NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION - HARIM, NOOR ADILLA (2020)
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.