 An Introduction to NURBS by David F. Rogers 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 Bezier Curves: Robin Forrest Chapter 2   Bezier Curves 2.1 Bezier Curve Definition Bezier Curve Algorithm 2.2 Matrix Representation of Bezier Curves 2.3 Bezier Curve Derivatives 2.4 Continuity Between Bezier Curves 2.5 Increasing the Flexibility of Bezier Curves Degree Elevation Subdivision Historical Perspective Biography: Pierre Bezier B-splines: Rich Riesenfeld Chapter 3   B-spline Curves 3.1 B-spline Curve Definition Properties of B-spline Curves 3.2 Convex Hull Properties of B-spline Curves 3.3 Knot Vectors 3.4 B-spline Basis Functions B-spline Curve Controls 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 B-spline Curves Start and End Points Start and End Point Derivatives Controlling Start and End Points Multiple Coincident Vertices Pseudovertices 3.10 B-spline Curve Derivatives 3.11 B-spline Curve Fitting 3.12 Degree Elevation Algorithms 3.13 Degree Reduction Bezier Curve Degree Reduction 3.14 Knot Insertion and B-spline Curve Subdivision 3.15 Knot Removal Pseudocode 3.16 Reparameterization Historical Perspective Subdivision: Elaine Cohen, Tom Lyche and Rich Riesenfeld Chapter 4   Rational B-spline Curves 4.1 Rational B-spline Curves (NURBS) Characteristics of NURBS 4.2 Rational B-spline Basis Functions and Curves Open Rational B-spline Basis Functions and Curves Periodic 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 Rational B-splines: Lewis Knapp Chapter 5   Bezier Surfaces 5.1 Mapping Parametric Surfaces 5.2 Bezier Surface Definition and Characteristic Matrix Representation 5.3 Bezier Surface Derivatives 5.4 Transforming Between Surface Descriptions Historical Perspective Nonuniform Rational B-splines: Ken Versprill 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 Implementation: Al Adams and Dave Rogers Chapter 7   Rational B-spline Surfaces 7.1 Rational B-spline Surfaces (NURBS) 7.2 Characteristics of Rational B-spline Surfaces Positive Homogeneous Weighting Factors Negative Homogeneous Weighting Factors Internally Nonuniform Knot Vector Reparameterization 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 Developable Surfaces 7.8 Surfaces of Revolution 7.9 Blending Surfaces 7.10 A Fast Rational B-spline Surface Algorithm Naive Algorithms A More Efficient Algorithm Incremental Surface Calculation Measure of Computational Effort Appendices A B-spline Surface File Format B Problems C Algorithms References Index About the Author