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Index Page recgeo_c

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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[3],
                       SpiceDouble          re,
                       SpiceDouble          f,
                       SpiceDouble        * lon,
                       SpiceDouble        * lat,
                       SpiceDouble        * alt        )

#### Abstract

       Convert from rectangular coordinates to geodetic coordinates.

#### Required_Reading

       None.

#### Keywords

       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'.

#### Parameters

       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.

#### Files

       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          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

#### 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)
       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_Entries

       rectangular to geodetic

#### Link to routine recgeo_c source file recgeo_c.c

    Fri Dec 31 18:41:11 2021