An Introduction to NURBS :With Historical Perspective ( The Morgan Kaufmann Series in Computer Graphics )

Publication subTitle :With Historical Perspective

Publication series :The Morgan Kaufmann Series in Computer Graphics

Author: Rogers   David F.  

Publisher: Elsevier Science‎

Publication year: 2000

E-ISBN: 9780080509204

P-ISBN(Paperback): 9781558606692

P-ISBN(Hardback):  9781558606692

Subject: TP39 computer application

Language: ENG

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Description

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.

  • 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.

Chapter

Chapter 1. Curve and Surface Representation

1.1 Introduction

1.2 Parametric Curves

1.3 Parametric Surfaces

1.4 Piecewise Surfaces

1.5 Continuity

Historical Perspective

Chapter 2. Bézier Curves

2.1 Bézier Curve Definition

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

Historical Perspective

Chapter 3. B-spline Curves

3.1 B-spline Curve Definition

3.2 Convex Hull Properties of B-spline Curves

3.3 Knot Vectors

3.4 B-spline Basis Functions

3.5 Open B-spline Curves

3.6 Nonuniform B-spline Curves

3.7 Periodic B-spline Curves

3.8 Matrix Formulation of B-spline Curves

3.9 End Conditions for Periodic

3.10 B-spline Curve Derivatives

3.11 B-spline Curve Fitting

3.12 Degree Elevation

3.13 Degree Reduction

3.14 Knot Insertion and B-spline Curve Subdivision

3.15 Knot Removal

3.16 Reparameterization

Historical Perspective

Chapter 4. Rational B-spline Curves

4.1 Rational B-spline Curves (NURBS)

4.2 Rational B-spline Basis Functions and Curves

4.3 Calculating Rational B-spline Curves

4.4 Derivatives of NURBS Curves

4.5 Conic Sections

Historical Perspective

Chapter 5. Bézier Surfaces

5.1 Mapping Parametric Surfaces

5.2 Bézier Surface Definition and Characteristics

5.3 Bézier Surface Derivatives

5.4 Transforming Between Surface Descriptions

Historical Perspective

Chapter 6. B-spline Surfaces

6.1 B-spline Surfaces

6.2 Convex Hull Properties

6.3 Local Control

6.4 Calculating Open B-spline Surfaces

6.5 Periodic B-spline Surfaces

6.6 Matrix Formulation of B-spline Surfaces

6.7 B-spline Surface Derivatives

6.8 B-spline Surface Fitting

6.9 B-spline Surface Subdivision

6.10 Gaussian Curvature and Surface Fairness

Historical Perspective

Chapter 7. Rational B-spline Surfaces

7.1 Rational B-spline Surfaces (NURBS)

7.2 Characteristics of Rational B-spline Surfaces

7.3 A Simple Rational B-spline Surface Algorithm

7.4 Derivatives of Rational B-spline Surfaces

7.5 Bilinear Surfaces

7.6 Sweep Surfaces

7.7 Ruled Rational B-spline Surfaces

7.8 Surfaces of Revolution

7.9 Blending Surfaces

7.10 A Fast Rational B-spline Surface Algorithm

Appendices

A B-spline Surface File Format

B Problems

C Algorithms

References

Index

About the Author

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