Curves and surfaces for CAGD : a practical guide
This fifth edition has been fully updated to cover the many advances made in CAGD and curve and surface theory since 1997, when the fourth edition appeared.Material has been restructured into theory and applications chapters.
Saved in:
| Main Author: | |
|---|---|
| Format: | eBook Book |
| Language: | English |
| Published: |
San Francisco, Calif
Morgan Kaufmann
2002
Elsevier Science & Technology |
| Edition: | 5 |
| Series: | The Morgan Kaufmann series in computer graphics and geometric |
| Subjects: | |
| ISBN: | 1558607374, 9781558607378 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 7.11 The Newton Form and Forward Differencing -- 7.12 Implementation -- 7.13 Problems -- Chapter 8. B-Spline Curves -- 8.1 Motivation -- 8.2 B-Spline Segments -- 8.3 B-Spline Curves -- 8.4 Knot Insertion -- 8.5 Degree Elevation -- 8.6 Greville Abscissae -- 8.7 Smoothness -- 8.8 B-Splines -- 8.9 B-Spline Basics -- 8.10 Implementation -- 8.11 Problems -- Chapter 9. Constructing Spline Curves -- 9.1 Greville Interpolation -- 9.2 Least Squares Approximation -- 9.3 Modifying B-Spline Curves -- 9.4 C2 Cubic Spline Interpolation -- 9.5 More End Conditions -- 9.6 Finding a Knot Sequence -- 9.7 The Minimum Property -- 9.8 C1 Piecewise Cubic Interpolation -- 9.9 Implementation -- 9.10 Problems -- Chapter 10. W. Boehm: Differential Geometry I -- 10.1 Parametric Curves and Arc Length -- 10.2 The Frenet Frame -- 10.3 Moving the Frame -- 10.4 The Osculating Circle -- 10.5 Nonparametric Curves -- 10.6 Composite Curves -- Chapter 11. Geometric Continuity -- 11.1 Motivation -- 11 2 The Direct Formulation -- 11 3 The γ, ν, and β Formulations -- 11 4 C2 Cubic Splines -- 11 5 Interpolating C2 Cubic Splines -- 11.6 Higher-Order Geometric Continuity -- 11.7 Implementation -- 11.8 Problems -- Chapter 12. Conic Sections -- 12.1 Projective Maps of the Real Line -- 12.2 Conies as Rational Quadratics -- 12.3 A de Casteljau Algorithm -- 12.4 Derivatives -- 12.5 The Implicit Form -- 12.6 Two Classic Problems -- 12.7 Classification -- 12.8 Control Vectors -- 12.9 Implementation -- 12.10 Problems -- Chapter 13. Rational Bézier and B-Spline Curves -- 13.1 Rational Bézier Curves -- 13.2 The de Casteljau Algorithm -- 13.3 Derivatives -- 13.4 Osculatory Interpolation -- 13.5 Reparametrization and Degree Elevation -- 13.6 Control Vectors -- 13.7 Rational Cubic B-Spline Curves -- 13.8 Interpolation with Rational Cubics -- 13.9 Rational B-Splines of Arbitrary Degree
- 19.2 The Local Frame -- 19.3 The Curvature of a Surface Curve -- 19.4 Meusnier's Theorem -- 19.5 Lines of Curvature -- 19.6 Gaussian and Mean Curvature -- 19.7 Euler's Theorem -- 19.8 Dupin's Indicatrix -- 19.9 Asymptotic Lines and Conjugate Directions -- 19.10 Ruled Surfaces and Developables -- 19.11 Nonparametric Surfaces -- 19.12 Composite Surfaces -- Chapter 20. Geometric Continuity for Surfaces -- 20.1 Introduction -- 20.2 Triangle-Triangle -- 20.3 Rectangle-Rectangle -- 20.4 Rectangle-Triangle -- 20.5 "Filling in" Rectangular Patches -- 20.6 "Filling in" Triangular Patches -- 20.7 Theoretical Aspects -- 20.8 Problems -- Chapter 21. Surfaces with Arbitrary Topology -- 21.1 Recursive Subdivision Curves -- 21.2 Doo-Sabin Surfaces -- 21.3 Catmull-Clark Subdivision -- 21.4 Midpoint Subdivision -- 21.5 Loop Subdivision -- 21.6 √3 Subdivision -- 21.7 Interpolating Subdivision Surfaces -- 21.8 Surface Splines -- 21.9 Triangular Meshes -- 21.10 Decimation -- 21.11 Problems -- Chapter 22. Coons Patches -- 22.1 Coons Patches: Bilinearly Blended -- 22.2 Coons Patches: Partially Bicubically Blended -- 22.3 Coons Patches: Bicubically Blended -- 22.4 Piecewise Coons Surfaces -- 22.5 Two Properties -- 22.6 Compatibility -- 22.7 Gordon Surfaces -- 22.8 Boolean Sums -- 22.9 Triangular Coons Patches -- 22.10 Problems -- Chapter 23. Shape -- 23.1 Use of Curvature Plots -- 23.2 Curve and Surface Smoothing -- 23.3 Surface Interrogation -- 23.4 Implementation -- 23.5 Problems -- Chapter 24. Evaluation of Some Methods -- 24.1 Bézier Curves or B-Spline Curves? -- 24.2 Spline Curves or B-Spline Curves? -- 24.3 The Monomial or the Bézier Form? -- 24.4 The B-Spline or the Hermite Form? -- 24.5 Triangular or Rectangular Patches? -- Appendix A. Quick Reference of Curve and Surface Terms -- Appendix B. List of Programs -- Appendix C. Notation -- References -- Index
- Front Cover -- Curves and Surfaces for CAGD: A Practical Guide -- Copyright Page -- 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 Constructing Affine Maps -- 2.4 Function Spaces -- 2.5 Problems -- Chapter 3. Linear Interpolation -- 3.1 Linear Interpolation -- 3.2 Piecewise Linear Interpolation -- 3.3 Menelaos' Theorem -- 3.4 Blossoms -- 3.5 Barycentric Coordinates in the Plane -- 3.6 Tessellations -- 3.7 Triangulations -- 3.8 Problems -- Chapter 4. The de Casteljau Algorithm -- 4.1 Parabolas -- 4.2 The de Casteljau Algorithm -- 4.3 Some Properties of Bézier Curves -- 4.4 The Blossom -- 4.5 Implementation -- 4.6 Problems -- Chapter 5. The Bernstein Form of a Bézier Curve -- 5.1 Bernstein Polynomials -- 5.2 Properties of Bézier Curves -- 5.3 The Derivatives of a Bézier Curve -- 5.4 Domain Changes and Subdivision -- 5.5 Composite Bézier Curves -- 5.6 Blossom and Polar -- 5.7 The Matrix Form of a Beziér Curve -- 5.8 Implementation -- 5.9 Problems -- Chapter 6. Bézier Curve Topics -- 6.1 Degree Elevation -- 6.2 Repeated Degree Elevation -- 6.3 The Variation Diminishing Property -- 6.4 Degree Reduction -- 6.5 Nonparametric Curves -- 6.6 Cross Plots -- 6.7 Integrals -- 6.8 The Bézier Form of a Bézier Curve -- 6.9 The Weierstrass Approximation Theorem -- 6.10 Formulas for Bernstein Polynomials -- 6.11 Implementation -- 6.12 Problems -- Chapter 7. Polynomial Curve Constructions -- 7.1 Aitken's Algorithm -- 7.2 Lagrange Polynomials -- 7.3 The Vandermonde Approach -- 7.4 Limits of Lagrange Interpolation -- 7.5 Cubic Hermite Interpolation -- 7.6 Quintic Hermite Interpolation -- 7.7 Point-Normal Interpolation -- 7.8 Least Squares Approximation -- 7.9 Smoothing Equations -- 7.10 Designing with Bézier Curves
- 13.10 Implementation -- 13.11 Problems -- Chapter 14. Tensor Product Patches -- 14.1 Bilinear Interpolation -- 14.2 The Direct de Casteljau Algorithm -- 14.3 The Tensor Product Approach -- 14.4 Properties -- 14.5 Degree Elevation -- 14.6 Derivatives -- 14.7 Blossoms -- 14.8 Curves on a Surface -- 14.9 Normal Vectors -- 14.10 Twists -- 14.11 The Matrix Form of a Bézier Patch -- 14.12 Nonparametric Patches -- 14.13 Problems -- Chapter 15. Constructing Polynomial Patches -- 15.1 Ruled Surfaces -- 15.2 Coons Patches -- 15.3 Translational Surfaces -- 15.4 Tensor Product Interpolation -- 15.5 Bicubic Hermite Patches -- 15.6 Least Squares -- 15.7 Finding Parameter Values -- 15.8 Shape Equations -- 15.9 A Problem with Unstructured Data -- 15.10 Implementation -- 15.11 Problems -- Chapter 16. Composite Surfaces -- 16.1 Smoothness and Subdivision -- 16.2 Tensor Product B-Spline Surfaces -- 16.3 Twist Estimation -- 16.4 Bicubic Spline Interpolation -- 16.5 Finding Knot Sequences -- 16.6 Rational Bézier and B-Spline Surfaces -- 16.7 Surfaces of Revolution -- 16.8 Volume Deformations -- 16.9 CONS and Trimmed Surfaces -- 16.10 Implementation -- 16.11 Problems -- Chapter 17. Bézier Triangles -- 17.1 The de Casteljau Algorithm -- 17.2 Triangular Blossoms -- 17.3 Bernstein Polynomials -- 17.4 Derivatives -- 17.5 Subdivision -- 17.6 Differentiability -- 17.7 Degree Elevation -- 17.8 Nonparametric Patches -- 17.9 The Multivariate Case -- 17.10 S-Patches -- 17.11 Implementation -- 17.12 Problems -- Chapter 18. Practical Aspects of Bézier Triangles -- 18.1 Rational Bézier Triangles -- 18.2 Quadrics -- 18.3 Interpolation -- 18.4 Cubic and Quintic Interpolants -- 18.5 The Clough-Tocher Interpolant -- 18.6 The Powell-Sabin Interpolant -- 18.7 Least Squares -- 18.8 Problems -- Chapter 19. W. Boehm: Differential Geometry II -- 19.1 Parametric Surfaces and Arc Element
- Color Plate Section