In this paper, we introduce the fuzzy Voronoi diagram as an extension of the Voronoi diagram. We assume Voronoi sites to be fuzzy points and then define the Voronoi diagram for this kind of sites, then we provide an algorithm for computing this diagram based on Fortune’s algorithm which costs O(n log n) time. Also we introduce the fuzzy Voronoi diagram for a set of fuzzy circles, rather than fu...

Objective Voronoi diagrams are important in many fields in a series of sciences. Network Voronoi diagrams are useful to investigate dominance regions in a grid street system or a radial-circular street system. However, all generators may have different effect. To deal with a network Voronoi diagram with varied functions of generators, it must be worth formulating a power network Voronoi diagram...

The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or partially outside of the domain, but in practice only the parts of the cells inside the domain are ...

This paper describes a series of dynamic update methods that can be applied to a family of Voronoi diagram types, so that changes can be updated incrementally, without the usual recourse to complete reconstruction of their underlying data structure. More efficient incremental update methods are described for the ordinary Voronoi diagram, the farthest-point Voronoi diagram, the order-k Voronoi d...

The farthest line-segment Voronoi diagram shows properties surprisingly different than the farthest point Voronoi diagram: Voronoi regions may be disconnected and they are not characterized by convexhull properties. In this paper we introduce the farthest line-segment hull, a cyclic structure that relates to the farthest line-segment Voronoi diagram similarly to the way an ordinary convex hull ...

Circles are frequently used for modelling the growth of particle aggregates through the Voronoi diagram of circles, that is a special instance of the Johnson-Mehl tessellation. The Voronoi diagram of a set of sites is a decomposition of space into proximal regions. The proximal region of a site is the locus of points closer to that site than to any other one. Voronoi diagrams allow one to answe...

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.

We present structural properties of the farthest line-segment Voronoi diagram in the piecewise linear L∞ and L1 metrics, which are computationally simpler than the standard Euclidean distance and very well suited for VLSI applications. We introduce the farthest line-segment hull, a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram, and is related...

A new generalized Voronoi diagram is defined on the surface of a river with unifonn flow; a point belongs to the territory of a site if and only if a boat starting from the site can reach the point faster than a boat starting from any other site. If the river runs slower than the boat, the Voronoi diagram can be obtained from the ordinary Voronoi diagram by a certain transformation, whereas if ...

We investigate the higher-order Voronoi diagrams of n point sites with respect to the geodesic distance in a simple polygon with h > 0 polygonal holes and c corners. Given a set of n point sites, the korder Voronoi diagram partitions the plane into several regions such that all points in a region share the same k nearest sites. The nearest-site (first-order) geodesic Voronoi diagram has already...