| recgeo_c |
|
Table of contents
Procedure
recgeo_c ( Rectangular to geodetic )
void recgeo_c ( ConstSpiceDouble rectan[3],
SpiceDouble re,
SpiceDouble f,
SpiceDouble * lon,
SpiceDouble * lat,
SpiceDouble * alt )
AbstractConvert from rectangular coordinates to geodetic coordinates. Required_ReadingNone. KeywordsCONVERSION COORDINATES Brief_I/OVARIABLE 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'.
ParametersNone. 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.
FilesNone. ParticularsGiven 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 radii [3];
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
./
bodvrd_c ( "EARTH", "RADII", 3, &n, radii );
/.
Compute flattening coefficient.
./
re = radii[0];
rp = radii[2];
f = ( re - rp ) / re;
/.
Set a body-fixed position.
./
rectan[0] = -2541.748162;
rectan[1] = 4780.333036;
rectan[2] = 3360.428190;
/.
Do the conversion.
./
recgeo_c ( rectan, radii[0], f, &lon, &lat, &alt );
printf( "Rectangular coordinates in km (x, y, z)\n" );
printf( " %13.6f %13.6f %13.6f\n", rectan[0], rectan[1], rectan[2] );
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:
radius: 6378.2064
flattening factor: 1./294.9787
Note: the values shown above may not be current or suitable
for your application.
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][3] = {
{ 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[0] rectan[1] rectan[2] 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][0], rectan[i][1], rectan[i][2] );
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[0] rectan[1] rectan[2] 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
RestrictionsNone. Literature_References
[1] R. Bate, D. Mueller, and J. White, "Fundamentals of
Astrodynamics," Dover Publications Inc., 1971.
Author_and_InstitutionC.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)
Minor headers edits.
-CSPICE Version 1.2.2, 02-JUL-2007 (NJB)
In -Examples section of header, heading and description of
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)
Various header changes were made to improve clarity. Some
minor header corrections were made.
-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)
Made input vector const.
-CSPICE Version 1.0.0, 08-FEB-1998 (EDW)
Index_Entriesrectangular to geodetic |
Fri Dec 31 18:41:11 2021