Mathematica 9 is now available

Wolfram Library Archive


Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings
Title

Convexity Preserving Interpolation by Algebraic Curves and Surfaces
Authors

D. Levin
E. Nadler
Journal / Anthology

Numerical Algorithms
Year: 1995
Volume: 9
Page range: 113-139
Description

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 R3 by algebraic surfaces.
Subjects

*Mathematics > Geometry > Plane Geometry
*Mathematics > Geometry > Surfaces