# ncl_c_ftkurvpd - Man Page

interpolation and derivative calculation for closed parametric curves

## Function Prototype

int c_ftkurvpd (int, float [], float [], int, float [],
float [], float [], float [], float [],
float [], float []);

## Synopsis

`int c_ftkurvpd (n, xi, yi, m, t, xo, yo, xd, yd, xdd, ydd);`

## Description

n

The number of input data points. (n > 1)

xi

An array containing the abscissae for the input function.

yi

An array containing the functional values (y[k] is the functional value  at x[k] for k=0,n).

m

The number of desired interpolated points.

t

Contains an array of values for the parameter mapping onto the interpolated curve. Any interval [tt,tt+1.] maps onto the entire curve.

xo

An array containing the X values for the interpolated points.  t[k] maps to (xo[k],yo[k]) for k=0,n-1.

yo

An array containing the Y values for the interpolated points.

xd

Contains the first derivatives of the X component with respect to t.

yd

Contains the first derivatives of the Y component with respect to t.

xdd

Contains the second derivatives of the X component with respect to t.

ydd

Contains the second derivatives of the Y component with respect to t.

## Return Value

c_ftkurvpd returns an error value as per:

= 0 -- no error.
= 1 -- if n is less than 2.
= 2 -- if adjacent coordinate pairs coincide.

## Usage

This procedure behaves like ftkurvp except that in addition it returns  the first and second derivatives of the component functions in the parameterization.

Given a sequence of distinct input points  ( (x,y), ... , (x[n-1],y[n-1]), the interpolated curve is parameterized by mapping points in the interval [0.,1.] onto the  interpolated curve. The resulting curve has a parametric representation both of whose components are splines  under tension and functions of the polygonal arc length. The value 0. is mapped onto  (x,y) and the value 1. is mapped onto (x,y) as well (completing the closed curve).

c_ftkurvpd is called after all of the desired values for control parameters  have been set using the procedures c_ftseti, c_ftsetr, c_ftsetc. The  only control parameter that applies to c_ftkurvpd is: sig.

The value for the parameter sig specifies the 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. (the default).

## Access

To use c_ftkurvpd, load the NCAR Graphics library ngmath.