discrete-and-computational-geometry

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Discrete and Computational Geometry

Author : Satyan L. Devadoss
Publisher : Princeton University Press
ISBN 13 : 1400838983
Total Pages : 270 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Discrete and Computational Geometry by : Satyan L. Devadoss

Download or read book Discrete and Computational Geometry written by Satyan L. Devadoss and published by Princeton University Press. This book was released on 2011-04-11 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential introduction to discrete and computational geometry Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only).

Handbook of Discrete and Computational Geometry

Author : Csaba D. Toth
Publisher : CRC Press
ISBN 13 : 1498711421
Total Pages : 1928 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Handbook of Discrete and Computational Geometry by : Csaba D. Toth

Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 1928 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Discrete and Computational Geometry

Author : Jacob E. Goodman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871010
Total Pages : 394 pages
Book Rating : 4.8/5 (71 download)

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Book Synopsis Discrete and Computational Geometry by : Jacob E. Goodman

Download or read book Discrete and Computational Geometry written by Jacob E. Goodman and published by American Mathematical Soc.. This book was released on 1991-01-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first DIMACS special year, held during 1989-1990, was devoted to discrete and computational geometry. More than 200 scientists, both long- and short-term visitors, came to DIMACS to participate in the special year activities. Among the highlights were six workshops at Rutgers and Princeton Universities that defined the focus for much of the special year. The workshops addressed the following topics: geometric complexity, probabilistic methods in discrete and computational geometry, polytopes and convex sets, arrangements, and algebraic and practical issues in geometric computation. This volume presents some of the results growing out of the workshops and the special year activities. Containing both survey articles and research papers, this collection presents an excellent overview of significant recent progress in discrete and computational geometry. The diversity of these papers demonstrate how geometry continues to provide a vital source of ideas in theoretical computer science and discrete mathematics as well as fertile ground for interaction and simulation between the two disciplines.

Surveys on Discrete and Computational Geometry

Author : Jacob E. Goodman
Publisher : American Mathematical Soc.
ISBN 13 : 0821842390
Total Pages : 568 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Surveys on Discrete and Computational Geometry by : Jacob E. Goodman

Download or read book Surveys on Discrete and Computational Geometry written by Jacob E. Goodman and published by American Mathematical Soc.. This book was released on 2008 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains nineteen survey papers describing the state of current research in discrete and computational geometry as well as a set of open problems presented at the 2006 AMS-IMS-SIAM Summer Research Conference Discrete and Computational Geometry--Twenty Years Later, held in Snowbird, Utah, in June 2006. Topics surveyed include metric graph theory, lattice polytopes, the combinatorial complexity of unions of geometric objects, line and pseudoline arrangements, algorithmic semialgebraic geometry, persistent homology, unfolding polyhedra, pseudo-triangulations, nonlinear computational geometry, $k$-sets, and the computational complexity of convex bodies.

New Trends in Discrete and Computational Geometry

Author : Janos Pach
Publisher : Springer Science & Business Media
ISBN 13 : 3642580432
Total Pages : 342 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis New Trends in Discrete and Computational Geometry by : Janos Pach

Download or read book New Trends in Discrete and Computational Geometry written by Janos Pach and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete and computational geometry are two fields which in recent years have benefitted from the interaction between mathematics and computer science. The results are applicable in areas such as motion planning, robotics, scene analysis, and computer aided design. The book consists of twelve chapters summarizing the most recent results and methods in discrete and computational geometry. All authors are well-known experts in these fields. They give concise and self-contained surveys of the most efficient combinatorical, probabilistic and topological methods that can be used to design effective geometric algorithms for the applications mentioned above. Most of the methods and results discussed in the book have not appeared in any previously published monograph. In particular, this book contains the first systematic treatment of epsilon-nets, geometric tranversal theory, partitions of Euclidean spaces and a general method for the analysis of randomized geometric algorithms. Apart from mathematicians working in discrete and computational geometry this book will also be of great use to computer scientists and engineers, who would like to learn about the most recent results.

Discrete and Computational Geometry

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Discrete and Computational Geometry by :

Download or read book Discrete and Computational Geometry written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Twentieth Anniversary Volume: Discrete & Computational Geometry

Author : Jacob E. Goodman
Publisher : Springer Science & Business Media
ISBN 13 : 0387873635
Total Pages : 652 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Twentieth Anniversary Volume: Discrete & Computational Geometry by : Jacob E. Goodman

Download or read book Twentieth Anniversary Volume: Discrete & Computational Geometry written by Jacob E. Goodman and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This commemorative book contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal Discrete & Computational Geometry, and presents a comprehensive picture of the current state of the field. The articles in this volume, a number of which solve long-outstanding problems in the field, were chosen by the editors of DCG for the importance of their results, for the breadth of their scope, and to show the intimate connections that have arisen between discrete and computational geometry and other areas of both computer science and mathematics. Apart from the articles, the editors present an expanded preface, along with a set of photographs of groups and individuals who have played a major role in the history of the field during the past twenty years.

Discrete Geometry

Author : Andras Bezdek
Publisher : CRC Press
ISBN 13 : 0824747615
Total Pages : 500 pages
Book Rating : 4.8/5 (247 download)

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Book Synopsis Discrete Geometry by : Andras Bezdek

Download or read book Discrete Geometry written by Andras Bezdek and published by CRC Press. This book was released on 2003-02-04 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.

Discrete and Computational Geometry

Author : Jacob E. Goodman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821865958
Total Pages : 378 pages
Book Rating : 4.8/5 (659 download)

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Book Synopsis Discrete and Computational Geometry by : Jacob E. Goodman

Download or read book Discrete and Computational Geometry written by Jacob E. Goodman and published by American Mathematical Soc.. This book was released on 1991-01-01 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first DIMACS special year, held during 1989-1990, was devoted to discrete and computational geometry. The workshops addressed the following topics: geometric complexity, probabilistic methods in discrete and computational geometry, polytopes and convex sets, arrangements, and algebraic and practical issues in geometric computation. This volume presents results of the workshops and the special year activities. Containing both survey articles and research papers, this collection presents an excellent overview of discrete and computational geometry. The diversity of these papers demonstrate how geometry continues to provide a vital source of ideas in theoretical computer science and discrete mathematics as well as fertile ground for interaction and stimulation between the two disciplines.

Advances in Discrete and Computational Geometry

Author : Bernard Chazelle
Publisher : American Mathematical Soc.
ISBN 13 : 0821806742
Total Pages : 463 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advances in Discrete and Computational Geometry by : Bernard Chazelle

Download or read book Advances in Discrete and Computational Geometry written by Bernard Chazelle and published by American Mathematical Soc.. This book was released on 1999 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field. Articles are based on invited talks presented at the AMS-IMS-SIAM Summer Research Conference, ``Discrete and Computational Geometry: Ten Years Later'', held in 1996 at Mt. Holyoke College (So. Hadley, MA). Topics addressed range from tilings, polyhedra, and arrangements to computational topology and visibility problems. Included are papers on the interaction between real algebraic geometry and discrete and computational geometry, as well as on linear programming and geometric discrepancy theory.

Discrete and Computational Geometry

Author : Jin Akiyama
Publisher :
ISBN 13 : 9783662179277
Total Pages : 348 pages
Book Rating : 4.1/5 (792 download)

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Book Synopsis Discrete and Computational Geometry by : Jin Akiyama

Download or read book Discrete and Computational Geometry written by Jin Akiyama and published by . This book was released on 2014-01-15 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Discrete and Computational Geometry

Author : Boris Aronov
Publisher : Springer Science & Business Media
ISBN 13 : 3642555667
Total Pages : 853 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Discrete and Computational Geometry by : Boris Aronov

Download or read book Discrete and Computational Geometry written by Boris Aronov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 853 pages. Available in PDF, EPUB and Kindle. Book excerpt: An impressive collection of original research papers in discrete and computational geometry, contributed by many leading researchers in these fields, as a tribute to Jacob E. Goodman and Richard Pollack, two of the ‘founding fathers’ of the area, on the occasion of their 2/3 x 100 birthdays. The topics covered by the 41 papers provide professionals and graduate students with a comprehensive presentation of the state of the art in most aspects of discrete and computational geometry, including geometric algorithms, study of arrangements, geometric graph theory, quantitative and algorithmic real algebraic geometry, with important connections to algebraic geometry, convexity, polyhedral combinatorics, the theory of packing, covering, and tiling. The book serves as an invaluable source of reference in this discipline.

Lectures on Discrete Geometry

Author : Jiri Matousek
Publisher : Springer Science & Business Media
ISBN 13 : 1461300398
Total Pages : 491 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Lectures on Discrete Geometry by : Jiri Matousek

Download or read book Lectures on Discrete Geometry written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.

Discrete and Computational Geometry

Author : Jin Akiyama
Publisher : Springer
ISBN 13 : 3540465154
Total Pages : 340 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Discrete and Computational Geometry by : Jin Akiyama

Download or read book Discrete and Computational Geometry written by Jin Akiyama and published by Springer. This book was released on 2004-05-26 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of those papers presented at the Japan Conference on Discrete and Computational Geometry ’98. The conference was held 9-12 - cember 1998 at Tokai University in Tokyo. Close to a hundred participants from 10 countries participated. Interest in Computational Geometry surfaced among engineers in Japan - out twenty years ago, while interest in Discrete Geometry arose as a natural extension of the research of a group of graph theorists more recently. One of the goals of the conference was to bring together these two groups and to put them in contact with experts in these ?elds from abroad. This is the second conference in the series. The plan is to hold one every year and to publish the papers of the conferences every two years. The organizers thank the sponsors of the conference, namely, The Institute of Educational Development of Tokai University, Grant-in-Aid of the Ministry of Education of Japan (A.Saito;(A)10304008), Mitsubishi Research Institute, Sanada Institute of System Development, Japan Process, and Upward. They also thank especially T. Asano, D. Avis, V. Chv ́ atal, H. Imai, J. Pach, D. R- paport, M. Ruiz, J. O’Rourke, K. Sugihara, T. Tokuyama, and J. Urrutia for their interest and support.

Digital and Discrete Geometry

Author : Li M. Chen
Publisher : Springer
ISBN 13 : 3319120999
Total Pages : 322 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Digital and Discrete Geometry by : Li M. Chen

Download or read book Digital and Discrete Geometry written by Li M. Chen and published by Springer. This book was released on 2014-12-12 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData. The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and advanced topics. Chapters especially focus on the applications of these methods to other types of geometry, algebraic topology, image processing, computer vision and computer graphics. Digital and Discrete Geometry: Theory and Algorithms targets researchers and professionals working in digital image processing analysis, medical imaging (such as CT and MRI) and informatics, computer graphics, computer vision, biometrics, and information theory. Advanced-level students in electrical engineering, mathematics, and computer science will also find this book useful as a secondary text book or reference. Praise for this book: This book does present a large collection of important concepts, of mathematical, geometrical, or algorithmical nature, that are frequently used in computer graphics and image processing. These concepts range from graphs through manifolds to homology. Of particular value are the sections dealing with discrete versions of classic continuous notions. The reader finds compact definitions and concise explanations that often appeal to intuition, avoiding finer, but then necessarily more complicated, arguments... As a first introduction, or as a reference for professionals working in computer graphics or image processing, this book should be of considerable value." - Prof. Dr. Rolf Klein, University of Bonn.

Discrete and Computational Geometry

Author : Jin Akiyama
Publisher : Springer
ISBN 13 : 9783540671817
Total Pages : 340 pages
Book Rating : 4.6/5 (718 download)

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Book Synopsis Discrete and Computational Geometry by : Jin Akiyama

Download or read book Discrete and Computational Geometry written by Jin Akiyama and published by Springer. This book was released on 2000-02-16 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of those papers presented at the Japan Conference on Discrete and Computational Geometry ’98. The conference was held 9-12 - cember 1998 at Tokai University in Tokyo. Close to a hundred participants from 10 countries participated. Interest in Computational Geometry surfaced among engineers in Japan - out twenty years ago, while interest in Discrete Geometry arose as a natural extension of the research of a group of graph theorists more recently. One of the goals of the conference was to bring together these two groups and to put them in contact with experts in these ?elds from abroad. This is the second conference in the series. The plan is to hold one every year and to publish the papers of the conferences every two years. The organizers thank the sponsors of the conference, namely, The Institute of Educational Development of Tokai University, Grant-in-Aid of the Ministry of Education of Japan (A.Saito;(A)10304008), Mitsubishi Research Institute, Sanada Institute of System Development, Japan Process, and Upward. They also thank especially T. Asano, D. Avis, V. Chv ́ atal, H. Imai, J. Pach, D. R- paport, M. Ruiz, J. O’Rourke, K. Sugihara, T. Tokuyama, and J. Urrutia for their interest and support.

Forbidden Configurations in Discrete Geometry

Author : David Eppstein
Publisher : Cambridge University Press
ISBN 13 : 1108542972
Total Pages : 242 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Forbidden Configurations in Discrete Geometry by : David Eppstein

Download or read book Forbidden Configurations in Discrete Geometry written by David Eppstein and published by Cambridge University Press. This book was released on 2018-05-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.