    SPLINE(VI)                   5/15/74                   SPLINE(VI)

    NAME
         spline - interpolate smooth curve

    SYNOPSIS
         spline [ option ] ...

    DESCRIPTION
         Spline takes pairs of numbers from the standard input as ab-
         cissas 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 Engi-
         neers, 2nd ed., 349ff) has two continuous  derivatives,  and
         sufficiently  many  points  to look smooth when plotted, for
         example by plot(I).

         The following options are recognized, each as a separate ar-
         gument.

         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 points oc-
              cur 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).

    SEE ALSO
         plot(I)

    AUTHOR
         M. D. McIlroy

    BUGS
         A limit of 1000 input points is enforced silently.

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