## Handbook on Splines for the UserSplines find ever increasing application in the numerical methods, computer-aided design, and computer graphics areas. The Handbook on Splines for the User not only provides an excellent introduction to basic concepts and methods but also includes the SplineGuide-a computer diskette that allows the reader to practice using important programs.These programs help the user to build interpolating and smoothing cubic and bicubic splines of all classes. Programs are described in Fortran for spline functions and C for geometric splines. The Handbook describes spline functions and geometric splines and provides simple, but effective algorithms. It covers virtually all of the important types of cubic and bicubic splines, functions, variables, curves, and surfaces. The book is written in a straightforward manner and requires little mathematical background. When necessary, the authors give theoretical treatments in an easy-to-use form. Through the Handbook on Splines for the User, introduce yourself to the exciting world of splines and learn to use them in practical applications and computer graphics. |

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### Contents

Why splines? | 1 |

Spline functions | 9 |

Spline functions of two variables | 47 |

Geometric splines | 73 |

Spline surfaces | 141 |

Appendix A Programs of the sweep method for tridiagonal | 205 |

Bibliography | 217 |

### Common terms and phrases

algorithm applied diskette approximating polygon array of vertices Bernstein polynomials bicubic B-spline surface bicubic Bezier surface bicubic Hermite surface boundary conditions boundary curve calculate called Catmull-Rom spline composite Beta-spline surface composite bicubic B-spline composite cubic B-spline composite curve composite rational composite surface construct control polygon convex hull cubic B-spline curve cubic Bezier curve cubic Hermite curve cubic spline function curvature defined described elementary Beta-spline surface elementary Bezier surface elementary cubic elementary curves elementary fragments end conditions end points enddo example Figure formulas function S(x geometric Geometric continuity given array graph interpolating bicubic spline interpolating cubic spline interpolating spline joining point knots of grid Lagrange interpolating polynomial mixed derivative natural parametrization number of points nurbs parametric equations partial derivatives partition of unity planar points in control problem radius-vector rational cubic B-spline respect to variable second derivatives segment shape parameters smoothing spline support vertices tangent vector twist vectors VecCopy vertex