Geometric computation / editors Falai Chen, Dongming Wang.

Format:

Book

Contributor:

Chen, Falai.

Wang, Dongming.

Series:

Lecture notes series on computing ; v.11.

Lecture notes series on computing ; v.11

Language:

English

Subjects (All):

Geometry--Data processing.

Geometry.

Geometry--Computer programs.

Physical Description:

1 online resource (423 p.)

Edition:

1st ed.

Place of Publication:

River Edge, NJ : World Scientific, c2004.

Language Note:

English

Summary:

This book contains tutorial surveys and original research contributions in geometric computing, modeling, and reasoning. Highlighting the role of algebraic computation, it covers: surface blending, implicitization, and parametrization; automated deduction with Clifford algebra and in real geometry; and exact geometric computation. Basic techniques, advanced methods, and new findings are presented coherently, with many examples and illustrations. Using this book the reader will easily cross the frontiers of symbolic computation, computer aided geometric design, and automated reasoning. The boo

Contents:

CONTENTS ; Preface ; Chapter 1 Algebraic Methods in Computer Aided Geometric Design: Theoretical and Practical Applications ; 1. Introduction ; 2. Implicitization and Parametrization Problems ; 3. Applications in CAGD ; 4. Practical Performance of Algebraic Techniques in CAGD

References Chapter 2 Constructing Piecewise Algebraic Blending Surfaces ; 1. Introduction ; 2. Notations and Preliminaries ; 3. Direct Method ; 4. Grobner Basis Method ; 5. Wu's Method ; 6. Syzygy Module Method ; 7. Concluding Remark

Chapter 3 Rational Curves and Surfaces: Algorithms and Some Applications 1. Introduction ; 2. Algebraic Plane Curves ; 3. Rational Plane Curves ; 4. Parametrization of Rational Plane Curves ; 5. Properness and Inversion ; 6. Reparametrizations of Rational Plane Curves

7. Real Rational Curves 8. Parametrization of Rational Surfaces ; 9. Some Applications ; Chapter 4 Panorama of Methods for Exact Implicitization of Algebraic Curves and Surfaces ; 1. Introduction ; 2. Exact Implicitization of Algebraic Curves ; 3. Resultants ; 4. Grobner Bases

5. Characteristic Sets 6. Perturbations ; 7. Moving Lines Moving Planes Moving Curves and Moving Surfaces ; 8. Multidimensional Newton Formulae and Symmetric Functions ; 9. Eigenvalue Method ; 10. Conclusion ; Chapter 5 Implicitization and Offsetting via Regular Systems

1. Introduction

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611934729

9781281934727

1281934720

9789812794833

9812794832

OCLC:

879023561