## The NURBS bookThe NURBS book covers all aspects of non-uniform rational B-splines necessary to design geometry in a computer aided environment. Basic B-spline features, curve and surface algorithms, and state-of-the-art geometry tools are all discussed. Detailed code for design algorithms and computational tricks are covered too, in a lucid, easy-to-understand style, with a minimum of mathematics and using numerous worked examples. The book is a must for students, researchers, and implementors whose work involves the use of splines. |

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### Contents

Chapter One Curve and Surface Basics | 1 |

Chapter Two BSpline Basis Functions | 47 |

Chapter Three Bspline Curves and Surfaces | 81 |

Copyright | |

12 other sections not shown

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### Common terms and phrases

approximation array assume B-spline curve basis functions Bernstein polynomials Bezier curve Bezier form Bezier segment chord length circle circular arc coefficients compute conic constraints continuous control polygon convex hull coordinate cubic curve curve interpolation curve or surface curves and surfaces Cw(u defined degree elevation degree reduced denote direction ellipse equations error example geometric hence homogeneous space hyperbola Input internal knots knot insertion knot refinement knot removal knot span knot vector linear matrix method multiplicity Nlib nonrational nonzero number of control NURBS curve NURBS surface obtain Output parabola parameterization patch piecewise plane polynomial power basis form projection pth-degree quadratic curve rational Bezier rational curves reparameterization repositioning routine ruled surface section curves shown in Figure shows space specified spline surface interpolation surface of revolution tangent three-dimensional three-dimensional space Ui+i Ui+p Ui+p+i vspan warping weights yields zero