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CIAC

2010

Springer

2010

Springer

Higher order Delaunay triangulations are a generalization of the Delaunay triangulation which provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-k Delaunay if the circumcircle of each triangle of the triangulation contains at most k points. In this paper we study lower and upper bounds on the number of higher order Delaunay triangulations, as well as their expected number for randomly distributed points. We show that arbitrarily large point sets can have a single higher order Delaunay triangulation, even for large orders, whereas for ﬁrst order Delaunay triangulations, the maximum number is 2n−3 . Next we show that uniformly distributed points have an expected number of at least 2ρ1n(1+o(1)) ﬁrst order Delaunay triangulations, where ρ1 is an analytically deﬁned constant (ρ1 ≈ 0.525785), and for k > 1, the expected number of order-k Delaunay triangulations (which are not order-i for any i < k) is at lea...

Related Content

Added |
17 Jul 2010 |

Updated |
17 Jul 2010 |

Type |
Conference |

Year |
2010 |

Where |
CIAC |

Authors |
Dieter Mitsche, Maria Saumell, Rodrigo I. Silveira |

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