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georec

Table of contents
Procedure
Abstract
Required_Reading
Keywords
Declarations
Brief_I/O
Detailed_Input
Detailed_Output
Parameters
Exceptions
Files
Particulars
Examples
Restrictions
Literature_References
Author_and_Institution
Version

Procedure

     GEOREC ( Geodetic to rectangular coordinates )

     SUBROUTINE GEOREC ( LON, LAT, ALT,  RE, F,  RECTAN )

Abstract

     Convert geodetic coordinates to rectangular coordinates.

Required_Reading

     None.

Keywords

     CONVERSION
     COORDINATES

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   LON
     DOUBLE PRECISION   LAT
     DOUBLE PRECISION   ALT
     DOUBLE PRECISION   RE
     DOUBLE PRECISION   F
     DOUBLE PRECISION   RECTAN ( 3 )

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 a 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.

     2)  If the equatorial radius is less than or equal to zero,
         the error SPICE(VALUEOUTOFRANGE) is signaled.

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
              IMPLICIT NONE

        C
        C     SPICELIB functions
        C
              DOUBLE PRECISION      DPR
              DOUBLE PRECISION      RPD

        C
        C     Local variables
        C
              DOUBLE PRECISION      ALT
              DOUBLE PRECISION      F
              DOUBLE PRECISION      LAT
              DOUBLE PRECISION      LON
              DOUBLE PRECISION      RADII  ( 3 )
              DOUBLE PRECISION      RE
              DOUBLE PRECISION      RECTAN ( 3 )
              DOUBLE PRECISION      RP

              INTEGER               N

        C
        C     Load a PCK file containing a triaxial
        C     ellipsoidal shape model and orientation
        C     data for the Earth.
        C
              CALL FURNSH ( 'pck00010.tpc' )

        C
        C     Retrieve the triaxial radii of the Earth
        C
              CALL BODVRD ( 'EARTH', 'RADII', 3, N, RADII )

        C
        C     Compute flattening coefficient.
        C
              RE  =  RADII(1)
              RP  =  RADII(3)
              F   =  ( RE - RP ) / RE

        C
        C     Set a geodetic position.
        C
              LON = 118.D0 * RPD()
              LAT =  30.D0 * RPD()
              ALT =   0.D0

        C
        C     Do the conversion.
        C
              CALL GEOREC( LON, LAT, ALT, RADII(1), F, RECTAN )

              WRITE (*,*) 'Geodetic coordinates in deg and '
             . //         'km (lon, lat, alt)'
              WRITE (*,'(A,3F14.6)') ' ', LON * DPR(), LAT * DPR(), ALT
              WRITE (*,*) 'Rectangular coordinates in km (x, y, z)'
              WRITE (*,'(A,3F14.6)') ' ', RECTAN

              END


        When this program was executed on a Mac/Intel/gfortran/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:

           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. Input angles are in degrees.


        Example code begins here.


              PROGRAM GEOREC_EX2
              IMPLICIT NONE

        C
        C     SPICELIB functions
        C
              DOUBLE PRECISION      RPD

        C
        C     Local parameters.
        C
              INTEGER               NREC
              PARAMETER           ( NREC = 11 )

        C
        C     Local variables.
        C
              DOUBLE PRECISION      ALT    ( NREC )
              DOUBLE PRECISION      CLARKR
              DOUBLE PRECISION      CLARKF
              DOUBLE PRECISION      LAT    ( NREC )
              DOUBLE PRECISION      LON    ( NREC )
              DOUBLE PRECISION      RECTAN ( 3    )
              DOUBLE PRECISION      RLAT
              DOUBLE PRECISION      RLON

              INTEGER               I

        C
        C     Define the input geodetic coordinates. Angles in
        C     degrees.
        C
              DATA                 LON /  0.D0,   0.D0,  90.D0,
             .                            0.D0, 180.D0, -90.D0,
             .                            0.D0,  45.D0,   0.D0,
             .                           90.D0,  45.D0         /

              DATA                 LAT / 90.D0,     0.D0,     0.D0,
             .                           90.D0,     0.D0,     0.D0,
             .                          -90.D0,     0.D0,    88.707D0,
             .                           88.707D0, 88.1713D0         /

              DATA                 ALT /   -6356.5838D0,     0.D0,
             .                   0.D0,         0.D0,         0.D0,
             .                   0.D0,         0.D0,         0.D0,
             .               -6355.5725D0, -6355.5725D0, -6355.5612D0 /

        C
        C     Using the equatorial radius of the Clark66 spheroid
        C     (CLARKR = 6378.2064 km) and the Clark 66 flattening
        C     factor (CLARKF = 1.0 / 294.9787 ) convert from
        C     body fixed rectangular coordinates.
        C
              CLARKR = 6378.2064D0
              CLARKF = 1.0D0 / 294.9787D0

        C
        C     Print the banner.
        C
              WRITE(*,*) '   LON      LAT       ALT    '
             . //        ' RECTAN(1)  RECTAN(2)  RECTAN(3)'
              WRITE(*,*) ' -------  -------  --------- '
             . //        ' ---------  ---------  ---------'

        C
        C     Do the conversion.
        C
              DO I = 1, NREC

                 RLON = LON(I) * RPD()
                 RLAT = LAT(I) * RPD()

                 CALL GEOREC( RLON,   RLAT,   ALT(I),
             .                CLARKR, CLARKF, RECTAN )

                 WRITE (*,'(2F9.3,F11.3,3F11.3)')
             .             LON(I), LAT(I), ALT(I), RECTAN

              END DO

              END


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


            LON      LAT       ALT     RECTAN(1)  RECTAN(2)  RECTAN(3)
          -------  -------  ---------  ---------  ---------  ---------
            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)

Version

    SPICELIB Version 1.1.0, 01-OCT-2021 (JDR) (NJB)

        Changed the input argument name LONG to LON for consistency
        with other routines.

        Added IMPLICIT NONE statement.

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

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

        Minor headers edits.

    SPICELIB Version 1.0.2, 29-JUL-2003 (NJB) (CHA)

        Various header changes were made to improve clarity. Some
        minor header corrections were made.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 31-JAN-1990 (WLT) (HAN)
Fri Dec 31 18:36:23 2021