Several studies have exploited the properties of Voronoi diagrams to improve variations of the nearest neighbor search on stored datasets. However, the significance of Voronoi diagrams and their basic building blocks, Voronoi cells, has been neglected when the geometry data is incrementally becoming available as a data stream. In this paper, we study the problem of Voronoi cell computation for ...

We address the problem of computing critical area for open faults in a circuit layout in the presence of multilayer loops and redundant interconnects. The extraction of critical area is a fundamental problem in VLSI yield prediction. We first model the problem as a graph problem and then we solve it efficiently by exploiting its geometric nature. We introduce the open-fault Voronoi diagram of p...

Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems ...

Given a set of spheres in 3D, constructing its Voronoi diagram in Euclidean distance metric is not easy at all even though many mathematical properties of its structure are known. This Voronoi diagram has been known for many important applications from science and engineering. In this paper, we characterize the Voronoi diagram of spheres in three-dimensional Euclidean space, which is also known...

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...

We study the Hausdorff Voronoi diagram of a set S of polygonal objects in the plane, a generalization of Voronoi diagrams based on the maximum distance of a point from a polygon, and show that it is equivalent to the Voronoi diagram of S under the Hausdorff distance function. We investigate the structural and combinatorial properties of the Hausdorff Voronoi diagram and give a divide and conque...

Despite its important applications in various disciplines in science and engineering, the Euclidean Voronoi diagram for spheres, also known as an additively weighted Voronoi diagram, in 3D space has not been studied as much as it deserves. In this paper, we present an algorithm to compute the Euclidean Voronoi diagram for 3D spheres with different radii. The presented algorithm follows Voronoi ...

We present linear-time algorithms to construct tree-structured Voronoi diagrams, after the sequence of their regions at infinity or along a given boundary is known. We focus on Voronoi diagrams of line segments, including the farthest-segment Voronoi diagram, the order-(k+1) subdivision within a given order-k Voronoi region, and deleting a segment from a nearest-neighbor diagram. Although tree-...

Voronoi diagrams are a fundamental structure used in many areas of science. For a given set of objects, called sites, the Voronoi diagram separates the plane into regions, such that points belonging to the same region have got the same nearest site. This definition clearly depends on the type of given objects, they may be points, line segments, polygons, etc. and the distance measure used. To f...