# ncl_kurvpd man page

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/f…

## Copyright

Copyright (C) 2000

University Corporation for Atmospheric Research

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