Geometric Modeling With Splines - An Introduction

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.

List of contents

Part I: Introduction 1. Review of Basic Concepts Part II: Curves 2. Representation Issues 3. Conic Sections 4. Differential Geometry for Space Curves 5. Bezier Curves and Bernstein Approximation 6. B-Spline Curves 7. Linear Spaces of B-Splines 8. Choosing a B-Spline Space 9. Data Fitting with B-Splines 10. Other Polynomial Bases for Interpolation 11. Other Derivations of B-Splines Part III: Surfaces 12. Differential Geometry for Surfaces 13. Surface Representations 14. Fitting Surfaces 15. Modeling with B-Spline Surfaces Part IV: Advanced Techniques 16. Subdivision and Refinement for Splines 17. Subdivision and Refinement in Modeling 18. Set Operations to Effect Modeling 19. Model Data Structures 20. Subdivision Surfaces 21. Higher-Dimensional Tensor Product B-Splines

About the author

Elaine Cohen, Richard F. Riesenfeld, Gershon Elber

Summary

This book contains a comprehensive treatment of curves and surfaces with emphasis on B-spline techniques. It provides a wealth of material ranging from classical techniques to a broad coverage of new techniques, suitable for implementing splines and for designing with splines.

Product details

• Authors: Elaine Cohen, Elaine Riesenfeld Cohen, Gershon Elber, Elber Gershon, Richard F Riesenfeld, Richard F. Riesenfeld, Riesenfeld Richard F.
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Paperback / Softback
• Released: 31.12.2019
• EAN: 9780367447243
• ISBN: 978-0-367-44724-3
• No. of pages: 638
• Subjects: Guides; Natural sciences, medicine, IT, technology > Technology > Mechanical engineering, production engineering; MATHEMATICS / Applied, MATHEMATICS / Geometry / General, Mathematics, geometry, Applied mathematics, Graphical & digital media applications, Graphical and digital media applications, COMPUTERS / Design, Graphics & Media / Graphics Tools