NAME

       c_ftkurvpd - interpolation and derivative calculation for closed parametric curves

FUNCTION PROTOTYPE

       int c_ftkurvpd (int, float [], float [], int, float [],
                       float [], float [], float [], float [],
                       float [], float []);

SYNOPSIS

       int c_ftkurvpd (n, xi, yi, m, t, xo, yo, xd, yd, xdd, ydd);

DESCRIPTION

       n           The number of input data points. (n > 1)

       xi          An array containing the abscissae for the input function.

       yi          An  array  containing  the  functional values (y[k] is the functional value at
                   x[k] for k=0,n).

       m           The number of desired interpolated points.

       t           Contains an array of values for the parameter mapping  onto  the  interpolated
                   curve. Any interval [tt,tt+1.] maps onto the entire curve.

       xo          An  array  containing  the X values for the interpolated points.  t[k] maps to
                   (xo[k],yo[k]) for k=0,n-1.

       yo          An array containing the Y values for the interpolated points.

       xd          Contains the first derivatives of the X component with respect to t.

       yd          Contains the first derivatives of the Y component with respect to t.

       xdd         Contains the second derivatives of the X component with respect to t.

       ydd         Contains the second derivatives of the Y component with respect to t.

RETURN VALUE

       c_ftkurvpd returns an error value as per:

       = 0 -- no error.
       = 1 -- if n is less than 2.
       = 2 -- if adjacent coordinate pairs coincide.

USAGE

       This procedure behaves like ftkurvp except that in  addition  it  returns  the  first  and
       second derivatives of the component functions in the parameterization.

       Given  a  sequence  of  distinct  input  points  ( (x[0],y[0]), ... , (x[n-1],y[n-1]), the
       interpolated curve is parameterized by mapping points in the  interval  [0.,1.]  onto  the
       interpolated  curve.  The  resulting  curve  has a parametric representation both of whose
       components are splines under tension and functions of the polygonal arc length. The  value
       0.  is  mapped  onto  (x[0],y[0])  and  the  value  1.  is mapped onto (x[0],y[0]) as well
       (completing the closed curve).

       c_ftkurvpd is called after all of the desired values for control parameters have been  set
       using the procedures c_ftseti, c_ftsetr, c_ftsetc. The only control parameter that applies
       to c_ftkurvpd is: sig.

       The value for the parameter sig specifies the tension factor. Values near zero result in a
       cubic spline; large values (e.g. 50) result in nearly a polygonal line. A typical value is
       1. (the default).

ACCESS

       To use c_ftkurvpd, load the NCAR Graphics library ngmath.

SEE ALSO

       fitgrid_params, c_ftseti, c_ftsetr, c_ftsetc.

       Complete documentation for Fitgrid is available at URL
       http://ngwww.ucar.edu/ngdoc/ng/ngmath/fitgrid/fithome.html

COPYRIGHT

       Copyright (C) 2000
       University Corporation for Atmospheric Research

       The use of this Software is governed by a License Agreement.