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cgv2el_c

 Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

```   cgv2el_c ( Center and generating vectors to ellipse )

void cgv2el_c ( ConstSpiceDouble    center[3],
ConstSpiceDouble    vec1  [3],
ConstSpiceDouble    vec2  [3],
SpiceEllipse      * ellips    )

```

#### Abstract

```   Form a SPICE ellipse from a center vector and two generating
vectors.
```

```   ELLIPSES
```

#### Keywords

```   ELLIPSE
GEOMETRY

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
center,
vec1,
vec2       I   Center and two generating vectors for an ellipse.
ellips     O   The SPICE ellipse defined by the input vectors.
```

#### Detailed_Input

```   center,
vec1,
vec2        are a center and two generating vectors defining
an ellipse in three-dimensional space. The
ellipse is the set of points

center  +  cos(theta) * vec1  +  sin(theta) * vec2

where theta ranges over the interval (-pi, pi].
`vec1' and `vec2' need not be linearly independent.
```

#### Detailed_Output

```   ellips      is the SPICE ellipse defined by the input
vectors.
```

#### Parameters

```   None.
```

#### Exceptions

```   1)  If `vec1' and `vec2' are linearly dependent, `ellips' will be
degenerate. SPICE ellipses are allowed to represent
degenerate geometric ellipses.
```

#### Files

```   None.
```

#### Particulars

```   SPICE ellipses serve to simplify calling sequences and reduce
the chance for error in declaring and describing argument lists
involving ellipses.

The set of ellipse conversion routines is

cgv2el_c ( Center and generating vectors to ellipse )
el2cgv_c ( Ellipse to center and generating vectors )
```

#### Examples

```   The numerical results shown for these examples may differ across
platforms. The results depend on the SPICE kernels used as
input, the compiler and supporting libraries, and the machine
specific arithmetic implementation.

1) Create a SPICE ellipse given its center and two linearly
independent generating vectors of the ellipse.

Example code begins here.

/.
Program cgv2el_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables.
./
SpiceDouble          ecentr [3];
SpiceDouble          smajor [3];
SpiceDouble          sminor [3];

SpiceEllipse         ellips;

/.
Define the center and two linearly independent
generating vectors of an ellipse (the vectors need not
be linearly independent).
./
SpiceDouble          center [3] = { -1.0,  1.0, -1.0 };
SpiceDouble          vec1   [3] = {  1.0,  1.0,  1.0 };
SpiceDouble          vec2   [3] = {  1.0, -1.0,  1.0 };

/.
Create the `ellips'.
./
cgv2el_c ( center, vec1, vec2, &ellips );

/.
In a real application, please use CSPICE API el2cgv_c
to retrieve the center and generating vectors from the
ellipse structure (see next block).
./
printf( "SPICE ellipse:\n" );
printf( " Semi-minor axis: %9.6f %9.6f %9.6f\n",
ellips.semiMinor[0],
ellips.semiMinor[1],
ellips.semiMinor[2] );
printf( " Semi-major axis: %9.6f %9.6f %9.6f\n",
ellips.semiMajor[0],
ellips.semiMajor[1],
ellips.semiMajor[2] );
printf( " Center         : %9.6f %9.6f %9.6f\n",
ellips.center[0],
ellips.center[1],
ellips.center[2] );
printf( " \n" );

/.
Obtain the center and generating vectors from the
`ellips'.
./
el2cgv_c ( &ellips, ecentr, smajor, sminor );

printf( "SPICE ellipse (using el2cgv_c):\n" );
printf( " Semi-minor axis: %9.6f %9.6f %9.6f\n",
sminor[0], sminor[1], sminor[2] );
printf( " Semi-major axis: %9.6f %9.6f %9.6f\n",
smajor[0], smajor[1], smajor[2] );
printf( " Center         : %9.6f %9.6f %9.6f\n",
ecentr[0], ecentr[1], ecentr[2] );

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:

SPICE ellipse:
Semi-minor axis:  0.000000  1.414214  0.000000
Semi-major axis:  1.414214 -0.000000  1.414214
Center         : -1.000000  1.000000 -1.000000

SPICE ellipse (using el2cgv_c):
Semi-minor axis:  0.000000  1.414214  0.000000
Semi-major axis:  1.414214 -0.000000  1.414214
Center         : -1.000000  1.000000 -1.000000

2) Find the intersection of an ellipse with a plane.

Example code begins here.

/.
Program cgv2el_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables.
./
SpiceEllipse         ellips;
SpicePlane           plane;
SpiceDouble          xpts   [2][3];

SpiceInt             i;
SpiceInt             nxpts;

/.
The ellipse is defined by the vectors `center', `vec1', and
`vec2'. The plane is defined by the normal vector `normal'
and the `center'.
./
SpiceDouble          center [3] = {  0.0,  0.0,  0.0 };
SpiceDouble          vec1   [3] = {  1.0,  7.0,  2.0 };
SpiceDouble          vec2   [3] = { -1.0,  1.0,  3.0 };

SpiceDouble          normal [3] = {  0.0,  1.0,  0.0 };

/.
Make a SPICE ellipse and a plane.
./
cgv2el_c ( center, vec1, vec2, &ellips );
nvp2pl_c ( normal, center,     &plane  );

/.
Find the intersection of the ellipse and plane.
`nxpts' is the number of intersection points; `xpts'
are the points themselves.
./
inelpl_c ( &ellips, &plane, &nxpts, xpts[0], xpts[1] );

printf( "Number of intercept points: %2d\n", nxpts );

for ( i = 0; i < nxpts; i++ )
{
printf( " Point %1d: %9.6f %9.6f %9.6f\n", i,
xpts[i][0], xpts[i][1], xpts[i][2] );
}

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:

Number of intercept points:  2
Point 0:  1.131371  0.000000 -2.687006
Point 1: -1.131371 -0.000000  2.687006
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
```

#### Version

```   -CSPICE Version 1.1.0, 24-AUG-2021 (JDR)

Edited the header to comply with NAIF standard.
```   center and generating vectors to ellipse
`Fri Dec 31 18:41:02 2021`