Calculate the Fritsch-Carlson monotone cubic spline interpolation for the given abscissa vector x and ordinate vector y. All vectors must have conformant dimenions. The abscissa vector must be strictly increasing.

The Fritsch-Carlson interpolation produces a neat monotone piecewise cubic curve, which is especially suited for the presentation of scientific data. This is the state of the art to create curves that preserve monotonicity, although it is not so well known as Akima's interpolation. The commonly used Akima interpolation doesn't produce so pleasant results.

             Reference:
                F.N.Fritsch,R.E.Carlson: Monotone Piecewise Cubic
                Interpolation, SIAM J. Numer. Anal. Vol 17, No. 2,
                April 1980
            
             Copyright (C) 1991-1998 by Berndt M. Gammel
             Translated to C# by Dirk Lellinger.