery by constrained Delaunay tetrahedralization

• Published in: International journal for numerical methods in engineering Vol. 85; no. 11; pp. 1341 - 1364
• Main Authors: Si, H., Gärtner, K.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 18.03.2011; Wiley
• Subjects: Algorithms; Boundaries; boundary recovery; constrained Delaunay tetrahedralization; Constraints; Copyrights; Exact sciences and technology; Mathematical analysis; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Recovery; Sciences and techniques of general use; Segments; Steiner points; tetrahedral mesh generation; Three dimensional; Performance evaluation; Constraint; Tetrahedral shape; Delaunay triangulation; Automatic mesh generation; Modeling; Computational geometry; constrained Delaunay tetrahedralization; Algorithm complexity; boundary recovery; tetrahedral mesh generation; Steiner system; Mesh generation; Steiner points
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.3016

Three‐dimensional boundary recovery is a fundamental problem in mesh generation. In this paper, we propose a practical algorithm for solving this problem. Our algorithm is based on the construction of a constrained Delaunay tetrahedralization (CDT) for a set of constraints (segments and facets). The algorithm adds additional points (so‐called Steiner points) on segments only. The Steiner points are chosen in such a way that the resulting subsegments are Delaunay and their lengths are not unnecessarily short. It is theoretically guaranteed that the facets can be recovered without using Steiner points. The complexity of this algorithm is analyzed. The proposed algorithm has been implemented. Its performance is reported through various application examples. Copyright © 2010 John Wiley & Sons, Ltd.