spline(1G)                                             spline(1G)



     NAME
          spline - interpolate smooth curve

     SYNOPSIS
          spline [-a] [-k] [-n] [-p] [-x]

     DESCRIPTION
          spline takes pairs of numbers from the standard input as
          abscissas and ordinates of a function.  It produces a simi-
          lar 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
          Engineers, 2nd ed., pp. 349ff) has two continuous deriva-
          tives, and sufficiently many points to look smooth when
          plotted.

          The following flag 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:

                ''     ''      ''     ''
               y   = ky  ,    y   = ky
                0      1       n      n-1


               is set by the next argument (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 abscissas start at lower limit (default 0).

     EXAMPLES
               spline -n 10 > spline.out
               0 0
               1 2
               2 4
               3 9

          will create the file spline.out with the contents:

               3.000000   8.999999
               2.666667   7.096296



     April, 1990                                                     1

     spline(1G)                                             spline(1G)



               2.333333   5.370370
               2.000000   4.000000
               1.666667   3.096296
               1.333333   2.503703
               1.000000   2.000000
               0.666667   1.407407
               0.333333   0.725926
               0.000000   0.000000

     FILES
          /usr/bin/spline

     DIAGNOSTICS
          When data is not strictly monotone in x, spline reproduces
          the input without interpolating extra points.

     SEE ALSO
          graph(1G), tplot(1G).

     BUGS
          A limit of 1,000 input points is enforced silently.


































     2                                                     April, 1990