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 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 graph(1).

          The following options are recognized, each as a separate

          -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.