Discrete and Computational Geometry
Discrete and Computational Geometry

Author: Satyan L. Devadoss

Publisher: Princeton University Press

Published: 2011-04-11

Total Pages: 270

ISBN-13: 1400838983

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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
Handbook of Discrete and Computational Geometry

Author: Csaba D. Toth

Publisher: CRC Press

Published: 2017-11-22

Total Pages: 2354

ISBN-13: 1351645919

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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.

Handbook of Discrete and Computational Geometry
Handbook of Discrete and Computational Geometry

Author: Csaba D. Toth

Publisher: CRC Press

Published: 1997-07-15

Total Pages: 1008

ISBN-13: 9780849385247

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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.

New Trends in Discrete and Computational Geometry
New Trends in Discrete and Computational Geometry

Author: Janos Pach

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 342

ISBN-13: 3642580432

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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.

Lectures on Discrete Geometry
Lectures on Discrete Geometry

Author: Jiri Matousek

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 491

ISBN-13: 1461300398

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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.

Computational Geometry
Computational Geometry

Author: Franco P. Preparata

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 413

ISBN-13: 1461210984

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From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2

Forbidden Configurations in Discrete Geometry
Forbidden Configurations in Discrete Geometry

Author: David Eppstein

Publisher: Cambridge University Press

Published: 2018-05-17

Total Pages: 241

ISBN-13: 1108423914

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

Computational Geometry
Computational Geometry

Author: Mark de Berg

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 370

ISBN-13: 3662042452

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This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Classical Topics in Discrete Geometry
Classical Topics in Discrete Geometry

Author: Károly Bezdek

Publisher: Springer Science & Business Media

Published: 2010-06-23

Total Pages: 171

ISBN-13: 1441906002

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Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.