Journal of Prime Research in Mathematics

# Rational cubic spirals

Ayesha Shakeel
Department of Mathematics, University of the Punjab, Lahore, Pakistan.
Maria Hussain
Lahore College for Women University, Lahore, Pakistan.
Malik Zawwar Hussain
Department of Mathematics, University of the Punjab, Lahore, Pakistan.

$$^{1}$$Corresponding Author: ayesha031@hotmail.com

### Abstract

A parametric rational cubic approximation scheme is presented to preserve the monotone curvature profile of the given curve. The rational cubic curve has four control points and two free parameters. Values of control points are attained by $$C^1$$ -approximation. Simple sufficient data dependent constraints are obtained on the free parameters to preserve the monotonicity of curvature of given curve. Devised curvature-preserving approximation scheme is simple and robust.

#### Keywords:

Rational cubic parametric curve, monotone curvature, generalized Cornu spiral, free parameters, curvature-preservation.