## Abstract

The problem of interpolation by a convex curve to the vertices of a convex polygon is considered. A natural 1-parameter family of C^{∞} algebraic curves solving this problem is presented. This is extended to a solution, of a general Hermite-type problem, in, which the curve also interpolates to one or two prescribed tangents at any desired vertices of the polygon. The construction of these curves is a generalization of well known methods for generating conic sections. Several properties of this family of algebraic curves are discussed. In addition, the method is generalized to convex C^{∞} interpolation of strictly convex data sets in R^{3} by algebraic surfaces.

Original language | English |
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Pages (from-to) | 113-139 |

Number of pages | 27 |

Journal | Numerical Algorithms |

Volume | 9 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1995 |