In this paper we address the L∞ Voronoi diagram of polygonal objects and present applications in VLSI layout and manufacturing. We show that in L∞ the Voronoi diagram of segments consists only of straight line segments and is thus much simpler to compute than its Euclidean counterpart. Moreover, it has a natural interpretation. In applications where Euclidean precision is not particularly impor...

This paper introduces the Buffered Input Cell as a reciprocal collision avoidance method for multiple vehicles with high-order linear dynamics, extending recently proposed methods based on the Buffered Voronoi Cell [3] and generalized Voronoi diagrams [1]. We prove that if each vehicle’s control input remains in its Buffered Input Cell at each time step, collisions will be avoided indefinitely....

The concept of convex polygon-offset distance function was introduced in 2001 by Barequet, Dickerson, and Goodrich. Using this notion of point-to-point distance, they showed how to compute the corresponding nearestand farthest-site Voronoi diagram for a set of points. In this paper we generalize the polygon-offset distance function to be from a point to any convex object with respect to an m-si...

A Voronoi diagram of a set of n sites partitions a finite set of m points into regions of different areas, called the capacities of the sites. In this paper we are interested in Voronoi diagrams in which the capacities are given as constraints. We compute such capacity-constrained Voronoi diagrams in finite spaces by starting with an arbitrary partition that fulfills the capacity constraint wit...

For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain. 1991 Mathematics Subject classification: primary 52C07; secondary 11H55 An n-dimensional lattice determines two normal partitions of the ...

We present a new skeletonization algorithm well suited for the problem of handprinted character recognition. Our approach employs a novel algorithm for computing the Voronoi diagram of a polygon with holes. We show that Voronoi skeletons can serve as eecient shape descriptors because they preserve connectivity and Euclidean metrics. Compared to traditional skeletonization techniques, we suggest...

A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construct...

Abstract Voronoi diagrams were introduced by R . Klein [Kle89b, Kle88a, Kle88b] as an axiomatic basis ofVoronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(nlogn) by a randomized algorithm, which is based on Clarkson and Shor's randomized incremental construction technique [CS89]. The new algorithm has the following advantages over previous algorithms: • It can handle...

The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult problem in a practical way, we introduce the discrete Riemannian Voronoi diagram, a discrete structure that approximates the Riemannian Voronoi diagram. This struc...

This paper revisits the k-nearest-neighbor (k-NN) Voronoi diagram and presents the first output-sensitive paradigm for its construction. It introduces the k-NN Delaunay graph, which corresponds to the graph theoretic dual of the k-NN Voronoi diagram, and uses it as a base to directly compute the k-NN Voronoi diagram in R. In the L1, L∞ metrics this results in O((n + m) log n) time algorithm, us...