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 Conies -- 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.