Toughness and Delaunay triangulations

Voronoi Diagrams and Delaunay Triangulations

The Voronoi diagram of a set of sites partitions space into regions one per site the region for a site s consists of all points closer to s than to any other site The dual of the Voronoi diagram the Delaunay triangulation is the unique triangulation so that the circumsphere of every triangle contains no sites in its interior Voronoi diagrams and Delaunay triangulations have been rediscovered or...

Constrained Delaunay Triangulations and Algorithms

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...

Restricted Constrained Delaunay Triangulations

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...

Blocking Delaunay triangulations

Given a set B of n black points in general position, we say that a set of white points W blocks B if in the Delaunay triangulation of [Formula: see text] there is no edge connecting two black points. We give the following bounds for the size of the smallest set W blocking B: (i) [Formula: see text] white points are always sufficient to block a set of n black points, (ii) if B is in convex posit...

Higher Order Delaunay Triangulations