spline - interpolate smooth curve
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).
The following options are recognized, each as a separate
argument.
- -a
- 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.
- -k
- 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.
- -n
- Space output points so that approximately n intervals occur between
the lower and upper x limits. (Default n = 100.)
- -p
- Make output periodic, i.e. match derivatives at ends. First and last input
values should normally agree.
- -x
- 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).
When data is not strictly monotone in x, spline reproduces the
input without interpolating extra points.