\(C^2\) Rational quintic function

Maria Hussain
Department of Mathematics, University of the Punjab, Lahore, Pakistan.
Malik Zawwar Hussain
Department of Mathematics, University of the Punjab, Lahore, Pakistan.
Robert J. Cripps
Geometric Modelling Group, Mechanical and Manufacturing Engineering, University of Birmingham, Birmingham, England.

\(^{1}\)Corresponding Author: malikzawwar@math.pu.edu.pk

Copyright © 2009 Maria Hussain, Malik Zawwar Hussain, Robert J. Cripps. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2009.

Abstract

A two-parameter family of piecewise \(C^2\) rational quintic functions is presented along with an error investigation for the approximation of an arbitrary \(C^3\) function. The two parameters have a direct geometric interpretation making their use straightforward. Illustrations of their effect on the shape of the rational function are given. The relaxed continuity constraints and the increased flexibility via the two parameters make the
proposed function a suitable candidate for interactive CAD

Keywords:

\(C^2\) rational quintic function, free parameters, peono kernel.