WIAS Preprint No. 1530, (2010)

3D boundary recovery by constrained Delaunay tetrahedralization


  • Si, Hang
  • Gärtner, Klaus

2010 Mathematics Subject Classification

  • 52B55 65D18


  • tetrahedral mesh generation, boundary recovery, constrained Delaunay tetrahedralization, Steiner points


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 it 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.

Appeared in

  • Internat. J. Numer. Methods Engrg., 85 (2011) pp. 1341--1364.

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