عنوان

The NURBS Book

(Number (ISBN

364297385X

(Number (ISBN

9783642973857

Number

b576700

Title Proper

The NURBS Book

General Material Designation

[Book]

First Statement of Responsibility

by Les Piegl, Wayne Tiller.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1995

Specific Material Designation and Extent of Item

(XIV, 646 pages 334 illustrations).

Series Title

Monographs in visual communication.

Text of Note

One Curve and Surface Basics --; 1.1 Implicit and Parametric Forms --; 1.2 Power Basis Form of a Curve --; 1.3 Bézier Curves --; 1.4 Rational Bézier Curves --; 1.5 Tensor Product Surfaces --; Exercises --; Two B-Spline Basis Functions --; 2.1 Introduction --; 2.2 Definition and Properties of B-spline Basis Functions --; 2.3 Derivatives of B-spline Basis Functions --; 2.4 Further Properties of the Basis Functions --; 2.5 Computational Algorithms --; Exercises --; Three B-spline Curves and Surfaces --; 3.1 Introduction --; 3.2 The Definition and Properties of B-spline Curves --; 3.3 The Derivatives of a B-spline Curve --; 3.4 Definition and Properties of B-spline Surfaces --; 3.5 Derivatives of a B-spline Surface --; Exercises --; Four Rational B-spline Curves and Surfaces --; 4.1 Introduction --; 4.2 Definition and Properties of NURBS Curves --; 4.3 Derivatives of a NURBS Curve --; 4.4 Definition and Properties of NURBS Surfaces --; 4.5 Derivatives of a NURBS Surface --; Exercises --; Five Fundamental Geometric Algorithms --; 5.1 Introduction --; 5.2 Knot Insertion --; 5.3 Knot Refinement --; 5.4 Knot Removal --; 5.5 Degree Elevation --; 5.6 Degree Reduction --; Exercises --; Six Advanced Geometric Algorithms --; 6.1 Point Inversion and Projection for Curves and Surfaces --; 6.2 Surface Tangent Vector Inversion --; 6.3 Transformations and Projections of Curves and Surfaces --; 6.4 Reparameterization of NURBS Curves and Surfaces --; 6.5 Curve and Surface Reversal --; 6.6 Conversion Between B-spline and Piecewise Power Basis Forms --; Exercises --; Seven Conics and Circles --; 7.1 Introduction --; 7.2 Various Forms for Representing Conics --; 7.3 The Quadratic Rational Bézier Arc --; 7.4 Infinite Control Points --; 7.5 Construction of Circles --; 7.6 Construction of Conics --; 7.7 Conic Type Classification and Form Conversion --; 7.8 Higher Order Circles --; Exercises --; Eight Construction of Common Surfaces --; 8.1 Introduction --; 8.2 Bilinear Surfaces --; 8.3 The General Cylinder --; 8.4 The Ruled Surface --; 8.5 The Surface of Revolution --; 8.6 Nonuniform Scaling of Surfaces --; 8.7 A Three-sided Spherical Surface --; Nine Curve and Surface Fitting --; 9.1 Introduction --; 9.2 Global Interpolation --; 9.3 Local Interpolation --; 9.4 Global Approximation --; 9.5 Local Approximation --; Exercises --; Ten Advanced Surface Construction Techniques --; 10.1 Introduction --; 10.2 Swung Surfaces --; 10.3 Skinned Surfaces --; 10.4 Swept Surfaces --; 10.5 Interpolation of a Bidirectional Curve Network --; 10.6 Coons Surfaces --; Eleven Shape Modification Tools --; 11.1 Introduction --; 11.2 Control Point Repositioning --; 11.3 Weight Modification --; 11.4 Shape Operators --; 11.5 Constraint-based Curve and Surface Shaping --; Twelve Standards and Data Exchange --; 12.1 Introduction --; 12.2 Knot Vectors --; 12.3 Nurbs Within the Standards --; 12.4 Data Exchange to and from a NURBS System --; Thirteen B-spline Programming Concepts --; 13.1 Introduction --; 13.2 Data Types and Portability --; 13.3 Data Structures --; 13.4 Memory Allocation --; 13.5 Error Control --; 13.6 Utility Routines --; 13.7 Arithmetic Routines --; 13.8 Example Programs --; 13.9 Additional Structures --; 13.10 System Structure --; References.

Text of Note

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'U'R-BS Book to be part of the Monographs in Visual Communication Series. B-spline curves and surfaces have been an enduring element throughout my proƯ fessional life. The first edition of Mathematical Elements for Computer Graphics, published in 1972, was the first computer aided design/interactive computer graphƯ 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.

Computer science.

Computer-aided design.

Spline theory -- Data processing.

Class number

Book number

by Les Piegl, Wayne Tiller.

Les Piegl

Wayne Tiller

Electronic name

[Book]

Y