NAME

       KURVD - interpolation and derivatives for parametric curves

SYNOPSIS

       CALL KURVD (T, XS, YS, XST, YST, XSTT, YSTT, N, X, Y, XP, YP, S, SIGMA)

       This subroutine behaves like KURV2 except that in addition it returns the first and second
       derivatives of the component functions in the parameterization. The interval [0.,1.]  maps
       onto  a  curve  in the plane.  The resulting curve has a parametric representation both of
       whose components are splines under tension and functions  of  the  polygonal  arc  length.
       KURV1 must be called before calling KURVD.

DESCRIPTION

       T           (real,input)  A  value  to  be  mapped  to  a point on the curve. The interval
                   [0.,1.] is mapped onto the curve such that 0. is mapped to (X(1),Y(1)) and  1.
                   is mapped to (X(N),Y(N)). Values outside of [0.,1.] result in extrapolation.

       XS          (real,output) Contains the X coordinate of the point that T maps to.

       YS          (real,output) Contains the Y coordinate of the point that T maps to.

       XST         (real,output)  Contains  the first derivatives of the X component with respect
                   to T.

       YST         (real,output) Contains the first derivatives of the Y component  with  respect
                   to T.

       XSTT        (real,output)  Contains the second derivatives of the X component with respect
                   to T.

       YSTT        (real,output) Contains the second derivatives of the X component with  respect
                   to T.

       N           (integer,input) The number of input data points. (N > 1)

       X           (real,input) An array containing the X values of the input points.

       Y           (real,input)  An  array  containing the Y values of the input points. Adjacent
                   pairs of points must be distinct.

       XP          (real,input) An array of length N as computed by KURV1.

       YP          (real,input) An array of length N as computed by KURV1.

       S           (real,input) An array of length N containing the polygonal arc lengths of  the
                   curve, as computed by KURV1.

       SIGMA       (real,input)  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.

ACCESS

       To use KURVD, load the NCAR Graphics library ngmath.

SEE ALSO

       kurv1,kurv2, fitgrid_params.

       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.