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latrec_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

```   latrec_c ( Latitudinal to rectangular coordinates )

SpiceDouble    lon,
SpiceDouble    lat,
SpiceDouble    rectan[3] )

```

#### Abstract

```   Convert from latitudinal coordinates to rectangular coordinates.
```

```   None.
```

#### Keywords

```   CONVERSION
COORDINATES

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
radius     I   Distance of a point from the origin.
lon        I   Longitude of point in radians.
lat        I   Latitude of point in radians.
rectan     O   Rectangular coordinates of the point.
```

#### Detailed_Input

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

lon         is the longitude of the input point. This is the angle
between the prime meridian and the meridian containing
`rectan'. The direction of increasing longitude is from
the +X axis towards the +Y axis.

`lon' is measured in radians. On input, the range
of longitude is unrestricted.

lat         is the latitude of the input point. This is the angle
from the XY plane of the ray from the origin through the
point.

`lat' is measured in radians. On input, the range of
latitude is unrestricted.
```

#### Detailed_Output

```   rectan      are the rectangular coordinates of the input point.
`rectan' is a 3 vector.

The units associated with `rectan' are those
```

#### Parameters

```   None.
```

#### Exceptions

```   Error free.
```

#### Files

```   None.
```

#### Particulars

```   This routine returns the rectangular 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.
```

#### 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 latitudinal 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: latrec_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 latrec_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

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

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

/.
Convert the latitudinal to rectangular coordinates.
./

latrec_c ( radius, lon, lat, 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( "Rectangular coordinates from latrec_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

Rectangular coordinates from latrec_c:

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

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

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

Example code begins here.

/.
Program latrec_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{
/.
Local constants.
./
#define NPTS            11

/.
Local variables.
./
SpiceDouble             rectan[3];
SpiceDouble             rlon;
SpiceDouble             rlat;

SpiceInt                i;

/.
Define eleven sets of latitude coordinates, `lon'
and `lat' expressed in degrees.
./
SpiceDouble             radius[NPTS] = { 0.0,    1.0,    1.0,
1.0,    1.0,    1.0,
1.0,    1.4142, 1.4142,
1.4142, 1.732          };

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

SpiceDouble             lat   [NPTS] = {   0.0,  0.0,     0.0,
90.0,  0.0,     0.0,
-90.0,  0.0,    45.0,
45.0,  35.2643      };

/.
Print a header for the data output.
./
printf( "  radius    lon      lat    rect[0]  rect[1]  rect[2]\n" );
printf( " -------  -------  -------  -------  -------  -------\n" );

for ( i = 0; i < NPTS; i++ )
{
/.
Convert `lon' and `lat' from degrees to radians.
./
rlon = lon[i] * rpd_c();
rlat = lat[i] * rpd_c();

/.
Convert the coordinates from latitudinal to rectangular.
./
latrec_c ( radius[i], rlon, rlat, rectan );

/.
Output the row of the coordinate table.
./
printf ( "%8.3f %8.3f %8.3f %8.3f %8.3f %8.3f\n",
rectan[0], rectan[1], rectan[2] );
}

return( 0 );
}

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

radius    lon      lat    rect[0]  rect[1]  rect[2]
-------  -------  -------  -------  -------  -------
0.000    0.000    0.000    0.000    0.000    0.000
1.000    0.000    0.000    1.000    0.000    0.000
1.000   90.000    0.000    0.000    1.000    0.000
1.000    0.000   90.000    0.000    0.000    1.000
1.000  180.000    0.000   -1.000    0.000    0.000
1.000  -90.000    0.000    0.000   -1.000    0.000
1.000    0.000  -90.000    0.000    0.000   -1.000
1.414   45.000    0.000    1.000    1.000    0.000
1.414    0.000   45.000    1.000    0.000    1.000
1.414   90.000   45.000    0.000    1.000    1.000
1.732   45.000   35.264    1.000    1.000    1.000
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   C.H. Acton          (JPL)
N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
E.D. Wright         (JPL)
```

#### Version

```   -CSPICE Version 1.1.0, 04-JUL-2021 (JDR)

Changed input argument names "longitude" and "latitude to "lon"
and "lat" for consistency with other routines.

complete code examples based on existing example.

-CSPICE Version 1.0.1, 29-JUL-2003 (NJB) (CHA)

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