ABSTRACT

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.

part I|41 pages

Introduction

chapter 1|39 pages

Review of Basic Concepts

part II|295 pages

Curves

chapter 2|27 pages

Representation Issues

chapter 3|39 pages

Conic Sections

chapter 4|24 pages

Differential Geometry for Space Curves

chapter 5|33 pages

Bézier Curves and Bernstein Approximation

chapter 6|33 pages

B-Spline Curves

chapter 7|25 pages

Linear Spaces of B-Splines

chapter 8|28 pages

Choosing a B-Spline Space

chapter 9|32 pages

Data Fitting with B-Splines

chapter 10|25 pages

Other Polynomial Bases for Interpolation

chapter 11|21 pages

Other Derivations of B-Splines

part III|117 pages

Surfaces

chapter 12|40 pages

Differential Geometry for Surfaces

chapter 13|34 pages

Surface Representations

chapter 14|20 pages

Fitting Surfaces

chapter 15|21 pages

Modeling with B-Spline Surfaces

part IV|150 pages

Advanced Techniques

chapter 16|38 pages

Subdivision and Refinement for Splines

chapter 17|19 pages

Subdivision and Refinement in Modeling

chapter 18|39 pages

Set Operations to Effect Modeling

chapter 19|11 pages

Model Data Structures

chapter 20|20 pages

Subdivision Surfaces

chapter 21|16 pages

Higher-Dimensional Tensor Product B-Splines