New Trends in Discrete and Computational Geometry
Title | New Trends in Discrete and Computational Geometry PDF eBook |
Author | Janos Pach |
Publisher | Springer Science & Business Media |
Total Pages | 342 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642580432 |
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
Title | Discrete and Computational Geometry PDF eBook |
Author | Satyan L. Devadoss |
Publisher | Princeton University Press |
Total Pages | 270 |
Release | 2011-04-11 |
Genre | Mathematics |
ISBN | 1400838983 |
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).
New Trends in Discrete and Computational Geometry
Title | New Trends in Discrete and Computational Geometry PDF eBook |
Author | Janos Pach |
Publisher | |
Total Pages | 356 |
Release | 2014-01-15 |
Genre | |
ISBN | 9783642580444 |
Handbook of Discrete and Computational Geometry
Title | Handbook of Discrete and Computational Geometry PDF eBook |
Author | Csaba D. Toth |
Publisher | CRC Press |
Total Pages | 2879 |
Release | 2017-11-22 |
Genre | Computers |
ISBN | 1351645919 |
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
Title | Discrete and Computational Geometry PDF eBook |
Author | |
Publisher | |
Total Pages | |
Release | 2006 |
Genre | |
ISBN |
Discrete Geometry
Title | Discrete Geometry PDF eBook |
Author | Andras Bezdek |
Publisher | CRC Press |
Total Pages | 489 |
Release | 2003-02-04 |
Genre | Mathematics |
ISBN | 0203911210 |
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 analy
New Trends in Intuitive Geometry
Title | New Trends in Intuitive Geometry PDF eBook |
Author | Gergely Ambrus |
Publisher | Springer |
Total Pages | 458 |
Release | 2018-11-03 |
Genre | Mathematics |
ISBN | 3662574136 |
This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.