Journal of Prime Research in Mathematics

# $$C^2$$ 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

### 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.