Article history: Received 12 May 2009 Received in revised form 3 July 2009 Accepted 3 July 2009 Available online 9 July 2009 Communicated by C.R. Doering PACS: 89.75.Kd 02.50.Ng 02.10.-v

In this paper, we present a novel method for medial axis approximation based on Constrained Centroidal Voronoi Diagram of discrete data (image, volume). The proposed approach is based on the shape boundary subsampling by a clustering approach which generates a Voronoi Diagram well suited for Medial Axis extraction. The resulting Voronoi Diagram is further filtered so as to capture the correct t...

Given a set of point sites in a simple polygon, the geodesic farthest-point Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic metric. We present an O(n log log n+m logm)time algorithm to compute the geodesic farthest-point Voronoi diagram of m point sites in a simple n-gon. This i...

This paper describes a practical algorithm for the construction of the Voronoi diagram of a three dimensional polyhedron using approximate arithmetic. This algorithm is intended to be implemented in oating point arithmetic. The full two-dimensional version and sig-niicant portions of the three-dimensional version have been implemented and tested. The running time 1 of this algorithm is O(npnv l...

We define the spatial constraints and objective function for weight-proportional partitioning of information spaces. We evaluate existing methods in light of these definitions and find that none performs as desired. We then formulate an alternative approach based on an adaptive version of the multiplicatively weighted Voronoi diagram; i.e., the diagram’s weights are computed based on a set of p...

In this work we present a CGAL (Computational Geometry Algorithm Library) implementation of the line segment Voronoi diagram under the L∞ metric, building on top of the existing line segment Voronoi diagram under the Euclidean (L2) metric. CGAL is an open-source collection of geometric algorithms implemented in C++, used in both academia and industry. We also discuss a possible application of t...

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...

We modify the incremental algorithm for computing Voronoi diagrams in the Euclidean metric proposed by Ohya, Iri and Murota 6] in order to obtain an algorithm for computing Voronoi diagrams (resp. Delaunay triangulations) in Man-hattan and Maximum metric, that is rather simply to implement. We generalize the notions of \Voronoi diagram" and \Delaunay triangulation" in such a way that these stru...

1 The farthest-point Voronoi diagram of a set of n sites 2 is a tree with n leaves. We investigate whether arbi3 trary trees can be realized as farthest-point Voronoi di4 agrams. Given an abstract ordered tree T with n leaves 5 and prescribed edge lengths, we produce a set of n sites 6 S in O(n) time such that the farthest-point Voronoi di7 agram of S represents T . We generalize this algorithm...