Discrete and Computational Geometry

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.

Discrete and Computational Geometry

Author: Satyan L. Devadoss

Publisher: Princeton University Press

ISBN: 9781400838981

Page: 280

View: 245

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]

Handbook of Discrete and Computational Geometry Second Edition

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 ...

Handbook of Discrete and Computational Geometry  Second Edition

Author: Csaba D. Toth

Publisher: CRC Press

ISBN: 9781420035315

Page: 1560

View: 208

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

Handbook of Discrete and Computational Geometry Third Edition

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.

Handbook of Discrete and Computational Geometry  Third Edition

Author: Csaba D. Toth

Publisher: CRC Press

ISBN: 1351645919

Page: 1928

View: 913

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.

Discrete and Computational Geometry

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.

Discrete and Computational Geometry

Author: Japan) Jcdcg 9 (1998 Tokyo

Publisher: Springer Science & Business Media

ISBN: 3540671811

Page: 331

View: 939

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.

Differential Geometry and Topology Discrete and Computational Geometry

Differential Geometry and Topology  Discrete and Computational Geometry

Author: Mohamed Boucetta

Publisher: IOS Press

ISBN: 158603507X

Page: 373

View: 955

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.

Discrete and Computational Geometry

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.

Discrete and Computational Geometry

Author: Jin Akiyama

Publisher: Springer

ISBN: 9783540671817

Page: 340

View: 309

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.

Discrete and Computational Geometry

This book constitutes the thoroughly refereed post-proceedings of the Japanese Conference on Discrete Computational Geometry, JCDCG 2001, held in Tokyo, Japan in November 2001.

Discrete and Computational Geometry

Author: Jin Akiyama

Publisher: Springer

ISBN: 9783540423065

Page: 388

View: 557

This book constitutes the thoroughly refereed post-proceedings of the Japanese Conference on Discrete Computational Geometry, JCDCG 2001, held in Tokyo, Japan in November 2001. The 35 revised papers presented were carefully reviewed and selected. Among the topics covered are polygons and polyhedrons, divissible dissections, convex polygon packings, symmetric subsets, convex decompositions, graph drawing, graph computations, point sets, approximation, Delauny diagrams, triangulations, chromatic numbers, complexity, layer routing, efficient algorithms, and illumination problems.

Handbook of Discrete and Computational Geometry

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.

Handbook of Discrete and Computational Geometry

Author: Csaba D. Toth

Publisher: CRC Press

ISBN: 1498711421

Page: 1928

View: 398

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.

Differential Geometry and Topology Discrete and Computational Geometry

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.

Differential Geometry and Topology  Discrete and Computational Geometry

Author: Mohamed Boucetta

Publisher: Ios PressInc

ISBN: 9781586035075

Page: 373

View: 413

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.

Advances in Discrete and Computational Geometry

Advances in Discrete and Computational Geometry

Author: Bernard Chazelle

Publisher: American Univ in Cairo Press

ISBN: 9780821806746

Page: 463

View: 590

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

In 1984, after it had become clear that their work had implications not only in the
well-established discipline of discrete geometry but also in the then nascent field
of computational geometry, the opportunity arose of founding a journal devoted ...

Discrete and Computational Geometry

Author: Boris Aronov

Publisher: Springer Science & Business Media

ISBN: 9783540003717

Page: 853

View: 943

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.

Surveys on Discrete and Computational Geometry

Discrete and Computational Geometry, 32:567– 600, 2004. [42] D. Orden and F.
Santos. The polytope of non-crossing graphs on a planar point set. Discrete and
Computational Geometry, 33:275-305, 2005. [43] D. Orden, F. Santos, ...

Surveys on Discrete and Computational Geometry

Author: Jacob E. Goodman

Publisher: American Mathematical Soc.

ISBN: 0821842390

Page: 556

View: 951

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

Introduction In computational geometry it is a truism that problems in three-
dimensional space, R3 , are significantly more difficult and complex than the
corresponding problems in the two-dimensional plane, R' . Of course, reality is
not that ...

Discrete and Computational Geometry

Author: Jacob E. Goodman

Publisher: American Mathematical Soc.

ISBN: 9780821871010

Page: 378

View: 532

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 and Graphs

Computational Geometry in the Human Brain Kokichi Sugihara(B) Graduate
School of Advanced Mathematical ... Geometric information processing in the
human brain is very different from that in a computer: it is slow, local, and
imprecise.

Discrete and Computational Geometry and Graphs

Author: Jin Akiyama

Publisher: Springer

ISBN: 3319132873

Page: 191

View: 793

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.

Invariant Methods in Discrete and Computational Geometry

It is based on a sequence of four lectures given at the conference on " Invariant
Methods in Discrete and Computational Geometry " , Curacao , Netherlands
Antilles , June 1994. We thank the organizer , Neil White , for giving us the
opportunity ...

Invariant Methods in Discrete and Computational Geometry

Author: Neil L. White

Publisher: Springer Science & Business Media

ISBN: 9780792335481

Page: 328

View: 153

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.

Twentieth Anniversary Volume Discrete Computational Geometry

Jacob E. Goodman, János Pach, Richard Pollack. Twentieth Anniversary Volume
Discrete & Computational Geometry Twentieth Anniversary Volume Discrete &
Computational Geometry Editors Jacob E. 162642_1_En_FM1_OnlinePDF.pdf.

Twentieth Anniversary Volume  Discrete   Computational Geometry

Author: Jacob E. Goodman

Publisher: Springer Science & Business Media

ISBN: 0387873635

Page: 635

View: 617

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.

Lectures on Discrete Geometry

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 ...

Lectures on Discrete Geometry

Author: Ji?í Matoušek

Publisher: Springer Science & Business Media

ISBN: 9780387953731

Page: 486

View: 679

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.

Forbidden Configurations in Discrete Geometry

Unifies discrete and computational geometry by using forbidden patterns of points to characterize many of its problems.

Forbidden Configurations in Discrete Geometry

Author: David Eppstein

Publisher: Cambridge University Press

ISBN: 1108423914

Page: 194

View: 677

Unifies discrete and computational geometry by using forbidden patterns of points to characterize many of its problems.

Discrete Geometry

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 ...

Discrete Geometry

Author: Andras Bezdek

Publisher: CRC Press

ISBN: 0824747615

Page: 464

View: 193

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.