Computational Geometry in C

Author: Joseph O'Rourke

Publisher: Cambridge University Press

ISBN: 9780521649766

Category: Computers

Page: 376

View: 7730

DOWNLOAD NOW »

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 (http://cs.smith.edu/~orourke/) or by anonymous ftp.

Discrete and Computational Geometry

Author: Satyan L. Devadoss,Joseph O'Rourke

Publisher: Princeton University Press

ISBN: 9781400838981

Category: Mathematics

Page: 280

View: 8579

DOWNLOAD NOW »

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

Algorithms and Applications

Author: Mark de Berg

Publisher: Springer Science & Business Media

ISBN: 3540779736

Category: Computers

Page: 386

View: 2511

DOWNLOAD NOW »

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: 9870

DOWNLOAD NOW »

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

Polygon Mesh Processing

Author: Mario Botsch,Leif Kobbelt,Mark Pauly,Pierre Alliez,Bruno Levy

Publisher: CRC Press

ISBN: 1568814267

Category: Computers

Page: 250

View: 2708

DOWNLOAD NOW »

Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental website contains downloads and additional information.

Introduction to Geometric Computing

Author: Sherif Ghali

Publisher: Springer Science & Business Media

ISBN: 1848001150

Category: Computers

Page: 340

View: 1282

DOWNLOAD NOW »

Computing is quickly making much of geometry intriguing not only for philosophers and mathematicians, but also for scientists and engineers. What is the core set of topics that a practitioner needs to study before embarking on the design and implementation of a geometric system in a specialized discipline? This book attempts to find the answer. Every programmer tackling a geometric computing problem encounters design decisions that need to be solved. This book reviews the geometric theory then applies it in an attempt to find that elusive "right" design.

Delaunay Mesh Generation

Author: Siu-Wing Cheng,Tamal K. Dey,Jonathan Shewchuk

Publisher: CRC Press

ISBN: 1584887311

Category: Computers

Page: 410

View: 8420

DOWNLOAD NOW »

Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why these meshing algorithms work. The book is one of the first to integrate a vast amount of cutting-edge material on Delaunay triangulations. It begins with introducing the problem of mesh generation and describing algorithms for constructing Delaunay triangulations. The authors then present algorithms for generating high-quality meshes in polygonal and polyhedral domains. They also illustrate how to use restricted Delaunay triangulations to extend the algorithms to surfaces with ridges and patches and volumes with smooth surfaces. For researchers and graduate students, the book offers a rigorous theoretical analysis of mesh generation methods. It provides the necessary mathematical foundations and core theoretical results upon which researchers can build even better algorithms in the future. For engineers, the book shows how the algorithms work well in practice. It explains how to effectively implement them in the design and programming of mesh generation software.

Computational Geometry

An Introduction Through Randomized Algorithms

Author: Ketan Mulmuley

Publisher: Prentice Hall

ISBN: N.A

Category: Computers

Page: 447

View: 5276

DOWNLOAD NOW »

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.

The Geometry of Fractal Sets

Author: K. J. Falconer

Publisher: Cambridge University Press

ISBN: 9780521337052

Category: Mathematics

Page: 162

View: 2883

DOWNLOAD NOW »

This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.

Term Rewriting and All That

Author: Franz Baader,Tobias Nipkow

Publisher: Cambridge University Press

ISBN: 9780521779203

Category: Computers

Page: 316

View: 8311

DOWNLOAD NOW »

Unified and self-contained introduction to term-rewriting; suited for students or professionals.

Robotics: Concepts, Methodologies, Tools, and Applications

Concepts, Methodologies, Tools, and Applications

Author: Management Association, Information Resources

Publisher: IGI Global

ISBN: 146664608X

Category: Technology & Engineering

Page: 1873

View: 9416

DOWNLOAD NOW »

"This book explores some of the most recent developments in robotic motion, artificial intelligence, and human-machine interaction, providing insight into a wide variety of applications and functional areas"--Provided by publisher.

Data Refinement

Model-Oriented Proof Methods and Their Comparison

Author: Willem-Paul de Roever,Kai Engelhardt,Karl-Heinz Buth

Publisher: Cambridge University Press

ISBN: 0521641705

Category: Computers

Page: 423

View: 4886

DOWNLOAD NOW »

The goal of this book is to provide a comprehensive and systematic introduction to the important and highly applicable method of data refinement and the simulation methods used for proving its correctness. The authors concentrate in the first part on the general principles needed to prove data refinement correct. They begin with an explanation of the fundamental notions, showing that data refinement proofs reduce to proving simulation. The book's second part contains a detailed survey of important methods in this field, which are carefully analysed, and shown to be either incomplete, with counterexamples to their application, or to be always applicable whenever data refinement holds. This is shown by proving, for the first time, that all these methods can be described and analysed in terms of two simple notions: forward and backward simulation. The book is self-contained, going from advanced undergraduate level and taking the reader to the state of the art in methods for proving simulation.

A Course in Convexity

Author: Alexander Barvinok

Publisher: American Mathematical Soc.

ISBN: 0821829688

Category: Mathematics

Page: 366

View: 2800

DOWNLOAD NOW »

Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.

A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing

Foundations for Computer Graphics, Vision, and Image Processing

Author: Daniel Cohen-Or,Chen Greif,Tao Ju,Niloy J. Mitra,Ariel Shamir,Olga Sorkine-Hornung,Hao (Richard) Zhang

Publisher: CRC Press

ISBN: 1498706304

Category: Computers

Page: 246

View: 845

DOWNLOAD NOW »

A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing shows how to use a collection of mathematical techniques to solve important problems in applied mathematics and computer science areas. The book discusses fundamental tools in analytical geometry and linear algebra. It covers a wide range of topics, from matrix decomposition to curvature analysis and principal component analysis to dimensionality reduction. Written by a team of highly respected professors, the book can be used in a one-semester, intermediate-level course in computer science. It takes a practical problem-solving approach, avoiding detailed proofs and analysis. Suitable for readers without a deep academic background in mathematics, the text explains how to solve non-trivial geometric problems. It quickly gets readers up to speed on a variety of tools employed in visual computing and applied geometry.

3264 and All That

A Second Course in Algebraic Geometry

Author: David Eisenbud,Joe Harris

Publisher: Cambridge University Press

ISBN: 1316679381

Category: Mathematics

Page: N.A

View: 7596

DOWNLOAD NOW »

This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.

Solitons

An Introduction

Author: P. G. Drazin,R. S. Johnson

Publisher: Cambridge University Press

ISBN: 9780521336550

Category: Mathematics

Page: 226

View: 5500

DOWNLOAD NOW »

This textbook is an introduction to the theory of solitons in the physical sciences.

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: 2979

DOWNLOAD NOW »

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.

Computer Vision

Algorithms and Applications

Author: Richard Szeliski

Publisher: Springer Science & Business Media

ISBN: 9781848829350

Category: Computers

Page: 812

View: 5020

DOWNLOAD NOW »

Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques. Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

Spatial Databases

With Application to GIS

Author: Philippe Rigaux,Michel O. Scholl,Agnès Voisard

Publisher: Morgan Kaufmann

ISBN: 9781558605886

Category: Computers

Page: 410

View: 9489

DOWNLOAD NOW »

Spatial Databases is the first unified, in-depth treatment of special techniques for dealing with spatial data, particularly in the field of geographic information systems (GIS). This book surveys various techniques, such as spatial data models, algorithms, and indexing methods, developed to address specific features of spatial data that are not adequately handled by mainstream DBMS technology. The book also reviews commercial solutions to geographic data handling: ArcInfo, ArcView, and Smallworld GISs; and two extensions to the relational model, PostgreSQL and Oracle Spatial. The authors examine these underlying GIS technologies, assess their strengths and weaknesses, and consider specific uses for which each product is best suited. * Examines the strengths of various query languages and approaches to query processing. * Explains the use of computational geometry in spatial databases GISs, providing necessary background and an in-depth look at key algorithms. * Covers spatial access methods, including the R-tree and several space-driven structures, and is filled with dozens of helpful illustrations.