The NURBS Book

1. Front Matter

   Pages i-xiv

   PDF

2. Curve and Surface Basics

   • Les Piegl, Wayne Tiller

   Pages 1-46

3. B-Spline Basis Functions

   • Les Piegl, Wayne Tiller

   Pages 47-79

4. B-spline Curves and Surfaces

   • Les Piegl, Wayne Tiller

   Pages 81-116

5. Rational B-spline Curves and Surfaces

   • Les Piegl, Wayne Tiller

   Pages 117-139

6. Fundamental Geometric Algorithms

   • Les Piegl, Wayne Tiller

   Pages 141-228

7. Advanced Geometric Algorithms

   • Les Piegl, Wayne Tiller

   Pages 229-279

8. Conics and Circles

   • Les Piegl, Wayne Tiller

   Pages 281-331

9. Construction of Common Surfaces

   • Les Piegl, Wayne Tiller

   Pages 333-360

10. Curve and Surface Fitting

    • Les Piegl, Wayne Tiller

    Pages 361-453

11. Advanced Surface Construction Techniques

    • Les Piegl, Wayne Tiller

    Pages 455-507

12. Shape Modification Tools

    • Les Piegl, Wayne Tiller

    Pages 509-569

13. Standards and Data Exchange

    • Les Piegl, Wayne Tiller

    Pages 571-591

14. B-spline Programming Concepts

    • Les Piegl, Wayne Tiller

    Pages 593-628

15. Back Matter

    Pages 629-646

    PDF

Until recently B-spline curves and surfaces (NURBS) were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. Today we are seeing expanded use of NURBS in modeling objects for the visual arts, including the film and entertainment industries, art, and sculpture. NURBS are now also being used for modeling scenes for virtual reality applications. These applications are expected to increase. Consequently, it is quite appropriate for The.N'URBS Book to be part of the Monographs in Visual Communication Series. B-spline curves and surfaces have been an enduring element throughout my pro­ fessional life. The first edition of Mathematical Elements for Computer Graphics, published in 1972, was the first computer aided design/interactive computer graph­ ics textbook to contain material on B-splines. That material was obtained through the good graces of Bill Gordon and Louie Knapp while they were at Syracuse University. A paper of mine, presented during the Summer of 1977 at a Society of Naval Architects and Marine Engineers meeting on computer aided ship surface design, was arguably the first to examine the use of B-spline curves for ship design. For many, B-splines, rational B-splines, and NURBS have been a bit mysterious.

• Splines
• algorithms
• construction
• data exchange
• geometry

• Department of Computer Science and Engineering, University of South Florida, Tampa, USA

  Les Piegl

• GeomWare, Inc., Tyler, USA

  Wayne Tiller

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