A rational cubic spline for the visualization of monotonic data: An alternate approach

A smooth curve interpolation scheme for monotonic data was developed by Sarfraz (Comput. Graph. 24(4) (2000) 509). This scheme is reviewed and a new alternate approach, which was indicated in Sarfraz (Comput. Graph. 26(1) (2002) 193), has been introduced with all details and solid proofs here. In theory, the new scheme uses the same piecewise rational cubic functions as in Sarfraz (2000), but it utilizes a rational quadratic in practice. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the monotone shape of the data. The new rational spline scheme, like the old one in Sarfraz, 2000, has a unique representation. The degree of smoothness attained is C² and the method of computation is robust. Both, old as well as new shape preserving methods, seem to be equally competent. This is shown by a comparative analysis. There is a trade off between the two methods as far as computational aspects are concerned. However, the new method is superior to the old method as far as accuracy is concerned. This fact has been proved by making an error analysis over the actual and computed curves.