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SPLINE(1G)                                                          SPLINE(1G)

       spline - interpolate smooth curve

       spline [ option ] ...

       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(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.

       A limit of 1000 input points is enforced silently.