


      SSSSPPPPLLLLIIIINNNNEEEE((((1111))))                   ((((UUUUNNNNIIIIXXXX 5555....0000))))                  SSSSPPPPLLLLIIIINNNNEEEE((((1111))))



      NNNNAAAAMMMMEEEE
           spline - interpolate smooth curve

      SSSSYYYYNNNNTTTTAAAAXXXX
           sssspppplllliiiinnnneeee [ options ]

      DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
           _S_p_l_i_n_e 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, _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., pp. 349ff) has two
           continuous derivatives, and sufficiently many points to look
           smooth when plotted, for example by _g_r_a_p_h(1).

           The following _o_p_t_i_o_n_s are recognized, each as a separate
           argument:

           ----aaaa   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.

           ----kkkk   The constant _k used in the boundary value computation:
                     y907''9 = ky917''9,    y9n7''9 = ky9n-17''
9                is set by the next argument (default _k = 0).

           ----nnnn   Space output points so that approximately _n intervals
                occur between the lower and upper _x limits (default _n =
                100).

           ----pppp   Make output periodic, i.e., match derivatives at ends.
                First and last input values should normally agree.

           ----xxxx   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).

      SSSSEEEEEEEE AAAALLLLSSSSOOOO
           graph(1).

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

      BBBBUUUUGGGGSSSS
           A limit of 1,000 input points is enforced silently.








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