Handbook of Discrete and Computational GeometryHandbook of Discrete and Computational Geometry



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.

Author: Csaba D. Toth

Publisher: CRC Press

ISBN: 9781498711425

Category:

Page: 1928

View: 354

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 GeometryDiscrete and Computational Geometry



In J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 65, pages 1435–1463. CRC Press LLC, 2nd edition, 2004. Both the LEDA and CGAL libraries offer options for robust computation.

Author: Satyan L. Devadoss

Publisher: Princeton University Press

ISBN: 9781400838981

Category:

Page: 280

View: 295

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). To obtain access, please e-mail: [email protected]

Handbook of Computational GeometryHandbook of Computational Geometry



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.

Author: J.R. Sack

Publisher: Elsevier

ISBN: 0080529682

Category:

Page: 1075

View: 348

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.

Computational Geometry in CComputational Geometry in C



Farin (1993): Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. Faugeras (1993): ThreeDimensional Computer Vision: ... Goodman & O'Rourke (1997): Handbook of Discrete and Computational Geometry (CRC Press LLC).

Author: Joseph O'Rourke

Publisher: Cambridge University Press

ISBN: 9781107268630

Category:

Page:

View: 140

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.

Computational GeometryComputational Geometry



This leads to a geometric problem: given two geometric objects, determine how well they resemble each other. ... More information can also be found in the Handbook of Computational Geometry [293] and the Handbook of Discrete and ...

Author: Mark de Berg

Publisher: Springer Science & Business Media

ISBN: 9783662034279

Category:

Page: 367

View: 613

Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self-study.

Polyhedral and Algebraic Methods in Computational GeometryPolyhedral and Algebraic Methods in Computational Geometry



Handbook of Discrete and Computational Geometry, 2nd edn. Chapman & Hall/CRC, Boca Raton (2004) Gordan, P.: Neuer Beweis des Hilbert'schen Satzes über homogene Functionen. Nachr. Königl. Ges. Wiss.

Author: Michael Joswig

Publisher: Springer Science & Business Media

ISBN: 9781447148173

Category:

Page: 250

View: 350

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Voronoi Diagrams and Delaunay TriangulationsVoronoi Diagrams and Delaunay Triangulations



The nature and meaning of perturbations in geometric computing. Discrete & Computational Geometry 19 (1998), 1–17. R. Seidel. Convex hull computations. In: J.E. Goodman and J. O'Rourke (eds.), Handbook of Discrete and Computational ...

Author: Franz Aurenhammer

Publisher: World Scientific Publishing Company

ISBN: 9789814447652

Category:

Page: 348

View: 750

Voronoi diagrams partition space according to the influence certain sites exert on their environment. Since the 17th century, such structures play an important role in many areas like Astronomy, Physics, Chemistry, Biology, Ecology, Economics, Mathematics and Computer Science. They help to describe zones of political influence, to determine the hospital nearest to an accident site, to compute collision-free paths for mobile robots, to reconstruct curves and surfaces from sample points, to refine triangular meshes, and to design location strategies for competing markets. This unique book offers a state-of-the-art view of Voronoi diagrams and their structure, and it provides efficient algorithms towards their computation. Readers with an entry-level background in algorithms can enjoy a guided tour of gently increasing difficulty through a fascinating area. Lecturers might find this volume a welcome source for their courses on computational geometry. Experts are offered a broader view, including many alternative solutions, and up-to-date references to the existing literature; they might benefit in their own research or application development.

Handbook of Discrete and Combinatorial Mathematics Second EditionHandbook of Discrete and Combinatorial Mathematics Second Edition



Providing a ready reference for practitioners in the field, the Handbook of Discrete and Combinatorial Mathematics, Second Edition presents additional material on Google's matrix, random graphs, geometric graphs, computational topology, and ...

Author: Kenneth H. Rosen

Publisher: Chapman and Hall/CRC

ISBN: 158488780X

Category:

Page: 1408

View: 401

The importance of discrete and combinatorial mathematics continues to increase as the range of applications to computer science, electrical engineering, and the biological sciences grows dramatically. Providing a ready reference for practitioners in the field, the Handbook of Discrete and Combinatorial Mathematics, Second Edition presents additional material on Google's matrix, random graphs, geometric graphs, computational topology, and other key topics. New chapters highlight essential background information on bioinformatics and computational geometry. Each chapter includes a glossary, definitions, facts, examples, algorithms, major applications, and references.

Guide to Information Sources in Mathematics and StatisticsGuide to Information Sources in Mathematics and Statistics



Handbook of Algebraic Topology (James), 126 Handbook of Analytic-Computational Methods in Applied Mathematics (Anastassiou), ... 135 Handbook of Discrete and Computational Geometry (Goodman and O'Rourke), 123 Handbook of Econometrics ...

Author: Martha A. Tucker

Publisher: Libraries Unlimited

ISBN: 9781563087011

Category:

Page: 362

View: 947

Publisher description: This book is a reference for librarians, mathematicians, and statisticians involved in college and research level mathematics and statistics in the 21st century. Part I is a historical survey of the past 15 years tracking this huge transition in scholarly communications in mathematics. Part II of the book is the bibliography of resources recommended to support the disciplines of mathematics and statistics. These resources are grouped by material type. Publication dates range from the 1800's onwards. Hundreds of electronic resources-some online, both dynamic and static, some in fixed media, are listed among the paper resources. A majority of listed electronic resources are free.

Combinatorial and Computational GeometryCombinatorial and Computational Geometry



20th Annual ACM Symposium on Computational Geometry ( Brooklyn , NY , 2004 ) , ACM , New York , 2004 . ... 197-218 in Handbook of discrete and computational geometry , 2nd ed . , edited by J. E. Goodman and J. O'Rourke , CRC , Boca ...

Author: Jacob E. Goodman

Publisher: Cambridge University Press

ISBN: 0521848628

Category:

Page: 640

View: 533

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