New Trends In Discrete And Computational Geometry

Author : Janos Pach
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580437

Get Book

New Trends in Discrete and Computational Geometry by Janos Pach Pdf

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 : Janos Pach
Publisher : Unknown
Page : 356 pages
File Size : 53,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3642580440

Get Book

New Trends in Discrete and Computational Geometry by Janos Pach Pdf

Author : Satyan L. Devadoss,Joseph O'Rourke
Publisher : Princeton University Press
Page : 270 pages
File Size : 41,6 Mb
Release : 2011-04-11
Category : Mathematics
ISBN : 9781400838981

Get Book

Discrete and Computational Geometry by Satyan L. Devadoss,Joseph O'Rourke Pdf

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).

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 2879 pages
File Size : 40,8 Mb
Release : 2017-11-22
Category : Computers
ISBN : 9781351645911

Get Book

Handbook of Discrete and Computational Geometry by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,9 Mb
Release : 2006
Category : Electronic
ISBN : OCLC:500060102

Get Book

Discrete and Computational Geometry by Anonim Pdf

Author : Andras Bezdek
Publisher : CRC Press
Page : 489 pages
File Size : 52,8 Mb
Release : 2003-02-04
Category : Mathematics
ISBN : 9780203911211

Get Book

Discrete Geometry by Andras Bezdek Pdf

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

Author : Gergely Ambrus,Imre Bárány,Károly J. Böröczky,Gábor Fejes Tóth,János Pach
Publisher : Springer
Page : 458 pages
File Size : 41,5 Mb
Release : 2018-11-03
Category : Mathematics
ISBN : 9783662574133

Get Book

New Trends in Intuitive Geometry by Gergely Ambrus,Imre Bárány,Károly J. Böröczky,Gábor Fejes Tóth,János Pach Pdf

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 : Bernard Chazelle,Jacob E. Goodman,Richard Pollack
Publisher : American Mathematical Soc.
Page : 463 pages
File Size : 45,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821806746

Get Book

Advances in Discrete and Computational Geometry by Bernard Chazelle,Jacob E. Goodman,Richard Pollack Pdf

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 : Jacob E. Goodman
Publisher : American Mathematical Soc.
Page : 568 pages
File Size : 54,7 Mb
Release : 2008
Category : Combinatorial geometry
ISBN : 9780821842393

Get Book

Surveys on Discrete and Computational Geometry by Jacob E. Goodman Pdf

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 : Boris Aronov,Saugata Basu,Janos Pach,Micha Sharir
Publisher : Springer Science & Business Media
Page : 853 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642555664

Get Book

Discrete and Computational Geometry by Boris Aronov,Saugata Basu,Janos Pach,Micha Sharir Pdf

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 : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1557 pages
File Size : 48,7 Mb
Release : 2004-04-13
Category : Mathematics
ISBN : 9781420035315

Get Book

Handbook of Discrete and Computational Geometry, Second Edition by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

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 : Franco P. Preparata,Michael I. Shamos
Publisher : Springer Science & Business Media
Page : 413 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210986

Get Book

Computational Geometry by Franco P. Preparata,Michael I. Shamos Pdf

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

Author : Jin Akiyama,Reginaldo M. Marcelo,Mari-Jo P. Ruiz,Yushi Uno
Publisher : Springer Nature
Page : 196 pages
File Size : 49,6 Mb
Release : 2021-10-28
Category : Computers
ISBN : 9783030900489

Get Book

Discrete and Computational Geometry, Graphs, and Games by Jin Akiyama,Reginaldo M. Marcelo,Mari-Jo P. Ruiz,Yushi Uno Pdf

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 : Joseph O'Rourke
Publisher : Cambridge University Press
Page : 396 pages
File Size : 47,8 Mb
Release : 1998-10-13
Category : Computers
ISBN : 0521649765

Get Book

Computational Geometry in C by Joseph O'Rourke Pdf

This 1998 book explains the design of geometry algorithms, including discussion of implementation issues and working C code.

Author : J.R. Sack,J. Urrutia
Publisher : Elsevier
Page : 1075 pages
File Size : 54,8 Mb
Release : 1999-12-13
Category : Mathematics
ISBN : 0080529682

Get Book

Handbook of Computational Geometry by J.R. Sack,J. Urrutia Pdf

Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.