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.