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georec_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

```   georec_c ( Geodetic to rectangular coordinates )

void georec_c ( SpiceDouble lon,
SpiceDouble lat,
SpiceDouble alt,
SpiceDouble re,
SpiceDouble f,
SpiceDouble rectan[3] )

```

#### Abstract

```   Convert geodetic coordinates to rectangular coordinates.
```

```   None.
```

#### Keywords

```   CONVERSION
COORDINATES

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
lon        I   Geodetic longitude of point (radians).
lat        I   Geodetic latitude  of point (radians).
alt        I   Altitude of point above the reference spheroid.
re         I   Equatorial radius of the reference spheroid.
f          I   Flattening coefficient.
rectan     O   Rectangular coordinates of point.
```

#### Detailed_Input

```   lon         is the geodetic 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.

Longitude is measured in radians. On input, the
range of longitude is unrestricted.

lat         is the geodetic latitude of the input point. For a
point P on the reference spheroid, this is the angle
between the XY plane and the outward normal vector at
P. For a point P not on the reference spheroid, the
geodetic latitude is that of the closest point to P on
the spheroid.

Latitude is measured in radians. On input, the
range of latitude is unrestricted.

alt         is the altitude of point above the reference spheroid.
`alt' must be in the same units as `re'.

re          is the equatorial radius of a reference spheroid. This
spheroid is a volume of revolution: its horizontal
cross sections are circular. The shape of the
spheroid is defined by an equatorial radius `re' and
a polar radius `rp'. `re' must be in the same units
as `alt'.

f           is the flattening coefficient = (re-rp) / re,  where
`rp' is the polar radius of the spheroid.
```

#### Detailed_Output

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

The units associated with `rectan' are those associated
with the inputs `alt' and `re'.
```

#### Parameters

```   None.
```

#### Exceptions

```   1)  If the flattening coefficient is greater than or equal to one,
the error SPICE(VALUEOUTOFRANGE) is signaled by a routine in
the call tree of this routine.

2)  If the equatorial radius is less than or equal to zero, the
error SPICE(VALUEOUTOFRANGE) is signaled by a routine in the
call tree of this routine.
```

#### Files

```   None.
```

#### Particulars

```   Given the geodetic coordinates of a point, and the constants
describing the reference spheroid,  this routine returns the
bodyfixed rectangular coordinates of the point. The bodyfixed
rectangular frame is that having the X-axis pass through the
0 degree latitude 0 degree longitude point. The Y-axis passes
through the 0 degree latitude 90 degree longitude. The Z-axis
passes through the 90 degree latitude point. For some bodies
this coordinate system may not be a right-handed coordinate
system.
```

#### Examples

```   This routine can be used to convert body fixed geodetic
coordinates (such as the used for United States Geological
Survey topographic maps) to bodyfixed rectangular coordinates
such as the Satellite Tracking and Data Network of 1973.

1) Find the rectangular coordinates of the point having Earth
geodetic coordinates:

lon (deg) =  118.0
lat (deg) =   32.0
alt (km)  =    0.0

Use the PCK kernel below to load the required triaxial
ellipsoidal shape model and orientation data for the Earth.

pck00010.tpc

Example code begins here.

/.
Program georec_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables
./
SpiceDouble          alt;
SpiceDouble          f;
SpiceDouble          lat;
SpiceDouble          lon;
SpiceDouble          re;
SpiceDouble          rectan [3];
SpiceDouble          rp;

SpiceInt             n;

/.
Load a PCK file containing a triaxial
ellipsoidal shape model and orientation
data for the Earth.
./
furnsh_c ( "pck00010.tpc" );

/.
Retrieve the triaxial radii of the Earth
./

/.
Compute flattening coefficient.
./
f   =  ( re - rp ) / re;

/.
Set a geodetic position.
./
lon = 118.0 * rpd_c ( );
lat =  30.0 * rpd_c ( );
alt =   0.0;

/.
Do the conversion.
./
georec_c ( lon, lat, alt, radii[0], f, rectan );

printf( "Geodetic coordinates in deg and km (lon, lat, alt)\n" );
printf( " %13.6f %13.6f %13.6f\n",
lon * dpr_c ( ), lat * dpr_c ( ), alt );
printf( "Rectangular coordinates in km (x, y, z)\n" );
printf( " %13.6f %13.6f %13.6f\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:

Geodetic coordinates in deg and km (lon, lat, alt)
118.000000     30.000000      0.000000
Rectangular coordinates in km (x, y, z)
-2595.359123   4881.160589   3170.373523

2) Create a table showing a variety of rectangular coordinates
and the corresponding Earth geodetic coordinates. The
values are computed using the equatorial radius of the Clark
66 spheroid and the Clark 66 flattening factor:

flattening factor: 1./294.9787

Note: the values shown above may not be current or suitable

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

Example code begins here.

/.
Program georec_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.
./
#define NREC         11

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

SpiceInt             i;

/.
Define the input geodetic coordinates. Angles in
degrees.
./
SpiceDouble          lon    [NREC] = { 0.0,    0.0,  90.0,
0.0,  180.0, -90.0,
0.0,   45.0,   0.0,
90.0,    45.0       };

SpiceDouble          lat    [NREC] = {  90.0,    0.0,    0.0,
90.0,    0.0,    0.0,
-90.0,    0.0,   88.707,
88.707, 88.1713        };

SpiceDouble          alt    [NREC] = { -6356.5838,     0.0,
0.0,        0.0,        0.0,
0.0,        0.0,        0.0,
-6355.5725, -6355.5725, -6355.5612 };

/.
Using the equatorial radius of the Clark66 spheroid
(clarkr = 6378.2064 km) and the Clark 66 flattening
factor (clarkf = 1.0 / 294.9787 ) convert from
body fixed rectangular coordinates.
./
clarkr = 6378.2064;
clarkf = 1.0 / 294.9787;

/.
Print the banner.
./
printf( "   lon      lat       alt     rectan[0]  rectan[1] "
" rectan[2]\n" );
printf( " -------  -------  ---------  ---------  --------- "
" ---------\n" );

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

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

georec_c ( rlon, rlat, alt[i], clarkr, clarkf, rectan );

printf( "%8.3f %8.3f %10.3f", lon[i], lat[i], alt[i] );
printf( "%11.3f %10.3f %10.3f\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:

lon      lat       alt     rectan[0]  rectan[1]  rectan[2]
-------  -------  ---------  ---------  ---------  ---------
0.000   90.000  -6356.584      0.000      0.000      0.000
0.000    0.000      0.000   6378.206      0.000      0.000
90.000    0.000      0.000      0.000   6378.206      0.000
0.000   90.000      0.000      0.000      0.000   6356.584
180.000    0.000      0.000  -6378.206      0.000      0.000
-90.000    0.000      0.000      0.000  -6378.206      0.000
0.000  -90.000      0.000      0.000      0.000  -6356.584
45.000    0.000      0.000   4510.073   4510.073      0.000
0.000   88.707  -6355.573      1.000      0.000      1.000
90.000   88.707  -6355.573      0.000      1.000      1.000
45.000   88.171  -6355.561      1.000      1.000      1.000
```

#### Restrictions

```   None.
```

#### Literature_References

```   [1]  R. Bate, D. Mueller, and J. White, "Fundamentals of
Astrodynamics," Dover Publications Inc., 1971.
```

#### Author_and_Institution

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

#### Version

```   -CSPICE Version 1.0.4, 01-NOV-2021 (JDR)

Edited the header to comply with NAIF standard. Added two complete code
examples.

-CSPICE Version 1.0.3, 26-JUL-2016 (BVS)

-CSPICE Version 1.0.2, 30-JUL-2003 (NJB)

```   geodetic to rectangular coordinates
`Fri Dec 31 18:41:07 2021`