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...

We consider the Euclidean Voronoi diagram for a set of n parallel halflines in R. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, a simple plane-sweep algorithm is given that computes the Voronoi diagram for parallel halflines at logarithmic cost per face.

For a set P of n points in Rd, we define a new type of space decomposition. The new diagram provides an ε-approximation to the distance function associated with the Voronoi diagram of P , while being of near linear size, for d ≥ 2. This contrasts with the standard Voronoi diagram that has Ω ( ndd/2e ) complexity in the worst case.

This paper considers the eeect of site perturbations on Voronoi diagrams, where the sites are points in the plane. Given a bound on the distance that any site may move, we ask which pairs of Voronoi neighbors may become non-neighbors and which are guaranteed to remain neighbors. A pair of the second kind is called stable. The paper shows necessary and suucient conditions for stability. Algorith...

Euclidean Voronoi diagram of spheres in 3-dimensional space has not been explored as much as it deserves even though it has significant potential impacts on diverse applications in both science and engineering. In addition, studies on the data structure for its topology have not been reported yet. Presented in this paper is the topological representation for Euclidean Voronoi diagram of spheres...

A Voronoi diagram of image elements provides an intuitive and appealing definition of proximity, which has been suggested as an effective tool for the description of relations among the neighboring objects in a digital image. In this paper, an implementation algorithm based on direct calculation of the Freeman code of expanded contours is proposed for generating area Voronoi diagram of connecte...

In this paper we study the Voronoi diagram of lines in R. The Voronoi diagram of three lines in general position was studied in [14]. In this paper we complete this work by presenting a complete characterization of the Voronoi diagram of three arbitrary lines in R. As in the general case, we prove that the arcs of trisectors are always monotonic in some direction and we show how to separate the...

In this paper, we present an obstacle avoiding path planning method based on Voronoi diagram and composite Bezier curve algorithm which obtains the shortest path length. In our algorithm, a Voronoi diagram is constructed according to the global environment. The piecewise linear rough path in the Voronoi diagram which keeps away from the obstacles is obtained by performing Dijkstra’s shortest pa...

We extend the Voronoi diagram framework to compute the critical area of a circuit layout [15, 12, 16, 13, 14] with the ability to accurately compute critical area for via-blocks on via and contact layers in the presence of multilayer loops, redundant vias, and redundant interconnects. Critical area is a measure reflecting the sensitivity of a VLSI design to random defects during IC manufacturin...

Voronoi diagram on the earth surface is a powerful tool to study spatial proximity at continental or global scale. However, its computation remains challenging because geospatial features have complex shapes. This paper presents a raster-based algorithm to generate Voronoi diagrams on earth's surface. The algorithm approximates the exact point-to-point geographical distances using the cell-to-c...