Handbook Of Discrete And Computational Geometry

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1928 pages
File Size : 42,5 Mb
Release : 2017-11-22
Category : Computers
ISBN : 9781498711425

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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 : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1557 pages
File Size : 45,6 Mb
Release : 2004-04-13
Category : Mathematics
ISBN : 9781420035315

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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 : Satyan L. Devadoss,Joseph O'Rourke
Publisher : Princeton University Press
Page : 270 pages
File Size : 49,9 Mb
Release : 2011-04-11
Category : Mathematics
ISBN : 9781400838981

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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 : J.R. Sack,J. Urrutia
Publisher : Elsevier
Page : 1075 pages
File Size : 51,9 Mb
Release : 1999-12-13
Category : Mathematics
ISBN : 0080529682

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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.

Author : Jacob E. Goodman,Joseph O'Rourke,Csaba D. Tóth
Publisher : Unknown
Page : 0 pages
File Size : 47,7 Mb
Release : 2023
Category : Combinatorial geometry
ISBN : 757670652X

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Handbook of Discrete and Computational Geometry, 3e by Jacob E. Goodman,Joseph O'Rourke,Csaba D. Tóth Pdf

Author : Jacob E. Goodman,Janos Pach,Emo Welzl
Publisher : Cambridge University Press
Page : 640 pages
File Size : 51,9 Mb
Release : 2005-08-08
Category : Computers
ISBN : 0521848628

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Combinatorial and Computational Geometry by Jacob E. Goodman,Janos Pach,Emo Welzl Pdf

This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Author : Kenneth H. Rosen
Publisher : CRC Press
Page : 1611 pages
File Size : 41,5 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351644051

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Handbook of Discrete and Combinatorial Mathematics by Kenneth H. Rosen Pdf

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

Author : Franco P. Preparata,Michael I. Shamos
Publisher : Springer Science & Business Media
Page : 413 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210986

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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 : Jiri Matousek
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 40,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461300397

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Lectures on Discrete Geometry by Jiri Matousek Pdf

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.

Author : Joseph O'Rourke
Publisher : Cambridge University Press
Page : 128 pages
File Size : 53,6 Mb
Release : 1998-10-13
Category : Computers
ISBN : 9781107268630

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Computational Geometry in C by Joseph O'Rourke Pdf

This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp.

Author : Edward R. Fadell,Sufian Y. Husseini
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642564468

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Geometry and Topology of Configuration Spaces by Edward R. Fadell,Sufian Y. Husseini Pdf

With applications in mind, this self-contained monograph provides a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres, making the subject accessible to researchers and graduates with a minimal background in classical homotopy theory and algebraic topology.

Author : Károly Bezdek,Antoine Deza,Yinyu Ye
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 53,6 Mb
Release : 2013-07-09
Category : Mathematics
ISBN : 9783319002002

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Discrete Geometry and Optimization by Károly Bezdek,Antoine Deza,Yinyu Ye Pdf

​Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplay between these subjects. The purpose of the Workshop on Discrete Geometry, the Conference on Discrete Geometry and Optimization, and the Workshop on Optimization, held in September 2011 at the Fields Institute, Toronto, was to further stimulate the interaction between geometers and optimizers. This volume reflects the interplay between these areas. The inspiring Fejes Tóth Lecture Series, delivered by Thomas Hales of the University of Pittsburgh, exemplified this approach. While these fields have recently witnessed a lot of activity and successes, many questions remain open. For example, Fields medalist Stephen Smale stated that the question of the existence of a strongly polynomial time algorithm for linear optimization is one of the most important unsolved problems at the beginning of the 21st century. The broad range of topics covered in this volume demonstrates the many recent and fruitful connections between different approaches, and features novel results and state-of-the-art surveys as well as open problems.

Author : Meera Sitharam,Audrey St. John,Jessica Sidman
Publisher : CRC Press
Page : 605 pages
File Size : 51,9 Mb
Release : 2018-07-20
Category : Mathematics
ISBN : 9781498738927

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Handbook of Geometric Constraint Systems Principles by Meera Sitharam,Audrey St. John,Jessica Sidman Pdf

The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures Can be used for senior undergraduate or graduate topics course introduction to the area Detailed list of figures and tables About the Editors: Meera Sitharam is currently an Associate Professor at the University of Florida’s Department of Computer & Information Science and Engineering. She received her Ph.D. at the University of Wisconsin, Madison. Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst. Jessica Sidman is a Professor of Mathematics on the John S. Kennedy Foundation at Mount Holyoke College. She received her Ph.D. from the University of Michigan.

Author : Martin Aigner
Publisher : American Mathematical Society
Page : 402 pages
File Size : 46,9 Mb
Release : 2023-01-24
Category : Mathematics
ISBN : 9781470470630

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Discrete Mathematics by Martin Aigner Pdf

The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints and solutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition… This book is a well-written introduction to discrete mathematics and is highly recommended to every student of mathematics and computer science as well as to teachers of these topics. —Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of the MAA for expository writing, and his book Proofs from the BOOK with Günter M. Ziegler has been an international success with translations into 12 languages.

Author : Herbert Edelsbrunner
Publisher : Cambridge University Press
Page : 206 pages
File Size : 41,9 Mb
Release : 2001-05-28
Category : Mathematics
ISBN : 0521793092

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Geometry and Topology for Mesh Generation by Herbert Edelsbrunner Pdf

This graduate text combines geometry, topology, algorithms, and engineering and emphasizes topics that are both elementary and useful.