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...

Voronoi diagrams are a well-studied data structure of proximity information, and although most cases require Ω(n log n) construction time, it is interesting and useful to develop linear-time algorithms for certain Voronoi diagrams. We develop a linear-time algorithm for abstract Voronoi diagrams in a domain where each site has a unique face and no pair of bisectors intersect outside the domain....

Voronoi diagrams are a well-studied data structure of proximity information, and although most cases require Ω(n log n) construction time, it is interesting and useful to develop linear-time algorithms for certain Voronoi diagrams. For example, the Voronoi diagram of points in convex position, and the medial axis and constrained Voronoi diagram of a simple polygon are a tree or forest structure...

Abstract Voronoi diagrams were introduced by R. Klein (1988) as an axiomatic basis of Voronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(n log n) by a randomized algorithm, which is based on Clarkson and Shor’s randomized incremental construction technique (1989). The new algorithm has the following advantages over previous algorithms: l It can handle a much wider cl...

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 many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework...

Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voro...

We present some geometric relationships between the ordinary Voronoi diagram, and the Voronoi diagram in the Laguerre geometry. We derive from these properties an algorithm for the conversion of ordinary Voronoi diagrams into Voronoi diagrams in the Laguerre geometry.