Computational Geometry

Algorithms and Applications

Author: Mark de Berg

Publisher: Springer Science & Business Media

ISBN: 3540779736

Category: Computers

Page: 386

View: 1666

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.

Computational Geometry

An Introduction

Author: Franco P. Preparata,Michael I. Shamos

Publisher: Springer Science & Business Media

ISBN: 1461210984

Category: Mathematics

Page: 398

View: 429

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

Handbook of Discrete and Computational Geometry, Third Edition

Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 1351645919

Category: Computers

Page: 1928

View: 3366

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 ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly 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 ?eld 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.

Handbook of Computational Geometry

Author: J.R. Sack,J. Urrutia

Publisher: Elsevier

ISBN: 9780080529684

Category: Mathematics

Page: 1075

View: 2956

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.


An Introduction to Computational Geometry

Author: Marvin Minsky,Seymour A. Papert,Léon Bottou

Publisher: MIT Press

ISBN: 0262343940

Category: Computers

Page: 316

View: 9358

Reissue of the 1988 Expanded Edition with a new foreword by Léon Bottou In 1969, ten years after the discovery of the perceptron -- which showed that a machine could be taught to perform certain tasks using examples -- Marvin Minsky and Seymour Papert published Perceptrons, their analysis of the computational capabilities of perceptrons for specific tasks. As Léon Bottou writes in his foreword to this edition, "Their rigorous work and brilliant technique does not make the perceptron look very good." Perhaps as a result, research turned away from the perceptron. Then the pendulum swung back, and machine learning became the fastest-growing field in computer science. Minsky and Papert's insistence on its theoretical foundations is newly relevant. Perceptrons -- the first systematic study of parallelism in computation -- marked a historic turn in artificial intelligence, returning to the idea that intelligence might emerge from the activity of networks of neuron-like entities. Minsky and Papert provided mathematical analysis that showed the limitations of a class of computing machines that could be considered as models of the brain. Minsky and Papert added a new chapter in 1987 in which they discuss the state of parallel computers, and note a central theoretical challenge: reaching a deeper understanding of how "objects" or "agents" with individuality can emerge in a network. Progress in this area would link connectionism with what the authors have called "society theories of mind."

Computational Geometry in C

Author: Joseph O'Rourke

Publisher: Cambridge University Press

ISBN: 9780521649766

Category: Computers

Page: 376

View: 496

This is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. 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. A new "Sources" chapter points to supplemental literature for readers needing more information on any topic. A novel aspect is the inclusion of working C code for many of the algorithms, with discussion of practical implementation issues. 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 code in this new edition is significantly improved from the first edition, 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 ( or by anonymous ftp.

Effective Computational Geometry for Curves and Surfaces

Author: Jean-Daniel Boissonnat,Monique Teillaud

Publisher: Springer Science & Business Media

ISBN: 3540332596

Category: Mathematics

Page: 344

View: 6307

This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter fully details and provides a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice. Coverage includes references to open source software and discussion of potential applications of the presented techniques.

Discrete and Computational Geometry

Author: Satyan L. Devadoss,Joseph O'Rourke

Publisher: Princeton University Press

ISBN: 9781400838981

Category: Mathematics

Page: 280

View: 5071

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]

Computational Geometry

Curve and Surface Modeling

Author: Su Bu-qing,Liu Ding-yuan

Publisher: Elsevier

ISBN: 1483272281

Category: Mathematics

Page: 306

View: 7917

Computational Geometry: Curve and Surface Modeling provides information pertinent to the fundamental aspects of computational geometry. This book discusses the geometric properties of parametric polynomial curves by using the theory of affine invariants for algebraic curves. Organized into eight chapters, this book begins with an overview of the objects studies in computational geometry, namely surfaces and curves. This text then explores the developments in the theory and application of spline functions, which began with cubic spline functions. Other chapters consider the mechanical background of the cubic spline functions, which is the wooden spline with small deflection. This book discusses as well that in mathematical lofting the information of a geometric shape is given by a set of data points, while in geometric design other ways of representations are available. The final chapter deals with the concepts in the theory of algebraic curves. This book is a valuable resource for mathematicians.

Combinatorial and Computational Geometry

Author: Jacob E. Goodman,Janos Pach,Emo Welzl

Publisher: Cambridge University Press

ISBN: 9780521848626

Category: Computers

Page: 616

View: 1866

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

New Trends in Discrete and Computational Geometry

Author: Janos Pach

Publisher: Springer Science & Business Media

ISBN: 3642580432

Category: Mathematics

Page: 340

View: 7347

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.

On the Computational Geometry of Pocket Machining

Author: Martin Held

Publisher: Springer Science & Business Media

ISBN: 9783540541035

Category: Computers

Page: 178

View: 4885

This monograph presents a thorough geometrical investigation of practical and theoretical problems arising from NC pocket machining. Practical topics include selection of tool sizes and determination of optimal tool paths. A rigorous theoretical framework based on Voronoi diagrams is given.

Computational Geometry - Methods, Algorithms and Applications

International Workshop on Computational Geometry CG '91 Bern, Switzerland, March 21-22, 1991. Proceedings

Author: Hanspeter Bieri,Hartmut Noltemeier

Publisher: Springer Science & Business Media

ISBN: 9783540548911

Category: Computers

Page: 320

View: 4608

Radiocarbon After Four Decades: An Interdisciplinary Perspective commemorates the 40th anniversary of radiocarbon dating. The volume presents discussions of every aspect of this dating technique, as well as chronicles of its development and views of future advancements and applications. All of the 64 authors played major roles in establishment, development or application of this revolutionary scientific tool. The 35 chapters provide a solid foundation in the essential topics of radiocarbon dating: Historical Perspectives; The Natural Carbon Cycle; Instrumentation and Sample Preparation; Hydrology; Old World Archaeology; New World Archaeology; Earth Sciences; and Biomedical Applications.

Surveys on Discrete and Computational Geometry

Twenty Years Later : AMS-IMS-SIAM Joint Summer Research Conference, June 18-22, 2006, Snowbird, Utah

Author: Jacob E. Goodman

Publisher: American Mathematical Soc.

ISBN: 0821842390

Category: Mathematics

Page: 556

View: 4797

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.

Guide to Computational Geometry Processing

Foundations, Algorithms, and Methods

Author: J. Andreas Bærentzen,Jens Gravesen,François Anton,Henrik Aanæs

Publisher: Springer Science & Business Media

ISBN: 1447140753

Category: Computers

Page: 326

View: 5034

This book reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. Features: presents an overview of the underlying mathematical theory, covering vector spaces, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations; reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces; examines techniques for computing curvature from polygonal meshes; describes algorithms for mesh smoothing, mesh parametrization, and mesh optimization and simplification; discusses point location databases and convex hulls of point sets; investigates the reconstruction of triangle meshes from point clouds, including methods for registration of point clouds and surface reconstruction; provides additional material at a supplementary website; includes self-study exercises throughout the text.

Advances in Discrete and Computational Geometry

Proceedings of the 1996 AMS-IMS-SIAM Joint Summer Research Conference, Discrete and Computational Geometry--Ten Years Later, July 14-18, 1996, Mount Holyoke College

Author: Bernard Chazelle,Jacob E. Goodman,Richard Pollack

Publisher: American Mathematical Soc.

ISBN: 0821806742

Category: Mathematics

Page: 463

View: 7528

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.

Applied Computational Geometry. Towards Geometric Engineering

FCRC '96 Workshop, WACG '96, Philadelphia, PA, May 27 - 28, 1996, Selected Papers

Author: Ming C. Lin,Dinesh Manocha

Publisher: Springer Science & Business Media

ISBN: 9783540617853

Category: Computers

Page: 222

View: 5245

Content Description #Anthology selected from contributions to the First ACM Workshop on Applied Computational Geometry.#Includes bibliographical references and index.

Discrete and Computational Geometry

Papers from the DIMACS Special Year

Author: Jacob E. Goodman,Richard D. Pollack,William L. Steiger

Publisher: American Mathematical Soc.

ISBN: 9780821871010

Category: Mathematics

Page: 378

View: 5627

The first DIMACS special year, held during 1989-1990, was devoted to discrete and computational geometry. More than 200 scientists, both long- and short-term visitors, came to DIMACS to participate in the special year activities. Among the highlights were six workshops at Rutgers and Princeton Universities that defined the focus for much of the special year. The workshops addressed the following topics: geometric complexity, probabilistic methods in discrete and computational geometry, polytopes and convex sets, arrangements, and algebraic and practical issues in geometric computation. This volume presents some of the results growing out of the workshops and the special year activities. Containing both survey articles and research papers, this collection presents an excellent overview of significant recent progress in discrete and computational geometry. The diversity of these papers demonstrate how geometry continues to provide a vital source of ideas in theoretical computer science and discrete mathematics as well as fertile ground for interaction and simulation between the two disciplines.

Computational Geometry

An Introduction Through Randomized Algorithms

Author: Ketan Mulmuley

Publisher: Prentice Hall


Category: Computers

Page: 447

View: 4742

This introduction to computational geometry is designed for beginners. It emphasizes simple randomized methods, developing basic principles with the help of planar applications, beginning with deterministic algorithms and shifting to randomized algorithms as the problems become more complex. It also explores higher dimensional advanced applications and provides exercises.

Algorithmic Geometry

Author: Jean-Daniel Boissonnat,Mariette Yvinec

Publisher: Cambridge University Press

ISBN: 9780521565295

Category: Computers

Page: 519

View: 1904

The design and analysis of geometric algorithms have seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD. The goals of this book are twofold: first to provide a coherent and systematic treatment of the foundations; secondly to present algorithmic solutions that are amenable to rigorous analysis and are efficient in practical situations. When possible, the algorithms are presented in their most general d-dimensional setting. Specific developments are given for the 2- or 3-dimensional cases when this results in significant improvements. The presentation is confined to Euclidean affine geometry, though the authors indicate whenever the treatment can be extended to curves and surfaces. The prerequisites for using the book are few, which will make it ideal for teaching advanced undergraduate or beginning graduate courses in computational geometry.