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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