NAME

       c_ftkurvd - calculate interpolated values and derivatives for parametric curves

FUNCTION PROTOTYPE

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

SYNOPSIS

       int c_ftkurvd (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.

       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_ftkurvd 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 ftkurv except that in addition it returns the first and second
       derivatives of the component functions in the parameterization.

       Given  a  sequence  of 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[n-1],y[n-1]).

       c_ftkurvd  is  called after all of the desired values for control parameters have been set
       using the procedures c_ftseti,  c_ftsetr,  c_ftsetc.  Control  parameters  that  apply  to
       c_ftkurvd are: sig, sl1, sln, sf1.

       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).

       The value for parameter sl1 is in radians and contains the slope at (x[0],y[0]). The angle
       is measured counter-clockwise from the X axis and the  positive  sense  of  the  curve  is
       assumed  to  be  that  moving from point 0 to point n-1. A value for sl1 may be omitted as
       indicated by the switch sf1.

       The value for parameter sln is in radians and contains the slope at  (x[n-1],y[n-1]).  The
       angle is measured counter-clockwise from the X axis and the positive sense of the curve is
       assumed to be that moving from point 0 to point n-1. A value for sln  may  be  omitted  as
       indicated by the switch sf1.

       The  value  of  sf1  controls  whether to use the values for sl1 and sln, or compute those
       values internally.  Specifically, sf1

         = 0 if sl1 and sln are user-specified.
         = 1 if sl1 is user-specified, but sln is
             internally calculated.
         = 2 if sln is user-specified, but sl1 is
             internally calculated.
         = 3 if sl1 and sln are internally calculated.

ACCESS

       To use c_ftkurvd, 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.