KURVD - interpolation and derivatives for parametric curves

       To use KURVD, load the NCAR Graphics library ngmath.

       Copyright (C) 2000
       University Corporation for Atmospheric Research

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

UNIX                                               March 1998                                      KURVD(3NCARG)

       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.

       KURVD - interpolation and derivatives for parametric curves

       kurv1,kurv2, fitgrid_params.

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

       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.