Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code / Edition 4

Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code / Edition 4

by Gerald E. Farin
     
 

ISBN-10: 0122490541

ISBN-13: 9780122490545

Pub. Date: 05/28/1997

Publisher: Elsevier Science & Technology Books

In this fourth edition, the content has been thoroughly revised and updated to include a new chapter on recursive subdivision, new material on nonrectangular topology, surface faceting, stereo lithography, and new sections on triangulations and scattered data interpolants. The disk has been updated to include all of the data sets and the C code used in the book.

Overview

In this fourth edition, the content has been thoroughly revised and updated to include a new chapter on recursive subdivision, new material on nonrectangular topology, surface faceting, stereo lithography, and new sections on triangulations and scattered data interpolants. The disk has been updated to include all of the data sets and the C code used in the book.

Product Details

ISBN-13:
9780122490545
Publisher:
Elsevier Science & Technology Books
Publication date:
05/28/1997
Series:
Computer Science and Scientific Computing Series
Edition description:
Older Edition
Pages:
429
Product dimensions:
6.16(w) x 9.23(h) x 1.12(d)

Table of Contents

P. Bézier: How a Simple System Was Born.
Introductory Material: Points and Vectors.
Affine Maps.
Linear Interpolation.
Piecewise Linear Interpolation.
Menelaos' Theorem.
Barycentric Coordinates in the Plane.
Tessellations and Triangulations.
Function Spaces.
Problems.
The de Casteljau Algorithm: Parabolas.
The de Casteljau Algorithm.
Some Properties of Bézier Curves.
The Blossom.
Implementation.
Problems.
The Bernstein Form of a Bézier Curve: Bernstein Polynomials.
Properties of Bézier Curves.
The Derivative of a Bézier Curve.
Higher Order Derivatives.
Derivatives and the de Casteljau Algorithm.
Subdivision.
Blossom and Polar.
The Matrix Form of a Bézier Curve.
Implementation.
Problems.
Bézier Curve Topics: Degree Elevation.
Repeated Degree Elevation.
The Variation Diminishing Property.
Degree Reduction.
Nonparametric Curves.
Cross Plots.
Integrals.
The Bézier Form of a Bézier Curve.
The Barycentric Form of a Bézier Curve.
The Weierstrass Approximation Theorem.
Formulas for Bernstein Polynomials.
Implementation.
Problems.
Polynomial Interpolation: Aitken's Algorithm.
Lagrange Polynomials.
The Vandermonde Approach.
Limits of Lagrange Interpolation.
Cubic Hermite Interpolation.
Quintic Hermite Interpolation.
The Newton Form and Forward Differencing.
Implementation.
Problems.
Spline Curves in Bézier Form: Global and Local Parameters.
Smoothness Conditions.
C1 and C2 Continuity.
Finding a C1 Parametrization.
C1 Quadratic B-SplineCurves.
C2 Cubic B-Spline Curves.
Finding a Knot Sequence.
Design and Inverse Design.
Implementation.
Problems.
Piecewise Cubic Interpolation: C1 Piecewise Cubic Hermite Interpolation.
C1 Piecewise Cubic Interpolation I.
C1 Piecewise Cubic Interpolation II.
Point-Normal Interpolation.
Font Design.
Problems.
Cubic Spline Interpolation: The B-Spline Form.
The Hermite Form.
End Conditions.
Finding a Knot Sequence.
The Minimum Property.
Implementation.
Problems.
B-Splines: Motivation.
Knot Insertion.
The de Boor Algorithm.
Smoothness of B-Spline Curves.
The B-Spline Basis.
Two Recursion Formulas.
Repeated Knot Insertion.
B-Spline Properties.
B-Spline Blossoms.
Approximation.
B-Spline Basics.
Implementation.
Problems.
W.
Boehm: Differential Geometry I:
Parametric Curves and Arc Length.
The Frenet Frame.
Moving the Frame.
The Osculating Circle.
Nonparametric Curves.
Composite Curves.
Geometric Continuity: Motivation.
The Direct Formulation.
The g Formulation.
The n and b Formulation.
Comparison.
G2 Cubic Splines.
Interpolating G2 Cubic Splines.
Local Basis Functions for G2 Splines.
Higher Order Geometric Continuity.
Implementation.
Problems.
Conic Sections: Projective Maps of the Real Line.
Conics as Rational Quadratics.
A de Casteljau Algorithm.
Derivatives.
The Implicit Form.
Two Classic Problems.
Classification.
Control Vectors.
Implementation.
Problems.
Rational Bézier and B-Spline Curves: Rational Bézier Curves.
The de Casteljau Algorithm.
Derivatives.
Osculatory Interpolation.
Reparametrization and Degree Elevation.
Control Vectors.
Rational Cubic B-Spline Curves.
Interpolation with Rational Cubics.
Rational B-Splines of Arbitrary Degree.
Implementation.
Problems.
Tensor Product Patches: Bilinear Interpolation.
The Direct de Casteljau Algorithm.
The Tensor Product Approach.
Properties.
Degree Elevation.
Derivatives.
Blossoms.
Normal Vectors.
Twists.
The Matrix Form of a Bézier and B-Spline Surfaces.
Surfaces of Revolution.
Volume Deformations.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >