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recgeo_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

recgeo_c ( Rectangular to geodetic )

void recgeo_c ( ConstSpiceDouble     rectan,
SpiceDouble          re,
SpiceDouble          f,
SpiceDouble        * lon,
SpiceDouble        * lat,
SpiceDouble        * alt        )

Abstract

Convert from rectangular coordinates to geodetic coordinates.

None.

CONVERSION
COORDINATES

Brief_I/O

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

Detailed_Input

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

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

Detailed_Output

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.

`lon' is output in radians. The range of `lon' is
[-pi, pi].

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.

`lat' is output in radians. The range of `lat' is
[-pi/2, pi/2].

alt         is the altitude of point above the reference spheroid.

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

None.

Exceptions

1)  If the equatorial radius is non-positive, the error
SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call
tree of this routine.

2)  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.

3)  For points inside the reference ellipsoid, the nearest
point on the ellipsoid to `rectan' may not be unique, so
latitude may not be well-defined.

None.

Particulars

Given the body-fixed rectangular coordinates of a point, and the
constants describing the reference spheroid,  this routine
returns the geodetic coordinates of the point. The body-fixed
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

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

X (km) =  -2541.748162
Y (km) =   4780.333036
Z (km) =   3360.428190

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 recgeo_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables
./
SpiceDouble          alt;
SpiceDouble          f;
SpiceDouble          lat;
SpiceDouble          lon;
SpiceDouble          re;
SpiceDouble          rectan ;
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 body-fixed position.
./
rectan =  -2541.748162;
rectan =   4780.333036;
rectan =   3360.428190;

/.
Do the conversion.
./
recgeo_c ( rectan, radii, f, &lon, &lat, &alt );

printf( "Rectangular coordinates in km (x, y, z)\n" );
printf( " %13.6f %13.6f %13.6f\n", rectan, rectan, 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 );

return ( 0 );
}

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

Rectangular coordinates in km (x, y, z)
-2541.748162   4780.333036   3360.428190
Geodetic coordinates in deg and km (lon, lat, alt)
118.000000     31.999957      0.001916

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. Output angles are in degrees.

Example code begins here.

/.
Program recgeo_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.
./
#define NREC         11

/.
Local variables.
./
SpiceDouble          alt;
SpiceDouble          clarkr;
SpiceDouble          clarkf;
SpiceDouble          lat;
SpiceDouble          lon;

SpiceInt             i;

/.
Define the input rectangular coordinates.
./
SpiceDouble          rectan [NREC] = {
{    0.0,        0.0,        0.0   },
{ 6378.2064,     0.0,        0.0   },
{    0.0,     6378.2064,     0.0   },
{    0.0,        0.0,     6378.2064},
{-6378.2064,     0.0,        0.0   },
{    0.0,    -6378.2064,     0.0   },
{    0.0,        0.0,    -6378.2064},
{ 6378.2064,  6378.2064,     0.0   },
{ 6378.2064,     0.0,     6378.2064},
{    0.0,     6378.2064,  6378.2064},
{ 6378.2064,  6378.2064,  6378.2064} };

/.
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( " rectan  rectan  rectan    lon      lat   "
"    alt\n" );
printf( " ---------  ---------  ---------  -------  ------- "
" ---------\n" );

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

recgeo_c ( rectan[i], clarkr, clarkf, &lon, &lat, &alt );

printf( "%10.3f %10.3f %10.3f",
rectan[i], rectan[i], rectan[i] );
printf( "%9.3f %8.3f %10.3f\n",
lon * dpr_c ( ), lat * dpr_c ( ), alt );

}

return ( 0 );
}

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

rectan  rectan  rectan    lon      lat       alt
---------  ---------  ---------  -------  -------  ---------
0.000      0.000      0.000    0.000   90.000  -6356.584
6378.206      0.000      0.000    0.000    0.000      0.000
0.000   6378.206      0.000   90.000    0.000      0.000
0.000      0.000   6378.206    0.000   90.000     21.623
-6378.206      0.000      0.000  180.000    0.000      0.000
0.000  -6378.206      0.000  -90.000    0.000      0.000
0.000      0.000  -6378.206    0.000  -90.000     21.623
6378.206   6378.206      0.000   45.000    0.000   2641.940
6378.206      0.000   6378.206    0.000   45.137   2652.768
0.000   6378.206   6378.206   90.000   45.137   2652.768
6378.206   6378.206   6378.206   45.000   35.370   4676.389

None.

Literature_References

  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)
B.V. Semenov        (JPL)
E.D. Wright         (JPL)

Version

-CSPICE Version 1.2.4, 01-NOV-2021 (JDR)

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

-CSPICE Version 1.2.3, 26-JUL-2016 (BVS)

-CSPICE Version 1.2.2, 02-JUL-2007 (NJB)

right-hand table was updated to use correct names of columns.
Term "bodyfixed" is now hyphenated.

-CSPICE Version 1.2.1, 30-JUL-2003 (NJB) (CHA)

-CSPICE Version 1.2.0, 28-AUG-2001 (NJB)

Removed tab characters from source file. Include interface
macro definition file SpiceZim.h.

-CSPICE Version 1.1.0, 21-OCT-1998 (NJB)