In this paper we describe a generic C++ adaptor, that adapts a 2-dimensional triangulated Delaunay graph and to the corresponding a Voronoi diagram, represented as a doubly connected edge list (DCEL) data structure. Our adaptor has the ability to automatically eliminate, in a consistent manner, degenerate features of the Voronoi diagram, that are artifacts of the requirement that Delaunay graph...

We present an obstacle avoiding path planning method based on a Voronoi diagram. We use a tactical visibility measure to obtain the shortest path length with the lowest local probability to be discovered based on the map topology. A Voronoi-based navigation mesh for finding the shortest smooth path with the lowest visibility along the path is used. The piecewise linear rough path in the Voronoi...

Crowd Sensing is a new business model which allows large number of smart phones to be used not only for exchanging information but also for activities that may have a huge social impact including traffic or road monitoring, urban planning, social networking and environmental monitoring. Here, we present a novel approach for developing a sensing application to collect a specific dataset where re...

The largest empty circle (LEC) problem is defined on a set P and consists of finding the largest circle that contains no points in P and is also centered inside the convex hull of P . The LEC is always centered at either a vertex on the Voronoi diagram for P or on an intersection between a Voronoi edge and the convex hull of P . Thus, finding the LEC consists of constructing a Voronoi diagram a...

Voronoi diagrams are a central topic in Computational Geometry. They can be generalized in many ways. Suppose S is a finite set of geometric objects and there is a notion of Voronoi diagram V or(S) that we want to compute. One approach to designing algorithms for V or(S) is to (1) assume some general properties of S, and (2) describe an abstract algorithm based on the Real RAM model that has so...

Given a tesselation of the plane, defined by a planar straightline graph G, we want to find a minimal set S of points in the plane, such that the Voronoi diagram associated with S ‘fits’ G. This is the Generalized Inverse Voronoi Problem (GIVP), defined in [12] and rediscovered recently in [3]. Here we give an algorithm that solves this problem with a number of points that is linear in the size...

This paper studies the Voronoi diagrams on 2-manifold meshes based on geodesic metric (a.k.a. geodesic Voronoi diagrams or GVDs), which have polyline generators. We show that our general setting leads to situations more complicated than conventional 2D Euclidean Voronoi diagrams as well as point-source based GVDs, since a typical bisector contains line segments, hyperbolic segments and paraboli...

Given a complex polynomial p(z) with at least three distinct roots, we first prove no rational iteration function exists where the basin of attraction of a root coincides with its Voronoi cell. In spite of this negative result, we prove the Voronoi diagram of the roots can be well approximated through a high order sequence of iteration functions, the Basic Family, Bm(z), m ≥ 2. Let θ be a simpl...

Details of algorithms to construct the Voronoi diagrams and medial axes of planars domain bounded by free-form (polynomial or rational) curve segments are presented, based on theoretical foundations given in the rst installment Ramamurthy and Farouki, J. Comput. Appl. Math. (1999) 102 119–141 of this two-part paper. In particular, we focus on key topological and computational issues that arise ...