General-Dimensional Constrained Delaunay and Constrained Regular Triangulations, I: Combinatorial Properties
نویسندگان
چکیده
منابع مشابه
General-Dimensional Constrained Delaunay and Constrained Regular Triangulations, I: Combinatorial Properties
Two-dimensional constrained Delaunay triangulations are geometric structures that are popular for interpolation and mesh generation because they respect the shapes of user-specified domains, they have “nicely shaped” triangles that optimize several criteria, and they are easy to construct and update. The present work generalizes constrained Delaunay triangulations (CDTs) to higher dimensions, a...
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We introduce the restricted constrained Delaunay triangulation (restricted CDT). The restricted CDT generalizes the restricted Delaunay triangulation, allowing us to define a triangulation of a surface that includes a set of constraining segments. Under certain sampling conditions, the restricted CDT includes every constrained segment and suggests an algorithm that produces a triangulation of t...
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Two-dimensional constrained Delaunay triangulations (of a planar straight-linegraph) introduced independently by Lee et al. [2] and Chew [1] are well studied struc-tures and can be constructed in optimal time. However, the generalization of suchobjects to three and higher dimensions is much less discussed in literature.In this talk, we first define a constrained Delaunay tri...
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We extend the notion of higher-order Delaunay triangulations to constrained higherorder Delaunay triangulations and provide various results. We can determine the order k of a given triangulation in O(min(nk log n log k, n log n)) time. We show that the completion of a set of useful order-k Delaunay edges may have order 2k − 2, which is worst-case optimal. We give an algorithm for the lowest-ord...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-006-1236-0