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Voronoi Diagrams in Science and Engineering, 2007. ISVD '07. 4th International Symposium on

Date 9-11 July 2007

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  • 4th International Symposium on Voronoi Diagrams in Science and Engineering - Cover

    Publication Year: 2007, Page(s): c1
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  • 4th International Symposium on Voronoi Diagrams in Science and Engineering-Title

    Publication Year: 2007, Page(s):i - iii
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  • 4th International Symposium on Voronoi Diagrams in Science and Engineering-Copyright

    Publication Year: 2007, Page(s): iv
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  • 4th International Symposium on Voronoi Diagrams in Science and Engineering - TOC

    Publication Year: 2007, Page(s): v
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  • Foreword from the Editor

    Publication Year: 2007, Page(s):viii - ix
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  • Conference organisational structure

    Publication Year: 2007, Page(s): x
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  • From the Kneser-Poulsen conjecture to ball-polyhedra via Voronoi diagrams

    Publication Year: 2007, Page(s):3 - 6
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (116 KB) | HTML iconHTML

    A very fundamental geometric problem on finite systems of spheres was independently phrased by Kneser (1955) and Poulsen (1954). According to their well-known conjecture if a finite set of balls in Euclidean space is repositioned so that the distance between the centers of every pair of balls is decreased, then the volume of the union (resp., intersection) of the balls is decreased (resp., increas... View full abstract»

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  • Voronoi L-types and hypermetrics

    Publication Year: 2007, Page(s): 7
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (50 KB) | HTML iconHTML

    It is a survey/research lecture, on Voronoi and Delaunay polytopes of lattices in relation, especially, to the following problems: 1) Voronoi L-type domains and non-rigidity degree of lattices, 2) Hypermetric cone and non-rigidity degree of Delaunay polytopes, 3) Voronoi conjecture for tilings. View full abstract»

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  • Voronoi Diagrams in CGAL, the Computational Geometry Algorithms Library

    Publication Year: 2007, Page(s):8 - 14
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (595 KB) | HTML iconHTML

    CGAL, the computational geometry algorithms library, is a C++ library of geometric algorithms and data structures which is developed in the framework of the CGAL open source project. This talk gives an overview on the various types of Voronoi diagrams which are in the CGAL library or under development. View full abstract»

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  • The Voronoi diagram of circles made easy

    Publication Year: 2007, Page(s):15 - 24
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (245 KB) | HTML iconHTML

    Proximity queries among circles could be effectively answered if the Delaunay graph for sets of circles could be computed in an efficient and exact way. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how the Delaunay graph of circles (the dual graph of the Voronoi diagram of circles) can be computed exactly, and in... View full abstract»

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  • Voronoi Diagram with Respect to Criteria on Vision Information

    Publication Year: 2007, Page(s):25 - 32
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (199 KB) | HTML iconHTML

    Voronoi diagram for a set of geometric objects is a partition of the plane (or space in higher dimensions) into disjoint regions each dominated by some given object under a predetermined criterion. In this paper we are interested in various measures associated with criteria on goodness of an input line segment with respect to each point in the plane as the "point of view". These measures basically... View full abstract»

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  • Voronoi Diagrams for Oriented Spheres

    Publication Year: 2007, Page(s):33 - 37
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (142 KB) | HTML iconHTML

    We consider finite sets of oriented spheres in Rk-1 and, by interpreting such spheres as points in Rk, study the Voronoi diagrams they induce for several variants of distance between spheres. We give bounds on the combinatorial complexity of these diagrams in R2 and R3 and derive properties useful for constructing them. Our results are motivated by appli... View full abstract»

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  • Voronoi diagram in optimal path planning

    Publication Year: 2007, Page(s):38 - 47
    Cited by:  Papers (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (800 KB) | HTML iconHTML

    In this paper, we provide an algorithm based on Voronoi diagram to compute an optimal path between source and destination in the presence of simple disjoint polygonal obstacles. We evaluate the quality of the path based on clearance from obstacles, overall length and smoothness. We provide a detailed description of the algorithm for Voronoi diagram maintenance and dynamic updates. Experimental res... View full abstract»

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  • Local beta-Crusts for Simple Curves Reconstruction

    Publication Year: 2007, Page(s):48 - 57
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (301 KB) | HTML iconHTML

    In this paper, we consider the problem of curve reconstruction from a finite planar set of points. To solve this problem, we propose to use a family of neighborhood graphs included in the Gabriel graph. The neighborhood that we use is the beta-neighborhood, initially defined in the context of circle-based beta-skeletons, but applied to edges of the Voronoi diagram. This family of graphs includes t... View full abstract»

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  • Pursuit-Evasion Voronoi Diagrams in ell_1

    Publication Year: 2007, Page(s):58 - 65
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (194 KB) | HTML iconHTML

    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 fr... View full abstract»

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  • Distance Trisector of Segments and Zone Diagram of Segments in a Plane

    Publication Year: 2007, Page(s):66 - 73
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (236 KB) | HTML iconHTML

    Motivated by the work of Asano et al.[l], we consider the distance trisector problem and Zone diagram considering segments in the plane as the input geometric objects. As the most basic case, we first consider the pair of curves (distance trisector curves) trisecting the distance between a point and a line. This is a natural extension of the bisector curve (that is a parabola) of a point and a lin... View full abstract»

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  • Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

    Publication Year: 2007, Page(s):74 - 83
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (285 KB) | HTML iconHTML

    We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex polyhedral surface in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal cha... View full abstract»

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  • Maintaining the Spatial Relationships of Marine Vessels Using the Kinetic Voronoi Diagram

    Publication Year: 2007, Page(s):84 - 90
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1016 KB) | HTML iconHTML

    In this paper a new type of GIS system for maritime navigation safety is proposed. The system takes advantage of the properties of the kinetic Voronoi diagram (VD), and uses the "quad-edge" data structure for the maintenance of the spatial relationships of ships and other navigational objects. The locations of ships are updated in real-time using a standard onboard transponder, and moving-points V... View full abstract»

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  • Deploy and Search Strategy for Multi-agent systems using Voronoi partitions

    Publication Year: 2007, Page(s):91 - 100
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1554 KB) | HTML iconHTML

    In this paper we analyze a deploy and search strategy for multi-agent systems. Mobile agents equipped with sensors carry out search operation in the search space. The lack of information about the search space is modeled as an uncertainty density distribution over the space, and is assumed to be known to the agents a priori. In each step, the agents deploy themselves in an optimal way so as to max... View full abstract»

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  • Greedy Beta-Skeleton in Three Dimensions

    Publication Year: 2007, Page(s):101 - 109
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (383 KB) | HTML iconHTML

    In two dimensions, the beta-skeleton is one of the most practical methods for reconstructing smooth curves from a given unorganized point set because of its provable guarantee. In three dimensions, however, the beta-skeleton cannot be used for surface reconstruction because it may contain unwanted holes omnipresently, no matter how high sampling density is. To overcome this difficulty, an extensio... View full abstract»

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  • High Order Voronoi Sculpture

    Publication Year: 2007, Page(s):110 - 116
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1331 KB) | HTML iconHTML

    While techniques exist to compute three dimensional Voronoi diagrams and their higher-order and generalized cousins, visualizing Voronoi diagrams and their underlying distance functions remains challenging. In this paper we specifically consider visual representations that take the form of shapes or sculptures formed from three dimensional iso-surfaces. View full abstract»

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  • Computing the 3D Voronoi Diagram Robustly: An Easy Explanation

    Publication Year: 2007, Page(s):117 - 129
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (410 KB) | HTML iconHTML

    Many algorithms exist for computing the 3D Voronoi diagram, but in most cases they assume that the input is in general position. Because of the many degeneracies that arise in 3D geometric computing, their implementation is still problematic in practice. In this paper, I describe a simple 3D Voronoi diagram (and Delaunay tetrahedralization) algorithm, and I explain, by giving as many details and i... View full abstract»

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  • The Role of Quasi-Regular Tetrahedra in Dense Disordered Packings of Hard Spheres

    Publication Year: 2007, Page(s):130 - 134
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1298 KB) | HTML iconHTML

    Delaunay simplexes were used for structure analysis of hard sphere packings of different density. A special attention was paid to the simplexes of tetrahedral shape. Clusters of the tetrahedra adjacent by faces represent relatively dense aggregates of spheres atypical for crystalline structures. Such "polytetrahedral" aggregates reveal a characteristic feature of the dense disordered packings. The... View full abstract»

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  • Reversibility of the Quad-Edge operations in the Voronoi data structure

    Publication Year: 2007, Page(s):135 - 144
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (258 KB) | HTML iconHTML

    In geographic information systems the reversibility of map update operations have not been explored yet. In this paper we are using the Voronoi based quad-edge data structure to define reversible map update operations. The reversibility of the map operations have been formalised at the lowest level, as the basic algorithms for addition, deletion and moving of spatial objects. Having developed reve... View full abstract»

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  • Direct Diffusion Method for the Construction of Generalized Voronoi Diagrams

    Publication Year: 2007, Page(s):145 - 151
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (152 KB) | HTML iconHTML

    We propose a new method to construct discrete Voronoi diagrams, which we call the direct diffusion method. Once we implement it as software, we can easily modify it for various types of digital Voronoi diagrams by changing only the the distance function from a point to a generator represented by a general shape. Our method can construct discrete Voronoi diagrams even if the generator points are no... View full abstract»

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