spline - interpolate smooth curve
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 approxi-
mately equally spaced and includes the input set, on the standard out-
put. The cubic spline output (R. W. Hamming, Numerical Methods for
Scientists and Engineers, 2nd ed., 349ff) has two continuous deriva-
tives, and sufficiently many points to look smooth when plotted, for
example by graph(1G).
-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, that is, 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).
R. W. Hamming, Numerical Methods for Scientists and Engineers, 2nd ed.
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.
9 September 1987 SPLINE(1G)