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In this paper, we present a Delaunay refinement algorithm for meshing 3D medical images. We prove that (a) all the tetrahedra of the output mesh have \ratio\ less than 2, (b) all the boundary facets have planar angles larger than 30 degrees, (c) the symmetric (2-sided) Hausdorff distance between the object surface and mesh boundary is bounded from above by a user-specified parameter, and (d) the mesh...
We study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the Voronoi diagram has linear complexity and can be constructed in near-linear randomized expected time. Additionally, the level sets of the distances from the sites...
Traditionally, fabric prints were designed using a regular tiling pattern in a design step completely separate from garment pattern design and garment construction. With the emergence and ongoing spread of digital fabric printers, these different design steps may now be combined so that fabric prints can be designed as a function of how they will appear on the final garment, and then the stages of...
One of the challenging problems in computer vision is object reconstruction from cross sections. In this paper, we address the problem of 2D object reconstruction from arbitrary linear cross sections. This problem has not been much discussed in the literature, but holds great importance since it lifts the requirement of order within the cross sections in a reconstruction problem, consequently making...
Tremendous research activities took place on the proximity analysis of points and straight lines in three-dimensions using Voronoi diagrams. However, less attention has been paid to the proximity of curves in three-dimensions due to the complexity involved in computation. Hence, in this paper, we present a geometric approach to collision detection between curves of restricted topologies in a three-dimensional...
GIS (Geographic Information Systems) are concerned with the manipulation and analysis of spatial data at a "Geographic" scale. Apart from issues of storage, database query and visualization, they must deal with several significantly different types of spatial information. These may be roughly classified as: discrete objects; networks; polygonal maps; and surfaces. Each of these has a specific...
Voronoi diagram in the hyperbolic space, hyperbolic Voronoi diagrams for short, as well as that with respect to information-geometric divergences has been investigated since mid 1990's by Onishi et al. This paper revisits the hyperbolic Voronoi diagram from three standpoints, background theory, new applications, and geometric extensions. First, viewed from statistical estimation and information geometry,...
We assume we are given a set of points that have the property that their Voronoi diagram-restricted to some suitable bounding box-consists of only fat cells. We call such points well-spaced points. We give a linear-sized data structure for finding the nearest neighbor to a query point among well-spaced points in O(log n) time. We further show how to extend the results to higher dimensions. Finally,...
This paper presents a novel type of binary operation on medial axes: fusion of medial axes. A method for fusing medial axes of two-dimensional objects is described. The method is applicable to a pair of the medial axes of adjacent multiply-connected polygonal domains in the plane. The algorithm computes the medial axis from a structure called Delaunay graph which embodies information about adjacency...
Consider two point sets in the plane, a red set of size n, and a blue set of size m. In this paper we show how to find the minimum separating circle, which is the smallest circle that contains all points of the red set and as few points as possible of the blue set in its interior. If multiple minimum separating circles exist our algorithm finds all of them. We also give an exact solution for finding...
A variety of applications nowadays deal with complex dynamical problems where the data sets and interactions change over time. One of the ways to effectively deal with such problems is to employ Delaunay triangulation (DT). The structure however is well known to undergo significant changes when vertices are inserted or removed. A DT with dynamical updates displays visualization artifacts with non-smooth...
We consider a generalization of Voronoi diagrams, recently introduced by Barequet et al., in which the distance is measured from a pair of sites to a point. An easy way to define such distance was proposed together with the concept: it can be the sum-of, the product-of, or (the absolute value of) the difference-between Euclidean distances from either site to the respective point. We explore further...
Cenicaña has a good amount of information from different databases that are supplied by the sugar mills, farmers and the permanent research in Cenicaña. Based on the foregoing, the maximum productivity that each field with sugarcane had obtained in the period 1990 - 2008 was taken and there were generated six areas with different productivity level and stability. Once the areas were generated, they...
Recent advances in sensors technology have led to design and development of variety of geosensor networks and their applications in many disciplines. Such networks consist of a set of sensors laying on different locations and sensing various real world phenomena for environmental monitoring, object surveillance, tracking and controlling applications. A fundamental issue in a geosensor network optimization...
This paper's main result is presenting a new conception in the geometric modeling and visualization - a generalized efficient parallel-and-recursive algorithm with optimal bound complexity O(log2N). Voronoi diagram is one of key elements the algorithm. The algorithm solves in unified manner the variety of interrelated geometrical problems for the construction of visual models of complex phenomena...
An interesting property of the Voronoi tessellation is studied in the context of its application to the analysis of hydration shells in computer simulation of solutions. Namely the shells around a randomly chosen cell in a Voronoi tessellation attract extra volume from outside. There is a theoretical result which says that the mean volume of the first shell around a randomly chosen cell is greater...
We present a novel method for computing the Minkowski Functionals from isodensity surfaces extracted directly from the Delaunay tessellation of a point distribution. This is an important step forward compared to the previous cosmological studies when the isodensity surface was built in the field on a uniform cubic grid and therefore having a uniform spatial resolution. The density field representing...
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