We show that the Voronoi diagram of a nite sequence of points in the plane which gives sorted order of the points with respect to two perpendicular directions can be computed in linear time. In contrast, we observe that the problem of computing the Voronoi diagram of a nite sequence of points in the plane which gives the sorted order of the points with respect to a single direction requires (n ...

Local coordinates based on the Voronoi diagram are used in natural neighbour interpolation to quantify the “neighbourliness” of data sites. In an earlier paper, we have extended the natural neighbour or stolen area interpolation technique from ordinary Voronoi diagrams to Voronoi diagrams for sets of points and line segments, by providing direct vectorial formulas for the first order and second...

We review the model of the Voronoi Diagrams which allows to reproduce the large-scale structures of our universe as given by the astronomical catalogs. The observed number of galaxies in a given solid angle with a chosen flux/magnitude versus the redshift presents a maximum that is a function of the flux/magnitude ; it can be explained by a detailed analysis of the standard luminosity function ...

During the next decade and beyond, climate system models will be challenged to resolve scales and processes that are far beyond their current scope. Each climate system component has its prototypical example of an unresolved process that may strongly influence the global climate system, ranging from eddy activity within ocean models, to ice streams within ice sheet models, to surface hydrologic...

In this work, we investigate the possibility of using inspiration from the self-organizing property of organisms in nature for providing visual representation of an invisible pollutant profile. We present a novel mathematical model of the bacterium and use it to find pollutants in the environment. This model has the capability of exploring the environment to search for sparsely distributed poll...

Voronoi diagrams are a well-studied data structure of proximity information, and although most cases require Ω(n log n) construction time, it is interesting and useful to develop linear-time algorithms for certain Voronoi diagrams. We develop a linear-time algorithm for abstract Voronoi diagrams in a domain where each site has a unique face and no pair of bisectors intersect outside the domain....

The huge amount of data recorded by modern production systems definitely have the potential to provide information for product and process design, monitoring and control. This paper presents a soft-computing based approach for the extraction of knowledge from the historical data of production. Since Self-Organizing Maps (SOM) provide compact representation of the data distribution, efficient pr...

To fill a theory gap of Voronoi diagrams that there have been no reports of extended diagrams in spatial density so far. A new concept of spatial density Voronoi diagram was proposed. An important property was presented and proven. And a construction algorithm was presented. Spatial density can be used to indicate factors related to density such as conveyance and the traffic conditions. Some pr...

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...

In this paper, we concentrate on the problem of computing a Voronoi diagram using Hypercube model of computation. The main contribution of this work is the O(log n) parallel algorithm for computing Voronoi diagram on the Euclidean plane. Our technique parallelizes the wellknown seemingly inherent sequential technique of Shamos and Hoey, and makes use of a number of special properties of the div...