This work presents an algorithm that given a generalized planar graph obtains its constrained Delaunay triangulation (CDT). The proposed method, which follows the general approach of [3], works incrementally based on two improved procedures. The first improvement gives a procedure that inserts a new point in a CDT; the second one is an algorithm that enforces a new constraining edge in a CDT. I...

Given a set of points and a set of prototypes representing them, how to create a graph of the prototypes whose topology accounts for that of the points? This problem had not yet been explored in the framework of statistical learning theory. In this work, we propose a generative model based on the Delaunay graph of the prototypes and the ExpectationMaximization algorithm to learn the parameters....

In the context of robust computational geometry we focus on the problem of computing and checking Gabriel graphs with algorithms that are not aaected by degenaracies and have low arithmetic demand. A simple and practical linear-time algorithm is presented that constructs the Gabriel Graph of a nite point set on the plane from its Delaunay diagram. The degree of the algorithm, i.e. a measure of ...

This paper presents in detail how the techniques described in my previous work [Kallmann et al., 2003] can be used for efficiently computing collision-free paths in a triangulated planar environment. The method is based on a dynamic Constrained Delaunay Triangulation (CDT) where constraints are the obstacles in the planar environment. The main advantage of relying on a triangulated domain is th...

We propose the triangulation axis as an alternative skeletal structure for a simple polygon P . This axis is a straight-line tree that can be interpreted as an anisotropic medial axis of P , where inscribed disks are line segments or triangles. The underlying triangulation that specifies the anisotropy can be varied, to adapt the axis so as to reflect predominant geometrical and topological fea...

We present new graph-theoretical conditions for polyhedra of inscribable type and Delaunay triangulations. We establish several sufficient conditions of the following general form: if a polyhedron has a sufficiently rich collection of Hamiltonian subgraphs, then it is of inscribable type. These results have several consequences: • All 4-connected polyhedra are of inscribable type. • All simplic...

This paper presents a modification for robust minutiae based fingerprint verification methods that use Delaunay triangulations. The purpose of this modification is to decrease the number of comparison operations and the error rates within the matching process, by doing a full analysis of the Delaunay triangles. From this full analysis, a modified method was proposed. The identified minutiae rep...

Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known for random networks in planar domains. In this paper, we obtain upper and lower bounds that hold with parametric probability in any dimension, for points dist...

We rst describe a multiresolutional discretization scheme for the boundary of a planar connected shape, by means of the Haar wavelet transform. This scheme yields a hierarchy of polygons of increasing complexity that adaptively captures the shape's boundary at increasing resolutions. Next, we present a new morphological transform called the Chordal Axis Transform for planar shapes that leads to...