1.

Record Nr.

UNINA9910782118503321

Titolo

Geometric computation [[electronic resource] /] / editors Falai Chen, Dongming Wang

Pubbl/distr/stampa

River Edge, NJ, : World Scientific, c2004

ISBN

1-281-93472-0

9786611934729

981-279-483-2

Descrizione fisica

1 online resource (423 p.)

Collana

Lecture notes series on computing ; ; v.11

Altri autori (Persone)

ChenFalai

WangDongming

Disciplina

512.75

Soggetti

Geometry - Data processing

Geometry - Computer programs

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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

Sommario/riassunto

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