The interpolate(double, double) method returns a PolynomialSplineFunction
consisting of n cubic polynomials, defined over the subintervals determined by the x values,
x < x[i] ... < x[n]. The x values are referred to as "knot points."
The value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest
knot point and strictly less than the largest knot point is computed by finding the subinterval to which
x belongs and computing the value of the corresponding polynomial at x - x[i] where
i is the index of the subinterval. See PolynomialSplineFunction for more details.
x - x[i]
The interpolating polynomials satisfy:
The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires,
Numerical Analysis, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131.