


      SPLINE(1)			  (UNIX	5.0)		      SPLINE(1)



      NAME
	   spline - interpolate	smooth curve

      SYNTAX
	   spline [ options ]

      DESCRIPTION
	   Spline takes	pairs of numbers from the standard input as
	   abscissas 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 Engineers, 2nd ed., pp. 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:
		     y'' = ky'',    y''	= ky''
		is set0by the1next 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).

      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 1,000 input points is enforced silently.








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