NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION

The work on interpolation schemes by previous researches had limitations such as,
the inability to produce positive interpolating curves on the entire given intervals,
interpolating curves and surfaces that are not smooth and visually pleasing. Smoothness
and visually pleasing curves are important for computer graphics display. Hence, these
schemes are not suitable for shape preserving interpolation. In this study, a new rational
quartic spline function with three parameters of the form quartic numerator and
quadratic denominator is proposed to overcome these problems. These free parameters
can be used to modify the final shape of the interpolating curve as well as to reduce the
interpolation error. The proposed rational spline has a first order of parametric
continuity, C1. Furthermore, the proposed rational spline also can achieve C2 continuity
without the need to solve any tri-diagonal systems of linear equations unlike some other
splines that need linear systems of equation to be solved. The proposed scheme is tested
for 2D data interpolation as well as positivity-preserving interpolation. The main
advantage of the proposed scheme is that it will produce positive curves everywhere
for positive datasets unlike other schemes. Furthermore, an error analysis by calculating
the absolute error and root mean square error (RMSE) indicates that the proposed
scheme is better than some existing schemes.