# ncl_kurvpd - Man Page

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.