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.

UNIX                                               March 1998                                 c_ftkurvpd(3NCARG)