NDLI: Constrained Delaunay Triangulations and Algorithms

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Constrained Delaunay Triangulations and Algorithms

Content Provider	Semantic Scholar
Author	Si, Hang
Copyright Year	2007
Abstract	Two-dimensional constrained Delaunay triangulations (of a planar straight-line graph) introduced independently by Lee et al. [2] and Chew [1] are well studied structures and can be constructed in optimal time. However, the generalization of such objects to three and higher dimensions is much less discussed in literature. In this talk, we first define a constrained Delaunay triangulation (CDT) of a ddimensional geometric object called piecewise linear system (PLS) for d ≥ 0. Our definition is, in some sense, more general than that of Shewchuk’s [3] since it allows Steiner points (points which are not given in the input). We show several fundamental properties of such objects which are very close to those of Delaunay triangulations. We then propose an algorithm for constructing a CDT of any d-dimensional PLS, and show the correctness of this algorithm. Next we realize this algorithm for constructing CDTs of three-dimensional PLSs. An implementation of this algorithm can be found in the publicly available program TetGen [4]. Finally we discuss the complexity issues of this algorithm together with some examples. References [1] P. L. Chew. Constrained Delaunay triangulation. Algorithmica, 4:97–108, 1989. [2] D. T. Lee and A. K. Lin. Generalized Delaunay triangulations for planar graphs. Discrete and Computational Geometry, 1:201–217, 1986. [3] J. R. Shewchuk. General-dimensional constrained Delaunay and constrained regular triangulations i: Combinatorial properties. To appear in Discrete and Computational Geometry, 2007. [4] H. Si. TetGen. http://tetgen.berlios.de, 2007.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www-sop.inria.fr/geometrica/seminars/0708/0708.HSi.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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