We present a novel and robust algorithm for triangulating point clouds in R. It is based on a highly adaptive hexagonal subdivision scheme of the input domain. That hexagon mesh has a dual triangular mesh with the following properties: • any angle of any triangle lies in the range between 43.9◦ and 90◦, • the aspect ratio of triangles is bound to 1.20787, • the triangulation has the Delaunay pr...

We study a problem about shortest paths in Delaunay triangulations. Given two nodes s, t in the Delaunay triangulation of a point set P , we look for a new point p that can be added, such that the shortest path from s to t, in the Delaunay triangulation of P ∪ {p}, improves as much as possible. We study several properties of the problem, and give efficient algorithms to find such point when the...

Recently, application-layer multicast has emerged as an attempt to support group applications without the need for a network-layer multicast protocol, such as IP multicast. In application-layer multicast, applications arrange themselves as a logical overlay network and transfer data within the overlay network. In this paper, Delaunay triangulations are investigated as an overlay network topolog...

The paper deals with the parallelization of Delaunay triangulation algorithms, giving more emphasis to pratical issues and implementation than to theoretical complexity. Two parallel implementations are presented. The first one is built on DeWall, an E triangulator based on an original interpretation of the divide & conquer paradigm. The second is based on an incremental construction algorithm....

In this communication we propose an initial set of 2D Delaunay triangulation benchmarks for checking the correctness of algorithms and discovering possible flaws. A tool for verification of the generated triangulation is provided. The tool reports typical errors like the existence of unused points, missing edges, non-Delaunay triangles or degenerated triangles. While the tool has been primarily...

Given a set S of disjoint line segments in the plane, which we call sites, a segment triangulation of S is a partition of the convex hull of S into sites, edges, and faces. The set of faces is a maximal set of disjoint triangles such that the vertices of each triangle are on three distinct sites. The segment Delaunay triangulation of S is the segment triangulation of S whose faces are inscribab...