Curves and surfaces for CAGD : a practical guide / Gerald Farin.

Format:

Book

Author/Creator:

Farin, Gerald E.

Series:

Morgan Kaufmann series in computer graphics and geometric modeling.

Morgan Kaufmann series in computer graphics and geometric modeling

Language:

English

Subjects (All):

Computer graphics.

Computer-aided design.

Physical Description:

1 online resource (521 p.)

Edition:

5th ed.

Place of Publication:

San Francisco, CA ; London : Morgan Kaufmann, c2002.

Language Note:

English

System Details:

text file

Summary:

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. The theory material has been streamlined using the blossoming approach; the applications material includes least squares techniques in addition to the traditional interpolation methods. In all other respects, it is, thankfully, the same. This means you get the informal, friendly style and unique approach that has made Curves and Surfaces for CAGD: A Practical G

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 449-489) and index.

ISBN:

1-281-07290-7

9786611072902

0-08-050354-3

OCLC:

476112759