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: 206

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]

Discrete and Computational Geometry

Containing both survey articles and research papers, this collection presents an excellent overview of significant recent progress in discrete and computational geometry.

Discrete and Computational Geometry

Author: Jacob E. Goodman

Publisher: American Mathematical Soc.

ISBN: 9780821871010

Page: 378

View: 415

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

This is 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 ...

Discrete and Computational Geometry

Author: Boris Aronov

Publisher: Springer Science & Business Media

ISBN: 3642555667

Page: 853

View: 961

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

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 ...

Surveys on Discrete and Computational Geometry

Author: Jacob E. Goodman

Publisher: American Mathematical Soc.

ISBN: 0821842390

Page: 556

View: 896

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

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: 3540477381

Page: 388

View: 649

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.

New Trends in Discrete and Computational Geometry

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.

New Trends in Discrete and Computational Geometry

Author: Janos Pach

Publisher: Springer Science & Business Media

ISBN: 3642580432

Page: 340

View: 382

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.

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: 589

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.

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: 600

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

Advances in Discrete and Computational Geometry

This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field.

Advances in Discrete and Computational Geometry

Author: Bernard Chazelle

Publisher: American Mathematical Soc.

ISBN: 0821806742

Page: 463

View: 375

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.

Invariant Methods in Discrete and Computational Geometry

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.

Invariant Methods in Discrete and Computational Geometry

Author: Neil L. White

Publisher: Springer Science & Business Media

ISBN: 9401584028

Page: 328

View: 543

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.

Handbook of Discrete and Computational Geometry

The Handbook of Discrete and Computational Geometry brings together, for the first time, all of the major results in both these fields into one volume.

Handbook of Discrete and Computational Geometry

Author: Csaba D. Toth

Publisher: CRC Press

ISBN: 9780849385247

Page: 1008

View: 601

Jacob E. Goodman, co-founder and editor of Discrete & Computational Geometry, the preeminent journal on this area in the international mathematics and computer science community, joins forces with the distinguished computer scientist Joseph O'Rourke and other well-known authorities to produce the definitive handbook on these two interrelated fields. Over the past decade or so, researchers and professionals in discrete geometry and the newer field of computational geometry have developed a highly productive collaborative relationship, where each area benefits from the methods and insights of the other. At the same time that discrete and computational geometry are becoming more closely identified, applications of the results of this work are being used in an increasing number of widely differing areas, from computer graphics and linear programming to manufacturing and robotics. The authors have answered the need for a comprehensive handbook for workers in these and related fields, and for other users of the body of results. While much information can be found on discrete and computational geometry, it is scattered among many sources, and individual books and articles are often narrowly focused. Handbook of Discrete and Computational Geometry brings together, for the first time, all of the major results in both these fields into one volume. Thousands of results - theorems, algorithms, and tables - throughout the volume definitively cover the field, while numerous applications from many different fields demonstrate practical usage. The material is presented clearly enough to assist the novice, but in enough depth to appeal to the specialist. Every technical term is clearly defined in an easy-to-use glossary. Over 200 figures illustrate the concepts presented and provide supporting examples. Information on current geometric software - what it does, how efficiently it does it, and where to find it - is also included.

Twentieth Anniversary Volume Discrete Computational Geometry

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.

Twentieth Anniversary Volume  Discrete   Computational Geometry

Author: Jacob E. Goodman

Publisher: Springer Science & Business Media

ISBN: 0387873635

Page: 635

View: 828

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.

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: 165

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.

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: 718

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.

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: 299

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.

Applied Geometry and Discrete Mathematics

This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's 65th birthday in September 1990.

Applied Geometry and Discrete Mathematics

Author: Peter Gritzmann

Publisher: American Mathematical Soc.

ISBN: 9780821870839

Page: 608

View: 171

This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's 65th birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics, education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honour of Klee's achievements, this volume presents more than 40 papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, this book shows how different branches of mathematics interact. It is a fitting tribute to one of the leading figures in discrete mathematics.

Algorithms in Combinatorial Geometry

The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure.

Algorithms in Combinatorial Geometry

Author: Herbert Edelsbrunner

Publisher: Springer Science & Business Media

ISBN: 9783540137221

Page: 423

View: 844

Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.

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: 445

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

Computational Discrete Mathematics

This book is based on a graduate education program on computational discrete mathematics run for several years in Berlin, Germany, as a joint effort of theoretical computer scientists and mathematicians in order to support doctoral students ...

Computational Discrete Mathematics

Author: Helmut Alt

Publisher: Springer

ISBN: 354045506X

Page: 173

View: 601

This book is based on a graduate education program on computational discrete mathematics run for several years in Berlin, Germany, as a joint effort of theoretical computer scientists and mathematicians in order to support doctoral students and advanced ongoing education in the field of discrete mathematics and algorithmics. The 12 selected lectures by leading researchers presented in this book provide recent research results and advanced topics in a coherent and consolidated way. Among the areas covered are combinatorics, graph theory, coding theory, discrete and computational geometry, optimization, and algorithmic aspects of algebra.