## Curves and Surfaces for Computer-aided Geometric Design: A Practical Guide, Volume 1In 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. |

### What people are saying - Write a review

#### 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 | 12 |

The de Casteljau Algorithm | 33 |

The Bernstein Form of a Bezier Curve | 44 |

Copyright | |

21 other sections not shown

### Other editions - View all

### Common terms and phrases

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