New Trends In Discrete And Computational Geometry
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| 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.
| Author | : Bernard Chazelle |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 480 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821806742 |
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.
| Author | : Boris Aronov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 847 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642555667 |
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.
| Author | : Gergely Ambrus |
| Publisher | : Springer |
| Total Pages | : 461 |
| 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.
| Author | : Csaba D. Toth |
| Publisher | : CRC Press |
| Total Pages | : 1557 |
| Release | : 2004-04-13 |
| Genre | : Mathematics |
| ISBN | : 1420035312 |
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
| Author | : Jin Akiyama |
| Publisher | : Springer |
| Total Pages | : 187 |
| Release | : 2021-10-29 |
| Genre | : Computers |
| ISBN | : 9783030900472 |
This book constitutes the thoroughly refereed post-conference proceedings of the 21st Japanese Conference on Discrete and Computational Geometry and Graphs, JCDCGGG 2018, held in Quezon City, Philippines, in September 2018. The total of 14 papers included in this volume was carefully reviewed and selected from 25 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.
| Author | : Jacob E. Goodman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 568 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821842390 |
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.
| Author | : Mark de Berg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 370 |
| Release | : 2013-04-17 |
| Genre | : Computers |
| ISBN | : 3662042452 |
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.
| Author | : Sandip Das |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 418 |
| Release | : 2009-02-02 |
| Genre | : Computers |
| ISBN | : 3642002013 |
This book constitutes the refereed proceedings of the Third International Workshop on Algorithms and Computation, WALCOM 2009, held in Kolkata, India, in February 2009. The 30 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 102 submissions. The papers feature original research in the areas of design and analysis of algorithms, computational geometry, graph drawing and graph algorithms. The papers are organized in topical sections on computational geometry, graph algorithms, complexity, graph drawing, approximation algorithms, and randomized algorithms.
| Author | : Jiri Matousek |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 491 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461300398 |
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.
