In this paper, we construct an algorithm for determining whether a given tessellation on a sphere is a spherical Laguerre Voronoi diagram or not. For spherical Laguerre tessellations, not only the locations of the Voronoi generators, but also their weights are required to recover. However, unlike the ordinary spherical Voronoi diagram, the generator set is not unique, which makes the problem di...

The symmetrizable and converged Laplace–Beltrami operator ( M) is an indispensable tool for spectral geometrical analysis of point clouds. The M, introduced by Liu et al. [LPG12] is guaranteed to be symmetrizable, but its convergence degrades when it is applied to models with sharp features. In this paper, we propose a novel M, which is not only symmetrizable but also can handle the point-sampl...

We describe an automatic surface reconstruction technique from a set of planar data points organised in parallel sections. The reconstruction employs skeletal implicit surfaces. Two key points in this study are: Calculation of the 3D skeleton by establishing a correspondence between each pair of 2D Voronoi skeleton of two neighbouring sections, Use of a uniform field function necessitating the ...

This work presents a method for the registration of three-dimensional (3-D) shapes. The method is based on the iterative closest point (ICP) algorithm and improves it through the use of a 3-D volume containing the shapes to be registered. The Voronoi diagram of the "model" shape points is first constructed in the volume. Then this is used for the calculation of the closest point operator. This ...

We present a new algorithm for reliable point-location problem in a system of ddimensional hyperbolic surfaces. The problem is perpetual to many applications, including modeling of a molecular system represented as a set of polydisperse spheres through the use of the Euclidean d-dimensional Voronoi diagram. The algorithm is provided for the d-dimensional case and its implementation in a 3-dimen...

in this paper, using the best proximity theorems for an extensionof brosowski's theorem. we obtain other results on farthest points. finally, wedene the concept of e- farthest points. we shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (x; ||.||). if z in w is a e-farthest point from an x in x, then z is also a-best ...

The process of georeferencing is fundamentally a matter spatial relationships: where the point interest in relation to Prime Meridian, Equator, nearest landmark, etc. adding geographic coordinates and uncertainty measurements data coming from work others often complicated by interpretation subjectivity. Take for instance description, “found near city Springfield", which might be assigned coordi...

Voronoi diagrams are widely used to represent geographical distributions of information, but they are not readily stacked in a hierarchical fashion. We propose a simple mechanism whereby each index Voronoi cell contains the generators of several Voronoi cells in the next lower level. This allows various processes of indexing, paging, visualization and generalization to be performed on various t...

We are given m pursuers and one evader. Each pursuer and the evader has an associated starting point in the plane, a maximum speed, and a start time. We also have a set of line segment obstacles with a total of n endpoints. Our task is to find those points in the plane, called the evader’s region, that the evader can reach via evasive paths. A path is evasive if the evader can traverse the path...

One of most famous theorems in computational geometry is the duality between Voronoi diagram and Delaunay triangulation in Euclidean space. This paper proposes an extension of that theorem to the Voronoi diagram and Delaunay-type triangulation in dually at space. In that space, the Voronoi diagram and the triangulation can be computed e ciently by using potential functions. We also propose high...