We present an algorithm for fast computation of discrete generalized Voronoi diagrams. Given a set of geometric primitives, and a distance metric, our algorithm efficiently computes the Voronoi diagram along a uniform grid by evaluating distance fields. We use a multipass approach and divide the computation into intervals along each dimension. We present an efficient culling algorithm to reduce...

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...

In this paper, we present a Voronoi based algorithm for closed curve reconstruction and medial axis approximation from planar points. In principle, the algorithm estimates one of the poles (farthest Voronoi vertices of a Voronoi cell) and hence the normals at each sample point by drawing an analogy between a residential water distribution system and Voronoi diagram of input samples. The algorit...

in this paper, a new online robot motion planner is developed for systematically exploring unknown environâ¬ments by intelligent mobile robots in real-time applications. the algorithm takes advantage of sensory data to find an obstacle-free start-to-goal path. it does so by online calculation of the generalized voronoi graph (gvg) of the free space, and utilizing a combination of depth-first an...

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define various variants of Voronoi diagrams depending on the class of objects, the distance function and the embedding space. In this paper, we investigate a framewo...