Provided by: libncarg-dev_6.3.0-6build1_amd64

#### 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.

```

#### SEEALSO

```       kurvp1,kurvp2, fitgrid_params.

Complete documentation for Fitgrid is available at URL
http://ngwww.ucar.edu/ngdoc/ng/ngmath/fitgrid/fithome.html

```

```       Copyright (C) 2000