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...

Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology an...

This paper proposes a new generalization of the Voronoi diagram. Suppose that restaurants and bookstores are located in a city, and we want to visit both a restaurant and bookstore and return to our house. To each pair of a restaurant and a bookstore, we can assign a region such that a resident in this region can visit the restaurant and bookstore in a round tour that is shorter than that for a...

In a paper that considered arithmetic precision as a limited resource in the design and analysis of algorithms, Liotta, Preparata and Tamassia defined an “implicit Voronoi diagram” supporting logarithmictime proximity queries using predicates of twice the precision of the input and query coordinates. They reported, however, that computing this diagram uses five times the input precision. We def...

We present a real-time algorithm for computing the Voronoi diagram of planar freeform piecewise-spiral curves. The efficiency and robustness of our algorithm is based on a simple topological structure of Voronoi cells for spirals. Using a Möbius transformation, we provide an efficient search for maximal disks. The correct topology of Voronoi diagram is computed by sampling maximal disks systema...

This paper intends to generate the approximate Voronoi diagram in the geodesic metric for some unbiased samples selected from original points. The mesh model of seeds is then constructed on basis of the Voronoi diagram. Rather than constructing the Voronoi diagram for all original points, the proposed strategy is to run around the obstacle that the geodesic distances among neighboring points ar...

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...