Geometric Modeling with Splines: An Introduction

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Written by researchers who have helped found and shape the field, this book is a definitive introduction to geometric modeling. The authors present all of the necessary techniques for curve and surface representations in computer-aided modeling with a focus on how the techniques are used in design. They achieve a balance between mathematical rigor and broad applicability. Appropriate for readers with a moderate degree of mathematical maturity, this book is suitable as an undergraduate or graduate text, or particularly as a resource for self-study.

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Product Details

  • ISBN-13: 9781568811376
  • Publisher: Taylor & Francis
  • Publication date: 7/18/2001
  • Edition description: New Edition
  • Pages: 638

Table of Contents

I Introduction 1
1 Review of Basic Concepts 3
II Curves 43
2 Representation Issues 45
3 Conic Sections 73
4 Differential Geometry for Space Curves 113
5 Bezier Curves and Bernstein Approximation 137
6 B-Spline Curves 171
7 Linear Spaces of B-Splines 205
8 Choosing a B-Spline Space 231
9 Data Fitting with B-Splines 259
10 Other Polynomial Bases for Interpolation 291
11 Other Derivations of B-Splines 317
III Surfaces 339
12 Differential Geometry for Surfaces 341
13 Surface Representations 381
14 Fitting Surfaces 415
15 Modeling with B-Spline Surfaces 435
IV Advanced Techniques 457
16 Subdivision and Refinement for Splines 459
17 Subdivision and Refinement in Modeling 497
18 Set Operations to Effect Modeling 517
19 Model Data Structures 557
20 Subdivision Surfaces 569
21 Higher-Dimensional Tensor Product B-Splines 591
Bibliography 607
Index 613
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