The Voronoi tessellation is a natural way of space segmentation, which has many applications in various fields science and technology, as well social sciences visual art. varieties the methods are commonly used computational fluid dynamics, geometry, geolocation logistics, game dev programming, cartography, engineering, liquid crystal electronic machine learning, etc. very innovative results we...

The Voronoi diagram is a fundamental geometry structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact 3D domain (i.e. a finite 3D volume), some Voronoi cells of their Voronoi diagram are infinite, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellatio...

Graphics hardware has been progressively optimized to render more triangles with increasingly flexible shading. For highly detailed geometry, interactive applications restricted themselves to performing transforms on fixed geometry, since they could not incur the cost required to generate and transfer smooth or displaced geometry to the GPU at render time. As a result of recent advances in grap...

In this paper we present an innovative approach to incremental quad mesh simplification, i.e. the task of producing a low complexity quad mesh starting from a high complexity one. The process is based on a novel set of strictly local operations which preserve quad structure. We show how good tessellation quality (e.g. in terms of vertex valencies) can be achieved by pursuing uniform length and ...

Grain microstructures in polycrystalline materials can be approximated by tessellation models known from stochastic geometry. However, for a given set of microstructural data, the choice of a particular model is traditionally based on researcher intuition. The model should provide a sufficiently good approximation to the data, while keeping the number of parameters small. In this paper, we disc...

ÐPrioritized-Layered Projection (PLP) is a technique for fast rendering of high depth complexity scenes. It works by estimating the visible polygons of a scene from a given viewpoint incrementally, one primitive at a time. It is not a conservative technique, instead PLP is suitable for the computation of partially correct images for use as part of time-critical rendering systems. From a very hi...

SUMMARY Voronoi tessellation has proved to be a useful tool in protein structure analysis. We have developed PROVAT, a versatile public domain software that enables computation and visualization of Voronoi tessellations of proteins and protein complexes. It is a set of Python scripts that integrate freely available specialized software (Qhull, Pymol etc.) into a pipeline. The calculation compon...

Voronoi tessellation 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, a Voronoi tessellation based method is presented for word grouping in document images. The Voronoi neighborhoods are generated from the Voronoi tessellat...

King [3] introduced and examined the concepts of almost A-summable sequence, almost conservative matrix and almost regular matrix. In this paper, we introduce and examine the concepts of λ-almost A-summable sequence, λalmost conservative matrix and λ-almost regular matrix. Also we introduce statistically (V, λ)-summable sequence.

In 1911, Steinhaus presented the following theorem: if A is a regular matrix then there exists a sequence of 0’s and 1’s which is not A-summable. In 1943, R. C. Buck characterized convergent sequences as follows: a sequence x is convergent if and only if there exists a regular matrix A which sums every subsequence of x. In this paper, definitions for “subsequences of a double sequence” and “Pri...