Rational spline interpolation preserving the shape of the monotonic data

A curve interpolation scheme for monotonic data has been developed. This scheme uses piecewise rational cubic functions. The parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data as well as to control the shape if further modification is required. An algorithm has been constructed, for the economical C¹ curve implementation and pleasant demonstration. Furthermore, the C² case has also been considered for further smoothing the interpolant