Handbook of Discrete and Computational Geometry, Second Edition

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Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 9781420035315

Category: Mathematics

Page: 1560

View: 2312

While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies

Surveys on Discrete and Computational Geometry

Twenty Years Later : AMS-IMS-SIAM Joint Summer Research Conference, June 18-22, 2006, Snowbird, Utah

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Author: Jacob E. Goodman

Publisher: American Mathematical Soc.

ISBN: 0821842390

Category: Mathematics

Page: 556

View: 7319

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.

Discrete and Computational Geometry

Papers from the DIMACS Special Year

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Author: Jacob E. Goodman,Richard D. Pollack,William L. Steiger

Publisher: American Mathematical Soc.

ISBN: 9780821871010

Category: Mathematics

Page: 378

View: 7523

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.

Discrete and Computational Geometry

The Goodman-Pollack Festschrift

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Author: Boris Aronov,Saugata Basu,Janos Pach,Micha Sharir

Publisher: Springer Science & Business Media

ISBN: 3642555667

Category: Mathematics

Page: 853

View: 9804

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.

Discrete and Computational Geometry

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Author: Satyan L. Devadoss,Joseph O'Rourke

Publisher: Princeton University Press

ISBN: 9781400838981

Category: Mathematics

Page: 280

View: 2243

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). To obtain access, please e-mail: [email protected]

Advances in Discrete and Computational Geometry

Proceedings of the 1996 AMS-IMS-SIAM Joint Summer Research Conference, Discrete and Computational Geometry--Ten Years Later, July 14-18, 1996, Mount Holyoke College

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Author: Bernard Chazelle,Jacob E. Goodman,Richard Pollack

Publisher: American Mathematical Soc.

ISBN: 0821806742

Category: Mathematics

Page: 463

View: 9005

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

Japanese Conference, JCDCG 2004, Tokyo, Japan, October 8-11, 2004

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Author: Jin Akiyama

Publisher: Springer Science & Business Media

ISBN: 3540304673

Category: Computers

Page: 212

View: 1836

This volume consists of the refereed proceedings of the Japan Conference on Discrete and Computational Geometry (JCDCG 2004) held at Tokai University in Tokyo, Japan, October, 8-11, 2004, to honor Jan ́ os Pach on his 50th year. J ́ anos Pach has generously supported the e'orts to promote research in discrete and computational geometry among mathematicians in Asia for many years. The conference was attended by close to 100 participants from 20 countries. Since it was ?rst organized in 1997, the annual JCDCG has attracted a growing international participation. The earlier conferences were held in Tokyo, followed by conferences in Manila, Philippines, and Bandung, Indonesia. The proceedings of JCDCG 1998, 2000, 2002 and IJCCGGT 2003 were published by SpringeraspartoftheseriesLectureNotesinComputerScience(LNCS)volumes 1763, 2098, 2866 and 3330, respectively, while the proceedings of JCDCG 2001 were also published by Springer as a special issue of the journal Graphs and Combinatorics, Vol. 18, No. 4, 2002. The organizers of JCDCG 2004 gratefully acknowledge the sponsorship of Tokai University, the support of the conference secretariat and the partici- tion of the principal speakers: Ferran Hurtado, Hiro Ito, Alberto M ́ arquez, Ji? r ́ ? Matou? sek, Ja ́nos Pach, Jonathan Shewchuk, William Steiger, Endre Szemer ́ edi, G ́ eza T ́ oth, Godfried Toussaint and Jorge Urrutia.

Handbook of Discrete and Computational Geometry, Third Edition

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Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 1498711421

Category: Computers

Page: 1928

View: 9312

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 ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly 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 ?eld 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.

Differential Geometry and Topology, Discrete and Computational Geometry

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Author: Mohamed Boucetta,J.-M. Morvan

Publisher: IOS Press

ISBN: 158603507X

Category: Mathematics

Page: 373

View: 2599

The aim of this volume is to give an introduction and overview to differential topology, differential geometry and computational geometry with an emphasis on some interconnections between these three domains of mathematics. The chapters give the background required to begin research in these fields or at their interfaces. They introduce new research domains and both old and new conjectures in these different subjects show some interaction between other sciences close to mathematics. Topics discussed are; the basis of differential topology and combinatorial topology, the link between differential geometry and topology, Riemanian geometry (Levi-Civita connextion, curvature tensor, geodesic, completeness and curvature tensor), characteristic classes (to associate every fibre bundle with isomorphic fiber bundles), the link between differential geometry and the geometry of non smooth objects, computational geometry and concrete applications such as structural geology and graphism.

Invariant Methods in Discrete and Computational Geometry

Proceedings of the Curaçao Conference, 13–17 June, 1994

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Author: Neil L. White

Publisher: Springer Science & Business Media

ISBN: 9401584028

Category: Computers

Page: 328

View: 974

Invariant, or coordinate-free methods provide a natural framework for many geometric questions. Invariant Methods in Discrete and Computational Geometry provides a basic introduction to several aspects of invariant theory, including the supersymmetric algebra, the Grassmann-Cayler algebra, and Chow forms. It also presents a number of current research papers on invariant theory and its applications to problems in geometry, such as automated theorem proving and computer vision. Audience: Researchers studying mathematics, computers and robotics.

New Trends in Discrete and Computational Geometry

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Author: Janos Pach

Publisher: Springer Science & Business Media

ISBN: 3642580432

Category: Mathematics

Page: 340

View: 9934

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 and Graphs

16th Japanese Conference, JCDCGG 2013, Tokyo, Japan, September 17-19, 2013, Revised Selected Papers

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Author: Jin Akiyama,Hiro Ito,Toshinori Sakai

Publisher: Springer

ISBN: 3319132873

Category: Computers

Page: 191

View: 5794

This book constitutes the thoroughly refereed post-conference proceedings of the 16th Japanese Conference on Discrete and computational Geometry and Graphs, JDCDGG 2013, held in Tokyo, Japan, in September 2013. The total of 16 papers included in this volume was carefully reviewed and selected from 58 submissions. The papers feature advances made in the field of computational geometry and focus on emerging technologies, new methodology and applications, graph theory and dynamics.

Handbook of Discrete and Computational Geometry, Third Edition

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Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 1351645919

Category: Computers

Page: 1928

View: 6502

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 ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly 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 ?eld 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.

Combinatorial and Computational Geometry

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Author: Jacob E. Goodman,Janos Pach,Emo Welzl

Publisher: Cambridge University Press

ISBN: 9780521848626

Category: Computers

Page: 616

View: 2788

This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Advances in Discrete and Computational Geometry

Proceedings of the 1996 AMS-IMS-SIAM Joint Summer Research Conference, Discrete and Computational Geometry--Ten Years Later, July 14-18, 1996, Mount Holyoke College

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Author: Bernard Chazelle,Jacob E. Goodman,Richard Pollack

Publisher: American Univ in Cairo Press

ISBN: 9780821806746

Category: Mathematics

Page: 463

View: 4070

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

Japanese Conference, JCDCG'98 Tokyo, Japan, December 9-12, 1998 Revised Papers

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Author: Japan) Jcdcg 9 (1998 Tokyo,Jin Akiyama

Publisher: Springer Science & Business Media

ISBN: 3540671811

Category: Computers

Page: 331

View: 7929

This book constitutes the thoroughly refereed post-conference proceedings of the Second Japanese Conference on Discrete and Computational Geometry, JCDCG8, held in Tokyo, Japan, in December 1999. The 27 revised full papers presented were carefully reviewed and selected for inclusion in the post-conference proceedings. Among the topics addressed are approximation, convex hulls, lattice computations, tilings, graph computations, Voronoi diagrams, clustering, graph drawing, diagram design, and illumination problems.

Twentieth Anniversary Volume: Discrete & Computational Geometry

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Author: Jacob E. Goodman,János Pach,Richard Pollack

Publisher: Springer Science & Business Media

ISBN: 0387873635

Category: Mathematics

Page: 635

View: 3395

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.

Algorithmische Geometrie

Polyedrische und algebraische Methoden

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Author: Michael Joswig,Thorsten Theobald

Publisher: Springer-Verlag

ISBN: 3834894400

Category: Mathematics

Page: 266

View: 1272

In dem Lehrbuch wird eine mathematisch orientierte Einführung in die algorithmische Geometrie gegeben. Im ersten Teil werden „klassische“ Probleme und Techniken behandelt, die sich auf polyedrische (= linear begrenzte) Objekte beziehen. Hierzu gehören beispielsweise Algorithmen zur Berechnung konvexer Hüllen und die Konstruktion von Voronoi-Diagrammen. Im zweiten Teil werden grundlegende Methoden der algorithmischen algebraischen Geometrie entwickelt und anhand von Anwendungen aus Computergrafik, Kurvenrekonstruktion und Robotik illustriert. Das Buch eignet sich für ein fortgeschrittenes Modul in den derzeit neu konzipierten Bachelor-Studiengängen in Mathematik und Informatik.

Computational Geometry, Graphs and Applications

International Conference,CGGA 2010, Dalian, China, November 3-6, 2010, Revised, Selected Papers

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Author: Jin Akiyama,Bo Jiang,Mikio Kano,Xuehou Tan

Publisher: Springer Science & Business Media

ISBN: 3642249825

Category: Computers

Page: 227

View: 9372

This book constitutes the thoroughly refereed post-conference proceedings of the China-Japan Joint Conference on Computational Geometry, Graphs and Applications, CGGA 2010, held in Dalian, China, in November 2010. The 23 revised full papers presented were carefully selected during two rounds of reviewing and improvement from numerous submissions. All aspects of computational and discrete geometry, graph theory, graph algorithms, and their applications are covered.