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edlimb_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

```   edlimb_c ( Ellipsoid Limb )

void edlimb_c ( SpiceDouble           a,
SpiceDouble           b,
SpiceDouble           c,
ConstSpiceDouble      viewpt[3],
SpiceEllipse        * limb      )

```

#### Abstract

```   Find the limb of a triaxial ellipsoid, viewed from a specified
point.
```

```   ELLIPSES
```

#### Keywords

```   ELLIPSE
ELLIPSOID
GEOMETRY
MATH

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
a          I   Length of ellipsoid semi-axis lying on the x-axis.
b          I   Length of ellipsoid semi-axis lying on the y-axis.
c          I   Length of ellipsoid semi-axis lying on the z-axis.
viewpt     I   Location of viewing point.
limb       O   Limb of ellipsoid as seen from viewing point.
```

#### Detailed_Input

```   a,
b,
c           are the lengths of the semi-axes of a triaxial
ellipsoid. The ellipsoid is centered at the
origin and oriented so that its axes lie on the
x, y and z axes.  a, b, and c are the lengths of
the semi-axes that point in the x, y, and z
directions respectively.

viewpt      is a point from which the ellipsoid is viewed.
viewpt must be outside of the ellipsoid.
```

#### Detailed_Output

```   limb        is a SPICE ellipse that represents the limb of
the ellipsoid.
```

#### Parameters

```   None.
```

#### Exceptions

```   1)  If the length of any semi-axis of the ellipsoid is non-positive, the
error SPICE(INVALIDAXISLENGTH) is signaled by a routine in the call
tree of this routine. `limb' is not modified.

2)  If the length of any semi-axis of the ellipsoid is zero after the
semi-axis lengths are scaled by the reciprocal of the magnitude of
the longest semi-axis and then squared, the error
SPICE(DEGENERATECASE) is signaled by a routine in the call tree of
this routine. `limb' is not modified.

3)  If the viewing point `viewpt' is inside the ellipse, the error
SPICE(INVALIDPOINT) is signaled by a routine in the call tree of this
routine. `limb' is not modified.

4)  If the geometry defined by the input ellipsoid and viewing point is
so extreme that the limb cannot be found, the error
SPICE(DEGENERATECASE) is signaled by a routine in the call tree of
this routine.

5)  If the shape of the ellipsoid and the viewing geometry are
such that the limb is an excessively flat ellipsoid, the
limb may be a degenerate ellipse. You must determine whether
this possibility poses a problem for your application.
```

#### Files

```   None.
```

#### Particulars

```   The limb of a body, as seen from a viewing point, is the boundary
of the portion of the body's surface that is visible from that
viewing point. In this definition, we consider a surface point
to be `visible' if it can be connected to the viewing point by a
line segment that doesn't pass through the body. This is a purely
geometrical definition that ignores the matter of which portions
of the surface are illuminated, or whether the view is obscured by

If a body is modeled as a triaxial ellipsoid, the limb is always
an ellipse. The limb is determined by its center, a semi-major
axis vector, and a semi-minor axis vector.

We note that the problem of finding the limb of a triaxial
ellipsoid is mathematically identical to that of finding its
terminator, if one makes the simplifying assumption that the
terminator is the limb of the body as seen from the vertex of the
umbra. So, this routine can be used to solve this simplified
version of the problem of finding the terminator.
```

#### 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) Given an ellipsoid and a viewpoint exterior to it, calculate
the limb ellipse as seen from that viewpoint.

Example code begins here.

/.
Program edlimb_ex1
./
#include <math.h>
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local constants.
./
#define UBEL         9

/.
Local variables.
./
SpiceDouble          a;
SpiceDouble          b;
SpiceDouble          c;
SpiceDouble          ecentr [3];
SpiceEllipse         limb;
SpiceDouble          smajor [3];
SpiceDouble          sminor [3];

/.
Define a viewpoint exterior to the ellipsoid.
./
SpiceDouble          viewpt [3] = { 2.0,  0.0,  0.0 };

/.
Define an ellipsoid.
./
a = sqrt( 2.0 );
b = 2.0 * sqrt( 2.0 );
c = sqrt( 2.0 );

/.
Calculate the limb ellipse as seen by from the
viewpoint.
./
edlimb_c ( a, b, c, viewpt, &limb );

/.
Output the structure components.
./
el2cgv_c ( &limb, ecentr, smajor, sminor );

printf( "Limb ellipse as seen from viewpoint:\n" );
printf( "   Semi-minor axis: %10.6f %10.6f %10.6f\n",
sminor[0], sminor[1], sminor[2] );
printf( "   Semi-major axis: %10.6f %10.6f %10.6f\n",
smajor[0], smajor[1], smajor[2] );
printf( "   Center         : %10.6f %10.6f %10.6f\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:

Limb ellipse as seen from viewpoint:
Semi-minor axis:   0.000000   0.000000  -1.000000
Semi-major axis:   0.000000   2.000000  -0.000000
Center         :   1.000000   0.000000   0.000000

2) We'd like to find the apparent limb of Jupiter, corrected for
light time and stellar aberration, as seen from JUNO
spacecraft's position at a given UTC time.

Use the meta-kernel shown below to load the required SPICE
kernels.

KPL/MK

File name: edlimb_ex2.tm

This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.

In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.

The names and contents of the kernels referenced
by this meta-kernel are as follows:

File name                           Contents
---------                           --------
juno_rec_160522_160729_160909.bsp   JUNO s/c ephemeris
pck00010.tpc                        Planet orientation
naif0012.tls                        Leapseconds

\begindata

'pck00010.tpc',
'naif0012.tls'  )

\begintext

End of meta-kernel

Example code begins here.

/.
Program edlimb_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.
./
#define UTCSTR       "2016 Jul 14 19:45:00"

/.
Local variables.
./
SpiceDouble          center [3];
SpiceDouble          et;
SpiceDouble          jpos   [8];
SpiceEllipse         limb;
SpiceDouble          lt;
SpiceDouble          smajor [3];
SpiceDouble          sminor [3];
SpiceDouble          scpjfc [3];
SpiceDouble          scpos  [3];
SpiceDouble          tipm   [3][3];

SpiceInt             n;

/.
./
furnsh_c ( "edlimb_ex2.tm" );

/.
Find the viewing point in Jupiter-fixed coordinates. To
do this, find the apparent position of Jupiter as seen
from the spacecraft in Jupiter-fixed coordinates and
negate this vector. In this case we'll use light time
and stellar aberration corrections to arrive at the
apparent limb. `jpos' is the Jupiter's position as seen
from the spacecraft.  `scpos' is the spacecraft's position
relative to Jupiter.
./
str2et_c ( UTCSTR, &et );
spkpos_c ( "JUPITER", et, "J2000", "LT+S", "JUNO", jpos, &lt );

vminus_c ( jpos, scpos );

/.
Get Jupiter's semi-axis lengths...
./

/.
...and the transformation from J2OOO to Jupiter
equator and prime meridian coordinates. Note that we
use the orientation of Jupiter at the time of
emission of the light that arrived at the
spacecraft at time `et'.
./
pxform_c ( "J2000", "IAU_JUPITER", et-lt, tipm );

/.
Transform the spacecraft's position into Jupiter-
fixed coordinates.
./
mxv_c ( tipm, scpos, scpjfc );

/.
Find the apparent limb.  `limb' is a SPICE ellipse
representing the limb.
./

/.
`center', `smajor', and `sminor' are the limb's center,
semi-major axis of the limb, and a semi-minor axis
of the limb.  We obtain these from `limb' using the
CSPICE routine el2cgv_c ( Ellipse to center and
generating vectors ).
./
el2cgv_c ( &limb, center, smajor, sminor );

/.
Output the structure components.
./
printf( "Apparent limb of Jupiter as seen from JUNO:\n" );
printf( "   UTC time       :  %s\n", UTCSTR );
printf( "   Semi-minor axis: %13.6f %13.6f %13.6f\n",
sminor[0], sminor[1], sminor[2] );
printf( "   Semi-major axis: %13.6f %13.6f %13.6f\n",
smajor[0], smajor[1], smajor[2] );
printf( "   Center         : %13.6f %13.6f %13.6f\n",
center[0], center[1], center[2] );

return ( 0 );
}

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

Apparent limb of Jupiter as seen from JUNO:
UTC time       :  2016 Jul 14 19:45:00
Semi-minor axis:  12425.547643  -5135.572410  65656.053303
Semi-major axis:  27305.667297  66066.222576     -0.000000
Center         :    791.732472   -327.228993   -153.408849
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

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

#### Version

```   -CSPICE Version 1.1.1, 24-AUG-2021 (NJB) (JDR)

Edited the header to comply with NAIF standard.

-CSPICE Version 1.1.0, 24-JUN-2014 (NJB)

Edit to correct chkout_c call passing the wrong routine name.

-CSPICE Version 1.0.1, 24-OCT-2005 (NJB)

Header update: reference to bodvar_c was replaced with
reference to bodvcd_c.

-CSPICE Version 1.0.0, 13-JUN-1999 (NJB)
```

#### Index_Entries

```   ellipsoid limb
```
`Fri Dec 31 18:41:05 2021`