Updating and Constructing Constrained Delaunay and Constrained Regular Triangulations by Flips

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Updating and Constructing Constrained Delaunay and Constrained Regular Triangulations by Flips (2003)

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by Jonathan Richard Shewchuk

Venue:	Proc. Symp. Computational Geometry
Citations:	13 - 2 self

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@INPROCEEDINGS{Shewchuk03updatingand,
    author = {Jonathan Richard Shewchuk},
    title = {Updating and Constructing Constrained Delaunay and Constrained Regular Triangulations by Flips},
    booktitle = {Proc. Symp. Computational Geometry},
    year = {2003},
    pages = {181--190},
    publisher = {ACM Press}
}

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Abstract

I discuss algorithms based on bistellar flips for inserting and deleting constraining (d − 1)-facets in d-dimensional constrained Delaunay triangulations (CDTs) and weighted CDTs, also known as constrained regular triangulations. The facet insertion algorithm is likely to outperform other known algorithms on most inputs. The facet deletion algorithm is the first proposed for d> 2, short of recomputing the CDT from scratch. An incremental facet insertion algorithm that begins with an unconstrained Delaunay triangulation can construct the CDT of a ridge-protected piecewise linear log nv) time. Hence, in odd dimensions, CDT construction by incremental facet insertion is within a factor of log nv of worst-case optimal. Perhaps the most important feature of these algorithms is that they are relatively easy to implement. complex with nv vertices in O(n ⌊d/2⌋+1 v

Keyphrases

constrained regular triangulation constructing constrained delaunay d-dimensional constrained delaunay triangulation cdt construction weighted cdts important feature facet deletion algorithm nv vertex incremental facet insertion algorithm facet insertion algorithm incremental facet insertion odd dimension log nv bistellar flip unconstrained delaunay triangulation worst-case optimal ridge-protected piecewise linear log nv

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