Front Cover; Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide; Copyright Page; Table of Contents; Preface; Chapter 1. P. Bézier: How a Simple System Was Born; Chapter 2. Introductory Material; 2.1 Points and Vectors; 2.2 Affine Maps; 2.3 Linear Interpolation; 2.4 Piecewise Linear Interpolation; 2.5 Menelaos' Theorem; 2.6 Function Spaces; 2.7 Problems; Chapter 3. The de Casteljau Algorithm; 3.1 Parabolas; 3.2 The de Casteljau Algorithm; 3.3 Some Properties of Bézier Curves; 3.4 The Blossom; 3.5 Implementation; 3.6 Problems

Chapter 4. The Bernstein Form of a Bézier Curve4.1 Bernstein Polynomials; 4.2 Properties of Bézier Curves; 4.3 The Derivative of a Bézier Curve; 4.4 Higher Order Derivatives; 4.5 Derivatives and the de Casteljau Algorithm; 4.6 Subdivision; 4.7 Blossom and Polar; 4.8 The Matrix Form of a Bézier Curve; 4.9 Implementation; 4.10 Problems; Chapter 5. Bézier Curve Topics; 5.1 Degree Elevation; 5.2 Repeated Degree Elevation; 5.3 The Variation Diminishing Property; 5.4 Degree Reduction; 5.5 Nonparametric Curves; 5.6 Cross Plots; 5.7 Integrals; 5.8 The Bézier Form of a Bézier Curve

5.9 The Barycentric Form of a Bézier Curve5.10 The Weierstrass Approximation Theorem; 5.11 Formulas for Bernstein Polynomials; 5.12 Implementation; 5.13 Problems; Chapter 6. Polynomial Interpolation; 6.1 Aitken's Algorithm; 6.2 Lagrange Polynomials; 6.3 The Vandermonde Approach; 6.4 Limits of Lagrange Interpolation; 6.5 Cubic Hermite Interpolation; 6.6 Quintic Hermite Interpolation; 6.7 The Newton Form and Forward Differencing; 6.8 Implementation; 6.9 Problems; Chapter 7. Spline Curves in Bézier Form; 7.1 Global and Local Parameters; 7.2 Smoothness Conditions; 7.3 C1 Continuity

7.4 C2 Continuity7.5 Finding a C1 Parametrization; 7.6 C1 Quadratic B-spline Curves; 7.7 C2 Cubic B-spline Curves; 7.8 Parametrizations; 7.9 Design and Inverse Design; 7.10 Implementation; 7.11 Problems; Chapter 8. Piecewise Cubic Interpolation; 8.1 C1 Piecewise Cubic Hermite Interpolation; 8.2 C1 Piecewise Cubic Interpolation I; 8.3 C1 Piecewise Cubic Interpolation II; 8.4 Point-Normal Interpolation; 8.5 Font Generation; 8.6 Problems; Chapter 9. Cubic Spline Interpolation; 9.1 The B-spline Form; 9.2 The Hermite Form; 9.3 End Conditions; 9.4 Parametrization; 9.5 The Minimum Property

9.6 Implementation9.7 Problems; Chapter 10. B-splines; 10.1 Motivation; 10.2 Knot Insertion; 10.3 The de Boor Algorithm; 10.4 Smoothness of B-spline Curves; 10.5 The B-spline Basis; 10.6 Two Recursion Formulas; 10.7 Repeated Knot Insertion; 10.8 Additional Material; 10.9 B-spline Blossoms; 10.10 B-spline Basics; 10.11 Implementation; 10.12 Problems; Chapter 11. W. Boehm: Differential Geometry I; 11.1 Parametric Curves and Arc Length; 11.2 The Frenet Frame; 11.3 Moving the Frame; 11.4 The Osculating Circle; 11.5 Nonparametric Curves; 11.6 Composite Curves; Chapter 12. Geometric Continuity I