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inedpl_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

```   inedpl_c ( Intersection of ellipsoid and plane )

void inedpl_c ( SpiceDouble           a,
SpiceDouble           b,
SpiceDouble           c,
ConstSpicePlane     * plane,
SpiceEllipse        * ellips,
SpiceBoolean        * found    )

```

#### Abstract

```   Find the intersection of a triaxial ellipsoid and a plane.
```

```   ELLIPSES
PLANES
```

#### 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.
plane      I   Plane that intersects ellipsoid.
ellips     O   Intersection ellipse, when `found' is SPICETRUE.
found      O   Flag indicating whether ellipse was found.
```

#### 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.

plane       is a SPICE plane.
```

#### Detailed_Output

```   ellips      is the SPICE ellipse formed by the intersection
of the input plane and ellipsoid. `ellips' will
represent a single point if the ellipsoid and
plane are tangent.

If the intersection of the ellipsoid and plane is
empty, `ellips' is not modified.

found       is SPICETRUE if and only if the intersection of the
ellipsoid and plane is non-empty.
```

#### Parameters

```   None.
```

#### Exceptions

```   1)  If any of the lengths of the semi-axes of the input ellipsoid are
non-positive, the error SPICE(DEGENERATECASE) is signaled. `ellips'
is not modified. `found' is set to SPICEFALSE.

2)  If the input plane in invalid, in other words, if the input
plane as the zero vector as its normal vector, the error
SPICE(INVALIDPLANE) is signaled by a routine in the call tree
of this routine. `ellips' is not modified. `found' is set to
SPICEFALSE.

3)  If the input plane and ellipsoid are very nearly tangent,
roundoff error may cause this routine to give unreliable
results.

4)  If the input plane and ellipsoid are precisely tangent, the
intersection is a single point. In this case, the output
ellipse is degenerate, but `found' will still have the value
SPICETRUE. You must decide whether this output makes sense for
```

#### Files

```   None.
```

#### Particulars

```   An ellipsoid and a plane can intersect in an ellipse, a single
point, or the empty set.
```

#### 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) Suppose we wish to find the limb of a body, as observed from
location `loc' in body-fixed coordinates. The CSPICE routine
edlimb_c solves this problem. Here's how inedpl_c is used in
that solution.

We assume `loc' is outside of the body. The body is modeled as
a triaxial ellipsoid with semi-axes of length `a', `b', and `c'.

The notation

< x, y >

indicates the inner product of the vectors `x' and `y'.

The limb lies on the plane defined by

< x,  n >  =  1,

where the vector `n' is defined as

2              2              2
( loc[0] / a ,   loc[1] / b ,   loc[2] / c  )

The assignments

n[0] = loc[0] / (a*a);
n[1] = loc[1] / (b*b);
n[2] = loc[2] / (c*c);

and the calls

nvc2pl_c ( n,  1.0,  &plane );

inedpl_c ( a,  b,  c,  &plane,  &limb, &found );

el2cgv_c ( limb, center, smajor, sminor );

will return the center and semi-axes of the limb.

How do we know that  < x, n > = 1  for all `x' on the limb?
This is because all limb points `x' satisfy

< loc - x, surfnm(x) >  =  0,

where surfnm(x) is any surface normal at `x'. surfnm(x) is
parallel to the vector

2            2            2
v = (  x[0] / a ,   x[1] / b ,   x[2] / c   )

so we have

< loc - x, v >  =  0,

< loc, v >      =  < x, v >  =  1  (from the original
ellipsoid
equation)
and finally

< x, n >  =  1

where `n' is as defined above.

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.

This example is equivalent to the one in edlimb_c, but it uses
inedpl_c to compute the limb.

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

KPL/MK

File name: inedpl_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 inedpl_ex2
./
#include <math.h>
#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   [3];
SpiceEllipse         limb;
SpiceDouble          lt;
SpicePlane           plane;
SpiceDouble          smajor [3];
SpiceDouble          sminor [3];
SpiceDouble          scpos  [3];
SpiceDouble          tipm   [3][3];

SpiceInt             n;

SpiceBoolean         found;

/.
./
furnsh_c ( "inedpl_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 J2000 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, scpos );

/.
Normalize the position to factors of the radii.
./
scpos[0] = scpos[0] / pow( rad[0], 2 );
scpos[1] = scpos[1] / pow( rad[1], 2 );
scpos[2] = scpos[2] / pow( rad[2], 2 );

/.
Find the apparent limb.  `limb' is a SPICE ellipse
representing the limb.
./
nvc2pl_c ( scpos, 1.0, &plane );

/.
`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)
E.D. Wright         (JPL)
```

#### Version

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

Changed the output argument name "ellipse" to "ellips" for
consistency with other routines.

Edited the header to comply with NAIF standard.

-CSPICE Version 1.0.1, 06-FEB-2003 (EDW)

Corrected a typo in the header documentation,
input variable 'ellipse' not 'ellips'

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

#### Index_Entries

```   intersection of ellipsoid and plane
```
`Fri Dec 31 18:41:08 2021`