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SPLINE(1G)                                                          SPLINE(1G)

       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)