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recsph_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

```   recsph_c ( Rectangular to spherical coordinates )

void recsph_c ( ConstSpiceDouble     rectan[3],
SpiceDouble        * r,
SpiceDouble        * colat,
SpiceDouble        * slon      )

```

#### Abstract

```   Convert from rectangular coordinates to spherical coordinates.
```

```   None.
```

#### Keywords

```   CONVERSION
COORDINATES

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
rectan     I   Rectangular coordinates of a point.
r          O   Distance of the point from the origin.
colat      O   Angle of the point from the Z-axis in radians
slon       O   Longitude of the point in radians.
```

#### Detailed_Input

```   rectan      are the rectangular coordinates of a point.
```

#### Detailed_Output

```   r           is the distance of the point from the origin.

colat       is the angle between the point and the positive z-axis in
radians. The range of `colat' is [0, pi].

slon        is the longitude of the point in radians. This is the
angle between the positive X-axis and the orthogonal
projection of the point onto the XY plane. `slon'
increases in the counterclockwise sense about the
positive Z-axis. The range of `slon' is [-pi, pi].
```

#### Parameters

```   None.
```

#### Exceptions

```   Error free.
```

#### Files

```   None.
```

#### Particulars

```   This routine returns the spherical coordinates of a point
whose position is input in rectangular coordinates.

spherical coordinates are defined by a distance from a central
reference point, an angle from a reference meridian, and an angle
from the z-axis.
```

#### 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) Compute the spherical coordinates of the position of the Moon
as seen from the Earth, and convert them to rectangular
coordinates.

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

KPL/MK

File name: recsph_ex1.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
---------                     --------
de421.bsp                     Planetary ephemeris
naif0012.tls                  Leapseconds

\begindata

'naif0012.tls'  )

\begintext

End of meta-kernel

Example code begins here.

/.
Program recsph_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables.
./
SpiceDouble          colat;
SpiceDouble          et;
SpiceDouble          lt;
SpiceDouble          pos    [3];
SpiceDouble          rectan [3];
SpiceDouble          slon;

/.
Load SPK and LSK kernels, use a meta kernel for
convenience.
./
furnsh_c ( "recsph_ex1.tm" );

/.
Look up the geometric state of the Moon as seen from
the Earth at 2017 Mar 20, relative to the J2000
reference frame.
./
str2et_c ( "2017 Mar 20", &et );

spkpos_c ( "Moon", et, "J2000", "NONE", "Earth", pos, &lt );

/.
Convert the position vector `pos' to spherical
coordinates.
./
recsph_c ( pos, &radius, &colat, &slon );

/.
Convert the spherical coordinates to rectangular.
./
sphrec_c ( radius, colat, slon, rectan );

printf( " \n" );
printf( "Original rectangular coordinates:\n" );
printf( " \n" );
printf( " X           (km):  %19.8f\n", pos[0] );
printf( " Y           (km):  %19.8f\n", pos[1] );
printf( " Z           (km):  %19.8f\n", pos[2] );
printf( " \n" );
printf( "Spherical coordinates:\n" );
printf( " \n" );
printf( " Colatitude (deg):  %19.8f\n", colat*dpr_c ( ) );
printf( " Longitude  (deg):  %19.8f\n", slon*dpr_c ( ) );
printf( " \n" );
printf( "Rectangular coordinates from sphrec_c:\n" );
printf( " \n" );
printf( " X           (km):  %19.8f\n", rectan[0] );
printf( " Y           (km):  %19.8f\n", rectan[1] );
printf( " Z           (km):  %19.8f\n", rectan[2] );
printf( " \n" );

return ( 0 );
}

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

Original rectangular coordinates:

X           (km):      -55658.44323296
Y           (km):     -379226.32931475
Z           (km):     -126505.93063865

Spherical coordinates:

Colatitude (deg):         108.26566077
Longitude  (deg):         -98.34959789

Rectangular coordinates from sphrec_c:

X           (km):      -55658.44323296
Y           (km):     -379226.32931475
Z           (km):     -126505.93063865

2) Create a table showing a variety of rectangular coordinates
and the corresponding spherical coordinates.

Corresponding rectangular and spherical coordinates are
listed to three decimal places. Output angles are in degrees.

Example code begins here.

/.
Program recsph_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.
./
#define NREC         11

/.
Local variables.
./
SpiceDouble          colat;
SpiceDouble          slon;

SpiceInt             i;

/.
Define the input rectangular coordinates.
./
SpiceDouble          rectan [NREC][3] = {
{ 0.0,         0.0,         0.0},
{ 1.0,         0.0,         0.0},
{ 0.0,         1.0,         0.0},
{ 0.0,         0.0,         1.0},
{-1.0,         0.0,         0.0},
{ 0.0,        -1.0,         0.0},
{ 0.0,         0.0,        -1.0},
{ 1.0,         1.0,         0.0},
{ 1.0,         0.0,         1.0},
{ 0.0,         1.0,         1.0},
{ 1.0,         1.0,         1.0} };

/.
Print the banner.
./
printf( " rect[0]  rect[1]  rect[2]   radius   colat     slon\n" );
printf( " -------  -------  -------  -------  -------  -------\n" );

/.
Do the conversion. Output angles in degrees.
./
for ( i = 0; i < NREC; i++ )
{

recsph_c ( rectan[i], &radius, &colat, &slon );

printf( "%8.3f %8.3f %8.3f ", rectan[i][0], rectan[i][1],
rectan[i][2]               );
printf( "%8.3f %8.3f %8.3f\n", radius, colat * dpr_c(),
slon * dpr_c() );

}

return ( 0 );
}

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

rect[0]  rect[1]  rect[2]   radius   colat     slon
-------  -------  -------  -------  -------  -------
0.000    0.000    0.000    0.000    0.000    0.000
1.000    0.000    0.000    1.000   90.000    0.000
0.000    1.000    0.000    1.000   90.000   90.000
0.000    0.000    1.000    1.000    0.000    0.000
-1.000    0.000    0.000    1.000   90.000  180.000
0.000   -1.000    0.000    1.000   90.000  -90.000
0.000    0.000   -1.000    1.000  180.000    0.000
1.000    1.000    0.000    1.414   90.000   45.000
1.000    0.000    1.000    1.414   45.000    0.000
0.000    1.000    1.000    1.414   45.000   90.000
1.000    1.000    1.000    1.732   54.736   45.000
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
B.V. Semenov        (JPL)
W.L. Taber          (JPL)
E.D. Wright         (JPL)
```

#### Version

```   -CSPICE Version 1.2.0, 10-AUG-2021 (JDR)

Changed the output argument name "lon" to "slon" for consistency
with other routines.

Edited the header to comply with NAIF standard.

-CSPICE Version 1.1.2, 26-JUL-2016 (BVS)

-CSPICE Version 1.1.1, 07-JAN-2002 (NJB) (EDW)

Fixed description of slon in -Brief_I/O and Detailed_I/O
```   rectangular to spherical coordinates
`Fri Dec 31 18:41:11 2021`