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Curves and surfaces for CAGD [[electronic resource] ] : a practical guide / / Gerald Farin
| Curves and surfaces for CAGD [[electronic resource] ] : a practical guide / / Gerald Farin |
| Autore | Farin Gerald E |
| Edizione | [5th ed.] |
| Pubbl/distr/stampa | San Francisco, CA ; ; London, : Morgan Kaufmann, c2002 |
| Descrizione fisica | 1 online resource (521 p.) |
| Disciplina | 006.601516352 |
| Collana | Morgan Kaufmann series in computer graphics and geometric modeling |
| Soggetto topico |
Computer graphics
Computer-aided design |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-07290-7
9786611072902 0-08-050354-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 Algorithm4.3 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 Plots6.7 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; 7.11 The Newton Form and Forward Differencing 7.12 Implementation7.13 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 I10.1 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 |
| Record Nr. | UNINA-9910457961903321 |
Farin Gerald E
|
||
| San Francisco, CA ; ; London, : Morgan Kaufmann, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Curves and surfaces for CAGD [[electronic resource] ] : a practical guide / / Gerald Farin
| Curves and surfaces for CAGD [[electronic resource] ] : a practical guide / / Gerald Farin |
| Autore | Farin Gerald E |
| Edizione | [5th ed.] |
| Pubbl/distr/stampa | San Francisco, CA ; ; London, : Morgan Kaufmann, c2002 |
| Descrizione fisica | 1 online resource (521 p.) |
| Disciplina | 006.601516352 |
| Collana | Morgan Kaufmann series in computer graphics and geometric modeling |
| Soggetto topico |
Computer graphics
Computer-aided design |
| ISBN |
1-281-07290-7
9786611072902 0-08-050354-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 Algorithm4.3 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 Plots6.7 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; 7.11 The Newton Form and Forward Differencing 7.12 Implementation7.13 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 I10.1 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 |
| Record Nr. | UNINA-9910784531003321 |
|
Farin Gerald E
|
||
| San Francisco, CA ; ; London, : Morgan Kaufmann, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Curves and surfaces for CAGD : a practical guide / / Gerald Farin
| Curves and surfaces for CAGD : a practical guide / / Gerald Farin |
| Autore | Farin Gerald E |
| Edizione | [5th ed.] |
| Pubbl/distr/stampa | San Francisco, CA ; ; London, : Morgan Kaufmann, c2002 |
| Descrizione fisica | 1 online resource (521 p.) |
| Disciplina | 006.601516352 |
| Collana | Morgan Kaufmann series in computer graphics and geometric modeling |
| Soggetto topico |
Computer graphics
Computer-aided design |
| ISBN |
1-281-07290-7
9786611072902 0-08-050354-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 Algorithm4.3 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 Plots6.7 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; 7.11 The Newton Form and Forward Differencing 7.12 Implementation7.13 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 I10.1 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 |
| Record Nr. | UNINA-9910811679003321 |
|
Farin Gerald E
|
||
| San Francisco, CA ; ; London, : Morgan Kaufmann, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||