Delaunay Tetrahedralization And Its Dual Voronoi Diagrams

Author : Maria Vineeta
Publisher : GRIN Verlag
Page : 33 pages
File Size : 51,9 Mb
Release : 2017-05-10
Category : Computers
ISBN : 9783668444201

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Delaunay Tetrahedralization and its dual Voronoi Diagrams by Maria Vineeta Pdf

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.

Author : Franz Aurenhammer,Rolf Klein,Der-Tsai Lee
Publisher : World Scientific Publishing Company
Page : 348 pages
File Size : 53,6 Mb
Release : 2013-06-26
Category : Computers
ISBN : 9789814447652

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Voronoi Diagrams and Delaunay Triangulations by Franz Aurenhammer,Rolf Klein,Der-Tsai Lee Pdf

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.

Author : Franz Aurenhammer
Publisher : Unknown
Page : 128 pages
File Size : 48,9 Mb
Release : 2013
Category : Electronic
ISBN : 9814447641

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Voronoi Diagrams and Delaunay Triangulations by Franz Aurenhammer Pdf

Author : Øyvind Hjelle,Morten Dæhlen
Publisher : Springer Science & Business Media
Page : 239 pages
File Size : 43,9 Mb
Release : 2006-09-19
Category : Mathematics
ISBN : 9783540332619

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Triangulations and Applications by Øyvind Hjelle,Morten Dæhlen Pdf

This book will serve as a valuable source of information about triangulations for the graduate student and researcher. With emphasis on computational issues, it presents the basic theory necessary to construct and manipulate triangulations. In particular, the book gives a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. It also discusses various data structures used for the representation of triangulations.

Author : Michael F. Worboys,Matt Duckham
Publisher : CRC Press
Page : 456 pages
File Size : 40,7 Mb
Release : 2004-05-11
Category : Technology & Engineering
ISBN : 0415283752

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GIS by Michael F. Worboys,Matt Duckham Pdf

GIS: A Computing Perspective, Second Edition, provides a full, up-to-date overview of GIS, both Geographic Information Systems and the study of Geographic Information Science. Analyzing the subject from a computing perspective, the second edition explores conceptual and formal models needed to understand spatial information, and examines the representations and data structures needed to support adequate system performance. This volume also covers the special-purpose interfaces and architectures required to interact with and share spatial information, and explains the importance of uncertainty and time. The material on GIS architectures and interfaces as well as spatiotemporal information systems is almost entirely new. The second edition contains substantial new information, and has been completely reformatted to improve accessibility. Changes include: A new chapter on spatial uncertainty Complete revisions of the bibliography, index, and supporting diagrams Supplemental material is offset at the top of the page, as are references and links for further study Definitions of new terms are in the margins of pages where they appear, with corresponding entries in the index

Author : Nico Karssemeijer,Boudewijn Lelieveldt
Publisher : Springer
Page : 780 pages
File Size : 45,8 Mb
Release : 2007-07-14
Category : Computers
ISBN : 9783540732730

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Information Processing in Medical Imaging by Nico Karssemeijer,Boudewijn Lelieveldt Pdf

This book constitutes the refereed proceedings of the 20th International Conference on Information Processing in Medical Imaging, IPMI 2007, held in Kerkrade, The Netherlands, in July 2007. It covers segmentation, cardiovascular imaging, detection and labeling, diffusion tensor imaging, registration, image reconstruction, functional brain imaging, as well as shape models and registration.

Author : Marina L. Gavrilova
Publisher : Springer
Page : 316 pages
File Size : 51,9 Mb
Release : 2008-10-02
Category : Technology & Engineering
ISBN : 9783540851264

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Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence by Marina L. Gavrilova Pdf

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.

Author : Osvaldo Gervasi,Beniamino Murgante,Antonio Laganà,David Taniar,Youngsong Mun
Publisher : Springer
Page : 1283 pages
File Size : 52,6 Mb
Release : 2008-06-28
Category : Computers
ISBN : 9783540698395

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Computational Science and Its Applications - ICCSA 2008 by Osvaldo Gervasi,Beniamino Murgante,Antonio Laganà,David Taniar,Youngsong Mun Pdf

This two-volume set is assembled following the 2008 International Conference on Computational Science and Its Applications, ICCSA 2008, a premium int- national event held in Perugia, Italy, from June 30 to July 3, 2008. The collection of fully refereed high-quality original works accepted as theme papers for presentation at ICCSA 2008 are published in this LNCS proceedings set. This outstanding collection complements the volume of workshop papers, traditionally published by IEEE Computer Society. The continuous support of computational science researchers has helped ICCSA to become a ?rmly established forum in the area of scienti?c computing and the conference itself become a recurring scienti?c and professional meeting that cannot be given up. The computational science ?eld, based on fundamental disciplines such as mathematics, physics, and chemistry, is ?nding new computational approaches to foster the human progress in heterogeneous and fundamental areas such as aerospace and automotive industries, bioinformatics and nanotechnology studies, networks and grid computing, computational geometry and biometrics, computer education, virtual reality, and art. Due to the growing complexity of many ch- lenges in computational science, the use of sophisticated algorithms and eme- ing technologies is inevitable. Together, these far-reaching scienti?c areas help to shape this conference in the areas of state-of-the-art computational science research and applications, encompassing the facilitating theoretical foundations and the innovative applications of such results in other areas.

Author : M. H. Alsuwaiyel
Publisher : World Scientific
Page : 573 pages
File Size : 52,9 Mb
Release : 2016
Category : Mathematics
ISBN : 9789814723657

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Algorithms by M. H. Alsuwaiyel Pdf

"Problem solving is an essential part of every scientific discipline. It has two components: (1) problem identification and formulation, and (2) the solution to the formulated problem. One can solve a problem on its own using ad hoc techniques or by following techniques that have produced efficient solutions to similar problems. This requires the understanding of various algorithm design techniques, how and when to use them to formulate solutions, and the context appropriate for each of them. Algorithms: Design Techniques and Analysis advocates the study of algorithm design by presenting the most useful techniques and illustrating them with numerous examples -- emphasizing on design techniques in problem solving rather than algorithms topics like searching and sorting. Algorithmic analysis in connection with example algorithms are explored in detail. Each technique or strategy is covered in its own chapter through numerous examples of problems and their algorithms. Readers will be equipped with problem solving tools needed in advanced courses or research in science and engineering."--Provided by publisher.

Author : Luc Florack,Remco Duits,Geurt Jongbloed,Marie-Colette van Lieshout,Laurie Davies
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 44,6 Mb
Release : 2012-01-12
Category : Mathematics
ISBN : 9781447123538

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Mathematical Methods for Signal and Image Analysis and Representation by Luc Florack,Remco Duits,Geurt Jongbloed,Marie-Colette van Lieshout,Laurie Davies Pdf

Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living on an n-dimensional smooth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. In contrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed for the sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interested in the fundamental methodology per se. Covering many topics at the forefront of current research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduate students and researchers in the fields of computer vision, medical imaging and visual perception.

Author : M H Alsuwaiyel
Publisher : World Scientific
Page : 756 pages
File Size : 49,6 Mb
Release : 2021-11-08
Category : Computers
ISBN : 9789811238666

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Algorithms: Design Techniques And Analysis (Second Edition) by M H Alsuwaiyel Pdf

Problem solving is an essential part of every scientific discipline. It has two components: (1) problem identification and formulation, and (2) the solution to the formulated problem. One can solve a problem on its own using ad hoc techniques or by following techniques that have produced efficient solutions to similar problems. This required the understanding of various algorithm design techniques, how and when to use them to formulate solutions, and the context appropriate for each of them.This book presents a design thinking approach to problem solving in computing — by first using algorithmic analysis to study the specifications of the problem, before mapping the problem on to data structures, then on to the situatable algorithms. Each technique or strategy is covered in its own chapter supported by numerous examples of problems and their algorithms. The new edition includes a comprehensive chapter on parallel algorithms, and many enhancements.

Author : Marina L. Gavrilova
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 49,8 Mb
Release : 2008-10-13
Category : Mathematics
ISBN : 9783540851257

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Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence by Marina L. Gavrilova Pdf

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.

Author : Jean-Daniel Boissonnat,Monique Teillaud
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 43,5 Mb
Release : 2006-10-24
Category : Mathematics
ISBN : 9783540332596

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Effective Computational Geometry for Curves and Surfaces by Jean-Daniel Boissonnat,Monique Teillaud Pdf

This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter fully details and provides a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice. Coverage includes references to open source software and discussion of potential applications of the presented techniques.

Author : Atsuyuki Okabe,Barry Boots,Kokichi Sugihara,Sung Nok Chiu
Publisher : John Wiley & Sons
Page : 696 pages
File Size : 51,8 Mb
Release : 2009-09-25
Category : Mathematics
ISBN : 9780470317853

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Spatial Tessellations by Atsuyuki Okabe,Barry Boots,Kokichi Sugihara,Sung Nok Chiu Pdf

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.

Author : Olek C Zienkiewicz,Robert L. Taylor,J.Z. Zhu
Publisher : Elsevier
Page : 753 pages
File Size : 50,8 Mb
Release : 2005-05-26
Category : Technology & Engineering
ISBN : 9780080472775

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The Finite Element Method: Its Basis and Fundamentals by Olek C Zienkiewicz,Robert L. Taylor,J.Z. Zhu Pdf

The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms. • The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises • With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics. The classic introduction to the finite element method, by two of the subject's leading authors Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text