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reclat

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

     RECLAT ( Rectangular to latitudinal coordinates )

     SUBROUTINE RECLAT ( RECTAN, RADIUS, LON, LAT )

Abstract

     Convert from rectangular coordinates to latitudinal coordinates.

Required_Reading

     None.

Keywords

     CONVERSION
     COORDINATES

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   RECTAN ( 3 )
     DOUBLE PRECISION   RADIUS
     DOUBLE PRECISION   LON
     DOUBLE PRECISION   LAT

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     RECTAN     I   Rectangular coordinates of the point.
     RADIUS     O   Distance of a point from the origin.
     LON        O   Longitude of point in radians.
     LAT        O   Latitude of point in radians.

Detailed_Input

     RECTAN   are the rectangular coordinates of a point.

Detailed_Output

     RADIUS   is the distance of a point from the origin.

              The units associated with RADIUS are those
              associated with the input RECTAN.

     LON      is the longitude of the input point. This is the
              angle between the prime meridian and the meridian
              containing the point. 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 latitude of the input point. This is the angle
              from the XY plane of the ray from the origin through
              the point.

              LAT is output in radians. The range of LAT is
              [-pi/2, pi/2].

Parameters

     None.

Exceptions

     Error free.

     1)  If the X and Y components of RECTAN are both zero, the
         longitude is set to zero.

     2)  If RECTAN is the zero vector, longitude and latitude are
         both set to zero.

Files

     None.

Particulars

     This routine returns the latitudinal coordinates of a point
     whose position is input in rectangular coordinates.

     Latitudinal coordinates are defined by a distance from a central
     reference point, an angle from a reference meridian, and an angle
     above the equator of a sphere centered at the central reference
     point.

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) Compute the latitudinal coordinates of the position of the
        Moon as seen from the Earth, and convert them to rectangular
        coordinates.

        Use the meta-kernel shown below to load the required SPICE
        kernels.


           KPL/MK

           File name: reclat_ex1.tm

           This meta-kernel is intended to support operation of SPICE
           example programs. The kernels shown here should not be
           assumed to contain adequate or correct versions of data
           required by SPICE-based user applications.

           In order for an application to use this meta-kernel, the
           kernels referenced here must be present in the user's
           current working directory.

           The names and contents of the kernels referenced
           by this meta-kernel are as follows:

              File name                     Contents
              ---------                     --------
              de421.bsp                     Planetary ephemeris
              naif0012.tls                  Leapseconds


           \begindata

              KERNELS_TO_LOAD = ( 'de421.bsp',
                                  'naif0012.tls'  )

           \begintext

           End of meta-kernel


        Example code begins here.


              PROGRAM RECLAT_EX1
              IMPLICIT NONE

        C
        C     SPICELIB functions
        C
              DOUBLE PRECISION      DPR

        C
        C     Local parameters
        C
              CHARACTER*(*)         FMT1
              PARAMETER           ( FMT1 = '(A,F20.8)' )

        C
        C     Local variables
        C
              DOUBLE PRECISION      ET
              DOUBLE PRECISION      LAT
              DOUBLE PRECISION      LON
              DOUBLE PRECISION      LT
              DOUBLE PRECISION      POS    ( 3 )
              DOUBLE PRECISION      RADIUS
              DOUBLE PRECISION      RECTAN ( 3 )

        C
        C     Load SPK and LSK kernels, use a meta kernel for
        C     convenience.
        C
              CALL FURNSH ( 'reclat_ex1.tm' )

        C
        C     Look up the geometric state of the Moon as seen from
        C     the Earth at 2017 Mar 20, relative to the J2000
        C     reference frame.
        C
              CALL STR2ET ( '2017 Mar 20', ET )

              CALL SPKPOS ( 'Moon',  ET,  'J2000', 'NONE',
             .              'Earth', POS, LT               )

        C
        C     Convert the position vector POS to latitudinal
        C     coordinates.
        C
              CALL RECLAT ( POS, RADIUS, LON, LAT )

        C
        C     Convert the latitudinal to rectangular coordinates.
        C

              CALL LATREC ( RADIUS, LON, LAT, RECTAN )

              WRITE(*,*) ' '
              WRITE(*,*) 'Original rectangular coordinates:'
              WRITE(*,*) ' '
              WRITE(*,FMT1) '  X          (km): ', POS(1)
              WRITE(*,FMT1) '  Y          (km): ', POS(2)
              WRITE(*,FMT1) '  Z          (km): ', POS(3)
              WRITE(*,*) ' '
              WRITE(*,*) 'Latitudinal coordinates:'
              WRITE(*,*) ' '
              WRITE(*,FMT1) '  Radius     (km): ', RADIUS
              WRITE(*,FMT1) '  Longitude (deg): ', LON*DPR()
              WRITE(*,FMT1) '  Latitude  (deg): ', LAT*DPR()
              WRITE(*,*) ' '
              WRITE(*,*) 'Rectangular coordinates from LATREC:'
              WRITE(*,*) ' '
              WRITE(*,FMT1) '  X          (km): ', RECTAN(1)
              WRITE(*,FMT1) '  Y          (km): ', RECTAN(2)
              WRITE(*,FMT1) '  Z          (km): ', RECTAN(3)
              WRITE(*,*) ' '

              END


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


         Original rectangular coordinates:

          X          (km):      -55658.44323296
          Y          (km):     -379226.32931475
          Z          (km):     -126505.93063865

         Latitudinal coordinates:

          Radius     (km):      403626.33912495
          Longitude (deg):         -98.34959789
          Latitude  (deg):         -18.26566077

         Rectangular coordinates from LATREC:

          X          (km):      -55658.44323296
          Y          (km):     -379226.32931475
          Z          (km):     -126505.93063865


     2) Create a table showing a variety of rectangular coordinates
        and the corresponding latitudinal coordinates.

        Corresponding rectangular and latitudinal coordinates are
        listed to three decimal places. Output angles are in degrees.


        Example code begins here.


              PROGRAM RECLAT_EX2
              IMPLICIT NONE

        C
        C     SPICELIB functions
        C
              DOUBLE PRECISION      DPR

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

        C
        C     Local variables.
        C
              DOUBLE PRECISION      LAT
              DOUBLE PRECISION      LON
              DOUBLE PRECISION      RADIUS
              DOUBLE PRECISION      RECTAN ( 3, NREC )

              INTEGER               I
              INTEGER               J

        C
        C     Define the input rectangular coordinates.
        C
              DATA                 RECTAN /
             .                  0.D0,         0.D0,         0.D0,
             .                  1.D0,         0.D0,         0.D0,
             .                  0.D0,         1.D0,         0.D0,
             .                  0.D0,         0.D0,         1.D0,
             .                 -1.D0,         0.D0,         0.D0,
             .                  0.D0,        -1.D0,         0.D0,
             .                  0.D0,         0.D0,        -1.D0,
             .                  1.D0,         1.D0,         0.D0,
             .                  1.D0,         0.D0,         1.D0,
             .                  0.D0,         1.D0,         1.D0,
             .                  1.D0,         1.D0,         1.D0  /

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

        C
        C     Do the conversion. Output angles in degrees.
        C
              DO I = 1, NREC

                 CALL RECLAT( RECTAN(1,I), RADIUS, LON, LAT )

                 WRITE (*,'(6F9.3)') ( RECTAN(J,I), J=1,3 ),
             .              RADIUS, LON * DPR(), LAT * DPR()

              END DO

              END


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


          RECT(1)  RECT(2)  RECT(3)   RADIUS    LON      LAT
          -------  -------  -------  -------  -------  -------
            0.000    0.000    0.000    0.000    0.000    0.000
            1.000    0.000    0.000    1.000    0.000    0.000
            0.000    1.000    0.000    1.000   90.000    0.000
            0.000    0.000    1.000    1.000    0.000   90.000
           -1.000    0.000    0.000    1.000  180.000    0.000
            0.000   -1.000    0.000    1.000  -90.000    0.000
            0.000    0.000   -1.000    1.000    0.000  -90.000
            1.000    1.000    0.000    1.414   45.000    0.000
            1.000    0.000    1.000    1.414    0.000   45.000
            0.000    1.000    1.000    1.414   90.000   45.000
            1.000    1.000    1.000    1.732   45.000   35.264

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

     C.H. Acton         (JPL)
     N.J. Bachman       (JPL)
     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.1.0, 05-JUL-2021 (JDR)

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

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Removed
        unnecessary $Revisions section. Added complete code examples.

    SPICELIB Version 1.0.2, 30-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)
Fri Dec 31 18:36:42 2021