SPLINE(1G)					       SPLINE(1G)

NAME
       spline - interpolate smooth curve

SYNOPSIS
       spline [ option ] ...

DESCRIPTION
       Spline  takes  pairs of numbers from the standard input as
       abcissas 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 Scien-
       tists and Engineers, 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
       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

	      (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  lim-
	    its.   Normally  these limits are calculated from the
	    data.   Automatic  abcissas	 start	at  lower   limit
	    (default 0).

SEE ALSO
       graph(1)

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

BUGS
       A limit of 1000 input points is enforced silently.

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