Curves and surfaces for computer aided geometric design : a practical guide /

A leading expert in CAGD, Gerald Farin covers the representation, manipulation, and evaluation of geometric shapes in this the Third Edition of Curves and Surfaces for Computer Aided Geometric Design. The book offers an introduction to the field that emphasizes Bernstein-Bezier methods and presents...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Farin, Gerald E.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston : Academic Press, �1993.
Edición:3rd ed.
Colección:Computer science and scientific computing.
Temas:
Computer graphics.
Infographie.
computer graphics.
Computer graphics
Geometrische Modellierung
Graphics > Use of > Computers
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover; Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide; Copyright Page; Table of Contents; Preface; Chapter 1. P. B�ezier: 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 B�ezier Curves; 3.4 The Blossom; 3.5 Implementation; 3.6 Problems
  • Chapter 4. The Bernstein Form of a B�ezier Curve4.1 Bernstein Polynomials; 4.2 Properties of B�ezier Curves; 4.3 The Derivative of a B�ezier 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 B�ezier Curve; 4.9 Implementation; 4.10 Problems; Chapter 5. B�ezier 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 B�ezier Form of a B�ezier Curve
  • 5.9 The Barycentric Form of a B�ezier 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 B�ezier 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

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