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Voronoi Diagrams in Science and Engineering (ISVD), 2013 10th International Symposium on

Date 8-10 July 2013

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Displaying Results 1 - 23 of 23
  • [Front cover]

    Publication Year: 2013, Page(s): C4
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  • [Title page i]

    Publication Year: 2013, Page(s): i
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  • [Title page iii]

    Publication Year: 2013, Page(s): iii
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  • [Copyright notice]

    Publication Year: 2013, Page(s): iv
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  • Table of contents

    Publication Year: 2013, Page(s):v - vi
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  • Foreword

    Publication Year: 2013, Page(s): vii
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  • Committees

    Publication Year: 2013, Page(s): viii
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  • Program Committee

    Publication Year: 2013, Page(s): ix
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  • Delone Sets and Polyhedral Tilings: Local Rules and Global Order

    Publication Year: 2013, Page(s): 3
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (103 KB) | HTML iconHTML

    Summary form only given. An appropriate concept for describing an arbitrary discrete atomic structure is the Delone set (or an (r,R)-system). Structures with long-range order such as crystals involves a concept of the space group as well. A mathematical model of an ideal monocrystalline matter is defined now as a Delone set which is invariant with respect to some space group. One should emphasize ... View full abstract»

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  • Molecular Geometry: A New Challenge and Opportunity for Geometers

    Publication Year: 2013, Page(s): 4
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (81 KB) | HTML iconHTML

    Summary form only given. Molecular structure determines molecular function and the geometry is one of the most fundamental aspects of the molecular structure regardless it is organic or inorganic. Despite of its importance, the theory for understanding the geometry of molecules has not been sufficiently developed. In this talk, we will present a unified theory of molecular geometry (MG) as a new d... View full abstract»

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  • Delaunay Triangulations on the Word RAM: Towards a Practical Worst-Case Optimal Algorithm

    Publication Year: 2013, Page(s):7 - 15
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1966 KB) | HTML iconHTML

    The Delaunay triangulation of n points in the plane can be constructed in o(n log n) time when the coordinates of the points are integers from a restricted range. However, algorithms that are known to achieve such running times had not been implemented so far. We explore ways to obtain a practical algorithm for Delaunay triangulations in the plane that runs in linear time for small integers. For t... View full abstract»

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  • A Sweepline Algorithm for Higher Order Voronoi Diagrams

    Publication Year: 2013, Page(s):16 - 22
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (418 KB)

    We present an algorithm to construct order-k Voronoi diagrams with a sweepline technique. The sites can be points or line segments. The algorithm has O(nk2 log n) time complexity and O(nk) space complexity. View full abstract»

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  • Design of Pop-Up Cards Based on Weighted Straight Skeletons

    Publication Year: 2013, Page(s):23 - 28
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1059 KB) | HTML iconHTML

    We investigated the use of weighted straight skeletons in the computer-aided creation of pop-up cards. A pop-up card is a sheet of paper that can be folded to a flat plane but, when opened, produces a meaningful three-dimensional structure. Weighted straight skeletons are a special type of Voronoi diagrams, and they are closely related to the foldability of a sheet of paper along specified lines. ... View full abstract»

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  • On the Farthest-Neighbor Voronoi Diagram of Segments in Three Dimensions

    Publication Year: 2013, Page(s):31 - 36
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (155 KB) | HTML iconHTML

    We consider the farthest-neighbor Voronoi diagram of a set of line segments in three dimensions. To understand the structure of the diagram, we define the “farthest hull” of the segments and investigate it by its representation in a Gaussian map. We then provide lower and upper bounds on the worst-case complexities of the farthest hull and of the Voronoi diagram. View full abstract»

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  • Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input

    Publication Year: 2013, Page(s):37 - 46
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (263 KB) | HTML iconHTML

    A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon or planar straight-line graph. In this paper, we ask the reverse question: Given the straight skeleton (in form of a planar straight-line graph, with some rays to infinity), can we reconstruct a planar straight-line graph for which this was the straight skele... View full abstract»

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  • Voronoi Diagrams from (Possibly Discontinuous) Embeddings

    Publication Year: 2013, Page(s):47 - 50
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (856 KB) | HTML iconHTML

    We introduce a new metric framework which is based on an injective embedding of [0,1]2 into Rm, for m ≥ 2, and an additional scaling function for re-scaling the distances. The framework is used to construct a new type of generalized Voronoi diagrams in [0,1]2, which is possibly anisotropic. We present different possible applications of these Voronoi diagrams... View full abstract»

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  • Common Influence Region Queries

    Publication Year: 2013, Page(s):53 - 62
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (752 KB) | HTML iconHTML

    In this paper, we propose and solve several queries called common influence region queries. They are related to the simultaneous influence, i.e. capacity of attracting customers, of two sets of facilities of different type. In them a facility of the first type competes with the other facilities of the first type and cooperates with several facilities of the second type. The studied queries find ap... View full abstract»

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  • Spatio-temporal Map Generalizations with the Hierarchical Voronoi Data Structure

    Publication Year: 2013, Page(s):63 - 72
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1076 KB) | HTML iconHTML

    Map generalization leads to simplified maps that are needed for specific applications. However, in the map generalization process [18], the processing of the map objects and the operations applied to achieve this simplified map are usually lost. This is due to the transaction processing systems implemented in commercial GIS systems. In this research, we used the Voronoi spatial data model for map ... View full abstract»

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  • Centroidal Voronoi Tessellation of Streamlines for Flow Visualization

    Publication Year: 2013, Page(s):75 - 81
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (519 KB) | HTML iconHTML

    Centroidal Voronoi tessellation (CVT) and its extensions have a wide spectrum of applications including computational geometry, image processing, cellular biology and scientific visualization etc. In this paper, we propose the concept of the complete streamline and the CVT of streamlines, and then formulate the computation of CVT of complete streamlines as a continuous variational problem. To redu... View full abstract»

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  • Anomaly Occurrences in Quasi-triangulations and Beta-complexes

    Publication Year: 2013, Page(s):82 - 88
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (6108 KB) | HTML iconHTML

    Voronoi diagrams, quasi-triangulations, and beta-complexes are powerful for solving spatial problems among spherical particles with different radii. However, a quasi-triangulation, and thus a beta-complex as well, can be a non-simplicial complex due to an anomaly condition. While a beta-complex is straightforward to use when it is a simplicial complex, it may not seem obvious if it is not. In this... View full abstract»

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  • Open Problem:  A Formula for Calculation of the Voronoi S-region Volume

    Publication Year: 2013, Page(s):89 - 90
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (296 KB) | HTML iconHTML

    Fast and accurate calculation of the volume of additively weighted Voronoi region (Johnson-Mehl nucleus, or Voronoi S-region) is needed in various physical applications. The problem will be solved if an analytical expression could be derived for volume calculation of the pyramid which base is a piece of the hyperboloid surface. View full abstract»

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  • Author index

    Publication Year: 2013, Page(s): 91
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  • [Publisher's information]

    Publication Year: 2013, Page(s): 92
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