ved. Among the five flavors [15] of sequential 2D Delaunay triangulation algorithms, incremental insertion methods (e.g., [8]) are most popular mainly because they are potentially dynamic, simple to implement and easy to be generalized to higher dimensions. However, normally they are not regarded as among the fastest methods. The basic principle of constructing Delaunay triangulation (DT) by in...

This paper presents an algorithm for obtaining a constrained Delaunay triangulation from a given planar graph. The main advantage towards other algorithms is that I use an efficient Žalik’s algorithm, using a plane subdivison for obtaining a Delaunay triangulation. It is used for insertion of points into existing triangulation. The other part of algorithm presents a method for inserting edges, ...

The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code; It is implemented in cg...

We propose a new algorithm that preprocess a set of n disjoint unit disks to be able to compute the Delaunay triangulation in O(n) expected time. Conversely to previous similar results, our algorithm is actually faster than a direct computation in O(n log n) time. Key-words: Delaunay triangulation, uncertainties, randomization This work is partly supported by ANR grant Triangles (ANR-07-BLAN-03...

Some of the first routing algorithms for geographically aware wireless networks used the Delaunay triangulation among the network’s nodes as the underlying connectivity graph [4]. These solutions were considered impractical, however, because in general the Delaunay triangulation may contain arbitrarily long edges, and because calculating the Delaunay triangulation generally requires a global vi...

A b s t r a c t . Triangle is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunay refinement algorithm for quality mesh generation. Several implementation issues are discussed, including the choice of triangulation algorithms and data structures, the effect of several variants of the Delaunay refinement algorithm on mesh quality, and the use of a...

Several localized routing protocols [1] guarantee the delivery of the packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we more accurately model the network as a unit-disk graph UDG , in which a link in between two nodes exist o...