SPLINE(VI)                   5/15/74                   SPLINE(VI)


     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

     Engineers,  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


     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

          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



     plot (I)


     M. D. McIlroy


     A limit of 1000 input points is enforced silently.