An Introduction to NURBS

1st Edition

With Historical Perspective

Authors: David Rogers
Hardcover ISBN: 9781558606692
eBook ISBN: 9780080509204
Imprint: Morgan Kaufmann
Published Date: 21st July 2000
Page Count: 344
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Table of Contents

Preface Chapter 1 - Curve and Surface Representation 1.1 Introduction 1.2 Parametric Curves Extension to Three Dimensions Parametric Line 1.3 Parametric Surfaces 1.4 Piecewise Surfaces 1.5 Continuity Geometric Continuity Parametric Continuity Historical Perspective - Bézier Curves: A.R. Forrest Chapter 2 - Bézier Curves 2.1 Bézier Curve Deffnition Bézier Curve Algorithm 2.2 Matrix Representation of Bézier Curves 2.3 Bézier Curve Derivatives 2.4 Continuity Between Bézier Curves 2.5 Increasing the Flexibility of Bézier Curves Degree Raising Subdivision Historical Perspective - B-splines: Richard F. Riesenfeld Chapter 3 - B-spline Curves 3.1 B-spline Curve Deffnition Properties of B-spline Curves 3.2 Convex Hull Properties of B-spline Curves 3.3 Knot Vectors


The latest from a computer graphics pioneer, An Introduction to NURBS is the ideal resource for anyone seeking a theoretical and practical understanding of these very important curves and surfaces. Beginning with Bézier curves, the book develops a lucid explanation of NURBS curves, then does the same for surfaces, consistently stressing important shape design properties and the capabilities of each curve and surface type. Throughout, it relies heavily on illustrations and fully worked examples that will help you grasp key NURBS concepts and deftly apply them in your work. Supplementing the lucid, point-by-point instructions are illuminating accounts of the history of NURBS, written by some of its most prominent figures.

Whether you write your own code or simply want deeper insight into how your computer graphics application works, An Introduction to NURBS will enhance and extend your knowledge to a degree unmatched by any other resource.

Key Features

  • Presents vital information with applications in many different areas: CAD, scientific visualization, animation, computer games, and more.
  • Facilitates accessiblity to anyone with a knowledge of first-year undergraduate mathematics.
  • Details specific NURBS-based techniques, including making cusps with B-spline curves and conic sections with rational B-spline curves.
  • Presents all important algorithms in easy-to-read pseudocode-useful for both implementing them and understanding how they work.
  • Provides C-code implementations of worked examples at
  • Includes complete references to additional NURBS resources.


Computer graphics professionals and CAD designers of all kinds, including: engineering designers, architectural engineers, professionals in engineering, scientific visualization, animation, and game development.


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© Morgan Kaufmann 2001
Morgan Kaufmann
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About the Authors

David Rogers Author

David F. Rogers, Ph.D., is the author of two computer graphics classics, Mathematical Elements for Computer Graphics and Procedural Elements for Computer Graphics, as well as works on fluid dynamics. His early research on the use of B-splines and NURBS for dynamic manipulation of ship hull surfaces led to significant commercial and scientific advances in a number of fields. Founder and former director of the Computer Aided Design/Interactive Graphics Group at the U.S. Naval Academy, Dr. Rogers was an original member of the USNA's Aerospace Engineering Department. He sits on the editorial boards of The Visual Computer and Computer Aided Design and serves on committees for SIGGRAPH, Computer Graphics International, and other conferences.

Affiliations and Expertise

The United States Naval Academy, Annapolis, Maryland, U.S.A.