voronoi diagrams and delaunay triangulations

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Voronoi Diagrams And Delaunay Triangulations

Author : Franz Aurenhammer
ISBN : 9789814447652
Genre : Computers
File Size : 69. 80 MB
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Voronoi diagrams partition space according to the influence certain sites exert on their environment. Since the 17th century, such structures play an important role in many areas like Astronomy, Physics, Chemistry, Biology, Ecology, Economics, Mathematics and Computer Science. They help to describe zones of political influence, to determine the hospital nearest to an accident site, to compute collision-free paths for mobile robots, to reconstruct curves and surfaces from sample points, to refine triangular meshes, and to design location strategies for competing markets. This unique book offers a state-of-the-art view of Voronoi diagrams and their structure, and it provides efficient algorithms towards their computation. Readers with an entry-level background in algorithms can enjoy a guided tour of gently increasing difficulty through a fascinating area. Lecturers might find this volume a welcome source for their courses on computational geometry. Experts are offered a broader view, including many alternative solutions, and up-to-date references to the existing literature; they might benefit in their own research or application development.

Transactions On Computational Science Xiv

Author : Mir Abolfazl Mostafavi
ISBN : 9783642252488
Genre : Computers
File Size : 46. 60 MB
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The 14th issue of the Transactions on Computational Science journal contains nine papers, all revised and extended versions of papers presented at the International Symposium on Voronoi Diagrams 2010, held in Quebec City, Canada, in June 2010. The topics covered include: the development of new generalized Voronoi diagrams and algorithms including round-trip Voronoi diagrams, maximal zone diagrams, Jensen-Bregman Voronoi diagrams, hyperbolic Voronoi diagrams, and moving network Voronoi diagrams; new algorithms based on Voronoi diagrams for applications in science and engineering, including geosensor networks deployment and optimization and homotopic object reconstruction; and the application of Delaunay triangulation for modeling and representation of Cosmic Web and rain fall distribution.

Computing In Euclidean Geometry

Author : Ding-Zhu Du
ISBN : 9810218761
Genre : Mathematics
File Size : 35. 73 MB
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This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. Topics covered include the history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra, triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and Steiner trees. This second edition contains three new surveys covering geometric constraint solving, computational geometry and the exact computation paradigm.

Computing In Euclidean Geometry

Author : Dingzhu Du
ISBN : 9810209665
Genre : Mathematics
File Size : 69. 31 MB
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This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra; triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and steiner trees. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going.

Delaunay Mesh Generation

Author : Siu-Wing Cheng
ISBN : 9781584887317
Genre : Computers
File Size : 31. 37 MB
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Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why these meshing algorithms work. The book is one of the first to integrate a vast amount of cutting-edge material on Delaunay triangulations. It begins with introducing the problem of mesh generation and describing algorithms for constructing Delaunay triangulations. The authors then present algorithms for generating high-quality meshes in polygonal and polyhedral domains. They also illustrate how to use restricted Delaunay triangulations to extend the algorithms to surfaces with ridges and patches and volumes with smooth surfaces. For researchers and graduate students, the book offers a rigorous theoretical analysis of mesh generation methods. It provides the necessary mathematical foundations and core theoretical results upon which researchers can build even better algorithms in the future. For engineers, the book shows how the algorithms work well in practice. It explains how to effectively implement them in the design and programming of mesh generation software.

Generalized Voronoi Diagram A Geometry Based Approach To Computational Intelligence

Author : Marina L. Gavrilova
ISBN : 9783540851257
Genre : Mathematics
File Size : 31. 94 MB
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The year 2008 is a memorial year for Georgiy Vorono (1868-1908), with a number of events in the scientific community commemorating his tremendous contribution to the area of mathematics, especially number theory, through conferences and scientific gatherings in his honor. A notable event taking place in September 2008 a joint c- ference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessel- tions held in Kyiv, Georgiy Vorono ’s native land. The main ideas expressed by G. Vorono ’s through his fundamental works have influenced and shaped the key dev- opments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical en- neering, material sciences, terrain modeling, biometrics and other domains. This book is intended to provide the reader with in-depth overview and analysis of the fundamental methods and techniques developed following G. Voronoi ideas, in the context of the vast and increasingly growing area of computational intelligence. It represents the collection of state-of-the art research methods merging the bridges between two areas: geometric computing through Voronoi diagrams and intelligent computation techniques, pushing the limits of current knowledge in the area, impr- ing on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems.

Spatial Tessellations

Author : Atsuyuki Okabe
ISBN : 9780470317853
Genre : Mathematics
File Size : 90. 39 MB
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Spatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization. With such versatility, the Voronoi diagram and its relative, the Delaunay triangulation, provide valuable tools for the analysis of spatial data. This is a rapidly growing research area and in this fully updated second edition the authors provide an up-to-date and comprehensive unification of all the previous literature on the subject of Voronoi diagrams. Features: * Expands on the highly acclaimed first edition * Provides an up-to-date and comprehensive survey of the existing literature on Voronoi diagrams * Includes a useful compendium of applications * Contains an extensive bibliography A wide range of applications is discussed, enabling this book to serve as an important reference volume on this topic. The text will appeal to students and researchers studying spatial data in a number of areas, in particular, applied probability, computational geometry, and Geographic Information Science (GIS). This book will appeal equally to those whose interests in Voronoi diagrams are theoretical, practical or both.

Delaunay Tetrahedralization And Its Dual Voronoi Diagrams

Author : Maria Vineeta
ISBN : 9783668444201
Genre : Computers
File Size : 39. 45 MB
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Master's Thesis from the year 2014 in the subject Computer Science - Applied, grade: B+, Bournemouth University, course: Msc Computer Animation and Visual Effects, language: English, abstract: The Delaunay tetrahedralization (DT) is one of the most popular and common methods used for solving problems related to meshes. It is either used for generating a mesh or for breaking it up, as Voronoi diagrams, dual of the DT, is a commonly used process for that. The main task of this project is to implement a robust Delaunay Tetrahedralization structure, with a set of points generated from sampling a given 3D Mesh. Points within the volume of the mesh can be obtained by several methods. We present two such methods and discuss the result obtained. These points serve as vertices for the tetrahedrons that are a part of the combinatorial structure DT. 3D Delaunay Tetrahedralization is not as optimal as 2D Delaunay triangulations. Implementing them gives rise to several degeneracies, which are quite difficult to handle. In this project, we have implemented a simple Incremental Insertion Algorithm based on the paper presented by Ledoux (2007), inorder to construct the DT structure. Correctness of the structure is given utmost importance rather than its speed.

Computational Geometry In C

Author : Joseph O'Rourke
ISBN : 9781107268630
Genre : Computers
File Size : 26. 38 MB
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This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp.

A Short Course In Computational Geometry And Topology

Author : Herbert Edelsbrunner
ISBN : 9783319059570
Genre : Computers
File Size : 29. 31 MB
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This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.

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