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Voronoi Diagrams in Science and Engineering, 2006. ISVD '06. 3rd International Symposium on

Date 2-5 July 2006

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  • 3rd International Symposium on Voronoi Diagrams in Science and Engineering - Cover

    Publication Year: 2006 , Page(s): c1
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  • 3rd International Symposium on Voronoi Diagrams in Science and Engineering - Title

    Publication Year: 2006 , Page(s): i - iii
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  • 3rd International Symposium on Voronoi Diagrams in Science and Engineering - Copyright

    Publication Year: 2006 , Page(s): iv
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  • 3rd International Symposium on Voronoi Diagrams in Science and Engineering - Table of contents

    Publication Year: 2006 , Page(s): v - vii
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  • Foreword from the Editor

    Publication Year: 2006 , Page(s): viii
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  • Conference Organizational Structure

    Publication Year: 2006 , Page(s): x
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  • Voronoi Diagram and Delaunay Triangulation: Applications and Challenges in Bioinformatics

    Publication Year: 2006 , Page(s): 2 - 3
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (110 KB) |  | HTML iconHTML  

    This paper first covers the applications of Voronoi diagram and Delaunay triangulation based on the author's personal experience. On the successful part, it covers the history and development of the jump-and-walk algorithm, which is known as the first sublinear geometric algorithm nowadays and has been used in several famous software packages. On the bioinformatics applications, the paper focuses ... View full abstract»

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  • Recent Developments and Open Problems in Voronoi Diagrams

    Publication Year: 2006 , Page(s): 4 - 5
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (131 KB) |  | HTML iconHTML  

    This paper deals with some open problems in computational geometry related to Voronoi diagrams. The Voronoi diagram and Dealunay triangulation of n points in Ropfd has complexity Theta (n [d/2]) in the worst case. However, the complexity is not high if points are random. Statistical properties of Voronoi diagrams of random points have been studied for decades. The expected co... View full abstract»

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  • Voronoi and Delaunay Tilings for Lattices

    Publication Year: 2006 , Page(s): 6
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (64 KB) |  | HTML iconHTML  

    Summary form only given. In this paper the author considers two outstanding problems in the theory of Delaunay and Voronoi tilings for lattices. There is a new classification problem that has arisen from a new structure theorem. Sergei Ryshkov proved that: The Minkowski sum of two Voronoi polytopes is a Voronoi polytope, if and only if the corresponding Delaunay tilings are commensurate. This resu... View full abstract»

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  • Distance Trisector Curves in Regular Convex Distance Me

    Publication Year: 2006 , Page(s): 8 - 17
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (521 KB) |  | HTML iconHTML  

    Given two points A and B in the plane, we are interested in separating them by two curves Ca and Cb such that Ca is equidistant from A and Cb, and Cb is equidistant from B and Ca- Such curves generalize the familiar notion of a bisector curve, and form the basis of a new kind of Voronoi diagram called a Zone diagram. These curves, which are referred to as distance trisector curves, have been studi... View full abstract»

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  • Angular Voronoi Diagram with Applications

    Publication Year: 2006 , Page(s): 18 - 24
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (243 KB) |  | HTML iconHTML  

    Given a set of line segments in the plane, we define an angular Voronoi diagram as follows: a point belongs to a Voronoi region of a line segment if the visual angle of the line segment from the point is smallest among all line segments. The Voronoi diagram is interesting in itself and different from an ordinary Voronoi diagram for a point set. After introducing interesting properties, we present ... View full abstract»

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  • On the Stretch Factor of the Constrained Delaunay Triangulation

    Publication Year: 2006 , Page(s): 25 - 31
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (262 KB) |  | HTML iconHTML  

    Given a set P of n points in the plane and a set S of non-crossing line segments whose endpoints are in P, let CDT(P, S) be the constrained Delaunay triangulation of P with respect to S. Given any two visible points p,q isin P, we show that there exists a path from p to q in CDT(P, S), denoted SP CDT(p, q) such that every edge in the path has length at most pq and the ratio SP... View full abstract»

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  • Aspect-Ratio Voronoi Diagram with Applications

    Publication Year: 2006 , Page(s): 32 - 39
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (401 KB) |  | HTML iconHTML  

    This paper considers a problem of finding an optimal point within a polygon P in the sense that when we connect the point to every vertex of P by straight line then the worst aspect ratio among all resulting triangles is optimized. This problem has an important application to triangular mesh improvement. We propose three different approaches toward this problem. The first one is based on some new ... View full abstract»

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  • Stable and Topology-Preserving Extraction of Medial Axes

    Publication Year: 2006 , Page(s): 40 - 47
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (376 KB) |  | HTML iconHTML  

    The paper presents a simple method for extracting global medial axes in a stable manner. A new index, called the normalized boundary distance, is introduced in order to measure the degree of importance of a point on the conventional medial axis. This index has a remarkable property that the set of points whose index values are greater than an arbitrarily chosen threshold is topologically equivalen... View full abstract»

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  • On a Geometric Structure of Pure Multi-qubit Quantum States and Its Applicability to a Numerical Computation

    Publication Year: 2006 , Page(s): 48 - 53
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (242 KB) |  | HTML iconHTML  

    For one-qubit pure quantum states, it is already proved that the Voronoi diagrams with respect to two distances - Euclidean distance and the quantum divergence - coincide. This fact is a support for a known method to calculate the Holevo capacity. To consider an applicability of this method to quantum states of a higher level system, it is essential to check if the coincidence of the Voronoi diagr... View full abstract»

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  • Robust Point-Location in Generalized Voronoi Diagrams

    Publication Year: 2006 , Page(s): 54 - 59
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (250 KB) |  | HTML iconHTML  

    We address the problem of robust point-location in a generalized d-dimensional Voronoi diagram. The exact point location requires the solution for expressions of degree four. A natural question is what can be done using expression of smaller degree. We apply polyhedral metrics for this task. In general dimensions two Minkowski metrics can be used L1 (Manhattan metric) and L... View full abstract»

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  • Sphere-based Computation of Delaunay Diagrams on Points from 4d Grids

    Publication Year: 2006 , Page(s): 60 - 65
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (219 KB) |  | HTML iconHTML  

    The Delaunay diagram in d dimensions is the dual of the Voronoi diagram of a set of input sites. If we assume no degeneracies in the input, i.e. no d + 2 sites are co-spherical, then the diagram is a triangulation. Because this assumption is common, and can be enforced by symbolic perturbation, we often forget that Delaunay diagrams need not be triangulations. Input sets chosen from integer grids ... View full abstract»

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  • Voronoi Random Fields

    Publication Year: 2006 , Page(s): 66 - 75
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (357 KB) |  | HTML iconHTML  

    We propose a random field regarded as a generalization of Voronoi diagrams for the case where the positions of generators are distributed probabilistically. Our approach is a kind of stochastic approaches to Voronoi diagrams; however our definition is different from usual random Voronoi diagrams such as Poisson Voronoi diagrams. As numerical examples, first we discuss the case where the positions ... View full abstract»

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  • Kinetic Voronoi/Delaunay Drawing Tools

    Publication Year: 2006 , Page(s): 76 - 84
    Cited by:  Papers (2)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (2298 KB) |  | HTML iconHTML  

    We describe two reversible line-drawing methods for cartographic applications based on the kinetic (moving-point) Voronoi diagram. Our objectives were to optimize the user's ability to draw and edit the map, rather than to produce the most efficient batch- oriented algorithm for large data sets, and all our algorithms are based on local operations (except for basic point location). Because the del... View full abstract»

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  • An Efficient Swarm Neighborhood Management for a 3D Tactical Simulator

    Publication Year: 2006 , Page(s): 85 - 93
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (1646 KB) |  | HTML iconHTML  

    The paper presents a unique utilization of the dynamic Delaunay triangulation (DT) to devise a highly efficient algorithm for the neighborhood adjacency management which is a crucial component of a swarm-based simulation. This algorithm allows fast computation of the swarm neighborhood which is required to implement Boids flocking rules. The method also provides an efficient mechanism to detect an... View full abstract»

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  • Geometrical Algorithms to Detect Patterns from a Set of Points

    Publication Year: 2006 , Page(s): 94 - 101
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (413 KB) |  | HTML iconHTML  

    This article presents a new approach for detecting patterns, such as lines, parabolas and circles, from a two- dimensional cloud of points S. This scheme transforms the problem of detecting the patterns from S, to the problem of detecting simpler patterns from a set of points S1 computed from the Voronoi and Delaunay diagrams of S. It is based on the differential properties of the Voron... View full abstract»

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  • CRYSTAL - A new density-based fast and efficient clustering algorithm

    Publication Year: 2006 , Page(s): 102 - 111
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (762 KB) |  | HTML iconHTML  

    In this paper, we present a fast O(nlogn) clustering algorithm based on Delaunay triangulation for identifying clusters of different shapes, not necessarily convex. The clustering result is similar to human perception of clusters. The novelty of our method is the growth model we follow in the cluster formation that resembles the natural growth of a crystal. Our algorithm is able to identify dense ... View full abstract»

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  • Clustering of 3D Spatial Points Using Maximum Likelihood Estimator over Voronoi Tessellations: Study of the Galaxy Distribution in Redshift Space

    Publication Year: 2006 , Page(s): 112 - 121
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (435 KB) |  | HTML iconHTML  

    This paper describes an algorithm based on the 2D approach of Allard & Fraley that uses Voronoi tessellation and a non-parametric maximum likelihood estimator. We have designed a 3D version of this algorithm which detects multiple clusters of points immersed in background noise; its application to the detection of galaxy clusters in red-shift space, using the astronomical database of the 2-deg... View full abstract»

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  • Closed Curve Reconstruction from Unorganized Sample Points

    Publication Year: 2006 , Page(s): 122 - 131
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (423 KB) |  | HTML iconHTML  

    This paper considers the problem for reconstructing closed curves from unorganized sample points, where the curve to be reconstructed consists of a finite number of pairwise disjoint components of simple closed curves. This paper formulates this problem as a linear integer programming problem, and proposes an algorithm, called ZERO-ONE, based on it. In addition, two other heuristic algorithms call... View full abstract»

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  • 3D Facial Model Synthesis using Voronoi Approach

    Publication Year: 2006 , Page(s): 132 - 137
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandAbstract | PDF file iconPDF (3805 KB) |  | HTML iconHTML  

    Construction and animation of realistic human facial models is an important research field of computer graphics. How to efficiently create an individualized facial model for animation is still a challenge. In this paper, we present a method for 3D facial model synthesis that combines the traditional free-form deformation (FFD) model with techniques of data interpolation based on Dirichlet/Voronoi ... View full abstract»

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