## Curves and Surfaces for Computer Aided Geometric Design: A Practical GuideThe emphasis in this beautifully illustrated text is on the concepts of Bezier and B-spline methods for curves, rational Bezier and B-spline curves, geometric continuity, spline interpolation and Coon methods. While no prior geometric training is needed as a prerequisite for this text - a background in calculus and basic linear algebra is sufficient - two chapters written by W. Boehm have been included to introduce the reader to those concepts of differential geometry that are relevant to computer aided geometric design. The volume also contains one chapter by P. Bezier: How a Simple System Was Born. This book is of interest to software developers for CAD/CAM systems, geometric modeling researchers and graphics programmers. This third edition includes several new sections and numerical examples, a treatment of the new blossoming principle, and new C programs. All C programs are available on a disk included with the book. The Problems Sections at the end of each chapter have also been extended. |

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#### LibraryThing Review

User Review - tomhudson - LibraryThingHard reading, but I don't know a better book on the details of the subjects it covers. Some of these seem to be obsolete for the modern applications I deal with... Read full review

### Contents

Introductory Material | 13 |

The de Casteljau Algorithm | 29 |

The Bernstein Form of a Bezier Curve | 41 |

Copyright | |

23 other sections not shown

### Other editions - View all

Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide Gerald Farin Limited preview - 2014 |

### Common terms and phrases

affine map arc length B-spline polygon barycentric combination barycentric coordinates Bernstein polynomials Bezier curve Bezier form Bezier patch Bezier surface Bezier triangles bicubic bilinearly blended Coons blended Coons patch blossom Boor algorithm boundary curves called Casteljau algorithm Chapter coefficients collinear compute control points control polygon control vertices convex hull corresponding cross boundary derivatives cubic Hermite cubic spline curvature plot data points defined degree elevation denote differentiable end conditions equation evaluate example geometric continuity given Hermite form Hermite interpolation illustrated in Figure input interpolation problem intersection interval isoparametric curve junction points knot insertion knot sequence linear interpolation matrix method obtain parabola parameter values piecewise cubic piecewise linear piecewise polynomial planar polynomial curve polynomial interpolation projection rational B-spline rational Bezier curve reparametrization result ruled surface segment shown in Figure spline interpolation straight line tangent plane tangent vector tensor product theorem triangular patches twist univariate weights zero