Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations

@inproceedings{Shewchuk2000SweepAF,
  title={Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations},
  author={Jonathan Richard Shewchuk},
  booktitle={SCG '00},
  year={2000}
}
  • J. Shewchuk
  • Published in SCG '00 1 May 2000
  • Computer Science
I discuss algorithms for constructing constrained Delaunay triangulations (CDTs) in dimensions higher than two. If the CDT of a set of vertices and constraining simplices exists, it can be constructed in time, where is the number of input vertices and is the number of output -simplices. In practice, the running time is likely to be in all but the most pathological cases. The CDT of a star-shaped polytope can be constructed in time, yielding an efficient way to delete a vertex from a CDT. 
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81 Citations
Highly Influential Citations
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Background Citations
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81 Citations

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An algorithm for obtaining a constrained Delaunay triangulation from a given planar graph using an efficient Žalik’s algorithm, using a plane subdivison, is presented, which is fast and efficient and therefore appropriate for GIS applications.

The Strange Complexity of Constrained Delaunay Triangulation

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Computing the 3D Voronoi Diagram Robustly: An Easy Explanation

  • H. Ledoux
  • Computer Science
    4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)
  • 2007
TLDR
This paper describes a simple 3D Voronoi diagram (and Delaunay tetrahedralization) algorithm, and explains how to ensure that it outputs a correct structure, regardless of the spatial distribution of the points in the input.

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Star splaying can be a fast first step in repairing a high-quality finite element mesh that has lost the Delaunay property after its vertices have moved in response to simulated physical forces.

Incrementally constructing and updating constrained Delaunay tetrahedralizations with finite-precision coordinates

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This thesis proposes several new practical ways to speed-up some of the most important operations in a Delaunay triangulation, including a distribution-sensitive point location algorithm based on the classical Jump & Walk called Keep, Jump, & Walk and a filtering scheme based upon the concept of vertex tolerances.

General-Dimensional Constrained Delaunay and Constrained Regular Triangulations, I: Combinatorial Properties

TLDR
The main contributions are rigorous, theory-tested definitions of CDTs and piecewise linear complexes, a characterization of the combinatorial properties ofCDTs and weighted CDTs, the proof of several optimality properties of CDT when they are used for piecewiselinear interpolation, and a simple and useful condition that guarantees that a domain has a CDT.
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