## 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[0],y[0]), ... , (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[0],y[0]) and the value 1. is mapped onto (x[0],y[0]) 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.## COPYRIGHT

Copyright (C) 2000University Corporation for Atmospheric Research

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