Computational Geometry

Author: Ketan Mulmuley
Publisher: Prentice Hall
ISBN: STANFORD:36105003459646
Release Date: 1994
Genre: Computers

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.

Randomized Algorithms

Author: Rajeev Motwani
Publisher: Cambridge University Press
ISBN: 9781139643139
Release Date: 1995-08-25
Genre: Computers

For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.

Computational Geometry

Author: Mark de Berg
Publisher: Springer Science & Business Media
ISBN: 3540656200
Release Date: 2000-01-01
Genre: Computers

Algorithms are the focus of this introduction to computational geometry, which presents techniques applied to robotics, graphics, CAD/CAM, and geographic information systems.

Computational Geometry in C

Author: Joseph O'Rourke
Publisher: Cambridge University Press
ISBN: 0521649765
Release Date: 1998-10-13
Genre: Computers

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.

Handbook of Computational Geometry

Author: J.R. Sack
Publisher: Elsevier
ISBN: 0080529682
Release Date: 1999-12-13
Genre: Mathematics

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.

New Trends in Discrete and Computational Geometry

Author: Janos Pach
Publisher: Springer Science & Business Media
ISBN: 9783642580437
Release Date: 2012-12-06
Genre: Mathematics

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.

Proceedings of the Sixth Annual ACM SIAM Symposium on Discrete Algorithms

Publisher: SIAM
ISBN: 0898713498
Release Date: 1995-01-01
Genre: Computer algorithms

The proceedings of the January 1995 symposium, sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics, comprise 70 papers. Among the topics: on-line approximate list indexing with applications; finding subsets maximizing minimum structures; register allocation in structured programs; and splay trees for data compression. No index. Annotation copyright by Book News, Inc., Portland, OR

Probability and Computing

Author: Michael Mitzenmacher
Publisher: Cambridge University Press
ISBN: 0521835402
Release Date: 2005-01-31
Genre: Computers

Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols.Assuming only an elementary background in discrete mathematics, this textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses, including random sampling, expectations, Markov's and Chevyshev's inequalities, Chernoff bounds, balls and bins models, the probabilistic method, Markov chains, MCMC, martingales, entropy, and other topics.

Computational Geometry

Author: Franco P. Preparata
Publisher: Springer Science & Business Media
ISBN: 9781461210986
Release Date: 2012-12-06
Genre: Mathematics

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

Computer Graphics and Geometric Modelling

Author: Max K. Agoston
Publisher: Springer Science & Business Media
ISBN: 9781846281082
Release Date: 2005-12-06
Genre: Computers

Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Implementation and Algorithms, covers the computer graphics part of the field of geometric modelling and includes all the standard computer graphics topics. The first part deals with basic concepts and algorithms and the main steps involved in displaying photorealistic images on a computer. The second part covers curves and surfaces and a number of more advanced geometric modelling topics including intersection algorithms, distance algorithms, polygonizing curves and surfaces, trimmed surfaces, implicit curves and surfaces, offset curves and surfaces, curvature, geodesics, blending etc. The third part touches on some aspects of computational geometry and a few special topics such as interval analysis and finite element methods. The volume includes two companion programs.


Author: M. H. Alsuwaiyel
Publisher: World Scientific
ISBN: 9789814723657
Release Date: 2016
Genre: Mathematics

Algorithmic Geometry

Author: Jean-Daniel Boissonnat
Publisher: Cambridge University Press
ISBN: 0521565294
Release Date: 1998-03-05
Genre: Computers

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.

Introduction to Algorithms

Author: Thomas H. Cormen
Publisher: MIT Press
ISBN: 9780262533058
Release Date: 2009-07-31
Genre: Computers

A new edition of the essential text and professional reference, with substantial new material on such topics as vEB trees, multithreaded algorithms, dynamic programming, and edge-based flow.

Geometric Approximation Algorithms

Author: Sariel Har-Peled
Publisher: American Mathematical Soc.
ISBN: 9780821849118
Release Date: 2011
Genre: Mathematics

Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.