spline [-aknpx] ...
spline takes pairs of numbers from the standard input as abcissas and ordinates of a function. It produces a similar set, which is approximately equally spaced and includes the input set, on the standard output. The cubic spline output (R. W. Hamming, Numerical Methods for Scientists and Engineers,2nd ed., 349ff) has two continuous derivatives, and sufficiently many points to look smooth when plotted, for example by graph(1).
Supply abscissas automatically (they are missing from the input); spacing is given by the next argument, or is assumed to be 1 if next argument is not a number.
The constant k used in the boundary value computation
(2nd deriv. at end) = k*(2nd deriv. next to end)
is set by the next argument. By default k = 0.
Space output points so that approximately n intervals occur between the lower and upper x limits. (Default n = 100.)
Make output periodic, that is, match derivatives at ends. First and last input values should normally agree.
Next 1 (or 2) arguments are lower (and upper) x limits. Normally these limits are calculated from the data. Automatic abcissas start at lower limit (default 0).
See attributes(5) for descriptions of the following attributes:
When data is not strictly monotonic in x, spline reproduces the input without interpolating extra points.
A limit of 1000 input points is enforced silently.