SPLINE(1G)                                                          SPLINE(1G)



NAME
       spline - interpolate smooth curve

SYNOPSIS
       spline [ option ] ...

DESCRIPTION
       _S_p_l_i_n_e  takes  pairs of numbers from the standard input as abcissas and
       ordinates of a function.  It produces a similar set, which is  approxi‐
       mately  equally spaced and includes the input set, on the standard out‐
       put.  The cubic spline output (R. W.  Hamming,  _N_u_m_e_r_i_c_a_l  _M_e_t_h_o_d_s  _f_o_r
       _S_c_i_e_n_t_i_s_t_s  _a_n_d  _E_n_g_i_n_e_e_r_s_,  2nd ed., 349ff) has two continuous deriva‐
       tives, and sufficiently many points to look smooth  when  plotted,  for
       example by _g_r_a_p_h(1G).

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

SEE ALSO
       graph(1G), plot(1G)

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

BUGS
       A limit of 1000 input points is enforced silently.



7th Edition                     April 29, 1985                      SPLINE(1G)