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latsph_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

```   latsph_c ( Latitudinal to spherical coordinates )

SpiceDouble    lon,
SpiceDouble    lat,
SpiceDouble *  rho,
SpiceDouble *  colat,
SpiceDouble *  slon )

```

#### Abstract

```   Convert from latitudinal coordinates to spherical coordinates.
```

```   None.
```

#### Keywords

```   CONVERSION
COORDINATES

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
radius     I   Distance of a point from the origin.
lon        I   Angle of the point from the XZ plane in radians.
lat        I   Angle of the point from the XY plane in radians.
rho        O   Distance of the point from the origin.
colat      O   Angle of the point from positive z axis (radians).
slon       O   Angle of the point from the XZ plane (radians).
```

#### Detailed_Input

```   radius      is the distance of a point from the origin.

lon         is the angle of the point from the XZ plane in radians.

lat         is the angle of the point from the XY plane in radians.
```

#### Detailed_Output

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

colat       is the angle between the vector from the origin to the point
and the positive z axis in radians. `colat' is computed
as pi/2 - `lat'.

slon        is the angle of the point from the XZ plane (radians). `slon'
is set equal to `lon'.
```

#### Parameters

```   None.
```

#### Exceptions

```   Error free.
```

#### Files

```   None.
```

#### Particulars

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

Latitudinal coordinates are defined by a distance from a central
reference point, an angle from a reference meridian, and an angle
above the equator of a sphere centered at the central reference
point.

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) Co-latitude is obtained by subtracting latitude from halfpi_c
Radius and longitude mean the same thing in both latitudinal
and spherical coordinates. The table below lists `lat' and
corresponding `colat' in terms of degrees.

LAT     COLAT
-----    -----
0        90
20        70
45        45
-30       120
90         0
-45       135

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

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

KPL/MK

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

\begindata

'naif0012.tls'  )

\begintext

End of meta-kernel

Example code begins here.

/.
Program latsph_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

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

/.
Load SPK and LSK kernels, use a meta kernel for
convenience.
./
furnsh_c ( "latsph_ex2.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 latitudinal
coordinates.
./
reclat_c ( pos, &radius, &lon, &lat );

/.
Convert the latitudinal coordinates to spherical.
./
latsph_c ( radius, lon, lat, &r, &colat, &slon );

/.
Convert the spherical coordinates to rectangular.
./
sphrec_c ( r, 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( "Latitudinal coordinates:\n" );
printf( " \n" );
printf( " Longitude  (deg):  %19.8f\n", lon*dpr_c ( ) );
printf( " Latitude   (deg):  %19.8f\n", lat*dpr_c ( ) );
printf( " \n" );
printf( "Spherical coordinates:\n" );
printf( " \n" );
printf( " Radius      (km):  %19.8f\n", r );
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

Latitudinal coordinates:

Longitude  (deg):         -98.34959789
Latitude   (deg):         -18.26566077

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

3) Create a table showing a variety of latitudinal coordinates
and the corresponding spherical coordinates.

Corresponding latitudinal and spherical coordinates are
listed to three decimal places. Input and output angles are
in degrees.

Example code begins here.

/.
Program latsph_ex3
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.
./
#define NREC         11

/.
Local variables.
./
SpiceDouble          colat;
SpiceDouble          r;
SpiceDouble          rlat;
SpiceDouble          rlon;
SpiceDouble          slon;

SpiceInt             i;

/.
Define the input latitudinal coordinates. Angles in
degrees.
./

SpiceDouble          radius [NREC] = {  0.0,  1.0,    1.0,
1.0,  1.4142, 1.0,
1.0,  1.0,    1.4142,
1.0,  0.0            };

SpiceDouble          lon    [NREC] = {  0.0,   0.0,  90.0,
0.0, 180.0, -90.0,
0.0,  45.0, 180.0,
180.0,  33.0        };

SpiceDouble          lat    [NREC] = { 90.0,  0.0,   0.0,
90.0, 45.0,   0.0,
-90.0,  0.0, -45.0,
90.0,  0.0        };

/.
Print the banner.
./
printf( "  radius    lon      lat       r      colat     slon\n" );
printf( " -------  -------  -------  -------  -------  ------- \n" );

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

rlon = lon[i] * rpd_c ( );
rlat = lat[i] * rpd_c ( );

latsph_c ( radius[i], rlon, rlat, &r, &colat, &slon );

printf( "%8.3f %8.3f %8.3f ", radius[i], lon[i], lat[i] );
printf( "%8.3f %8.3f %8.3f\n",
r, colat * dpr_c ( ), slon * dpr_c ( ) );

}

return ( 0 );
}

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

radius    lon      lat       r      colat     slon
-------  -------  -------  -------  -------  -------
0.000    0.000   90.000    0.000    0.000    0.000
1.000    0.000    0.000    1.000   90.000    0.000
1.000   90.000    0.000    1.000   90.000   90.000
1.000    0.000   90.000    1.000    0.000    0.000
1.414  180.000   45.000    1.414   45.000  180.000
1.000  -90.000    0.000    1.000   90.000  -90.000
1.000    0.000  -90.000    1.000  180.000    0.000
1.000   45.000    0.000    1.000   90.000   45.000
1.414  180.000  -45.000    1.414  135.000  180.000
1.000  180.000   90.000    1.000    0.000  180.000
0.000   33.000    0.000    0.000   90.000   33.000
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

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

#### Version

```   -CSPICE Version 1.1.0, 13-AUG-2021 (JDR)

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

Edited the header to comply with NAIF standard.

-CSPICE Version 1.0.2, 26-JUL-2016 (BVS)

-CSPICE Version 1.0.1, 13-DEC-2005 (EDW)

Corrected typo in -Detailed_Output, substituted
"colat" for "lat."

-CSPICE Version 1.0.0, 08-FEB-1998 (EDW) (WLT)
```

#### Index_Entries

```   latitudinal to spherical coordinates
```
`Fri Dec 31 18:41:08 2021`