NAME

       KURVPD - nterpolation and derivatives for closed  parametric curves

SYNOPSIS

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

       This  subroutine  behaves like KURVP2 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 closed 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. KURVP1 must be called before calling KURVPD.

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(1),Y(1)). Any
                   interval [TT,TT+1.] maps onto the entire closed curve.

       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 KURVP1.

       YP          (real,input) An array of length N as computed by KURVP1.

       S           (real,input)  An  array  of  length  N  containing the polygonal arc lengths of the curve, as
                   computed by KURVP1.

       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 KURVPD, load the NCAR Graphics library ngmath.

SEE ALSO

       kurvp1,kurvp2, 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.