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Index Page latsph_c
Table of contents
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
       latsph_c ( Latitudinal to spherical coordinates )

       void latsph_c ( SpiceDouble    radius,
                       SpiceDouble    lon,
                       SpiceDouble    lat,
                       SpiceDouble *  rho,
                       SpiceDouble *  colat,
                       SpiceDouble *  slon )
#### Abstract
       Convert from latitudinal coordinates to spherical coordinates.
#### Required_Reading
       None.
#### Keywords
       CONVERSION
       COORDINATES
#### Brief_I/O
       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       radius     I   Distance of a point from the origin.
       lon        I   Angle of the point from the XZ plane in radians.
       lat        I   Angle of the point from the XY plane in radians.
       rho        O   Distance of the point from the origin.
       colat      O   Angle of the point from positive z axis (radians).
       slon       O   Angle of the point from the XZ plane (radians).
#### Detailed_Input
       radius      is the distance of a point from the origin.

       lon         is the angle of the point from the XZ plane in radians.

       lat         is the angle of the point from the XY plane in radians.
#### Detailed_Output
       rho         is the distance of the point from the origin.

       colat       is the angle between the vector from the origin to the point
                   and the positive z axis in radians. `colat' is computed
                   as pi/2 - `lat'.

       slon        is the angle of the point from the XZ plane (radians). `slon'
                   is set equal to `lon'.
#### Parameters
       None.
#### Exceptions
       Error free.
#### Files
       None.
#### Particulars
       This routine returns the spherical coordinates of a point
       whose position is input in latitudinal 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.

       Spherical coordinates are defined by a distance from a central
       reference point, an angle from a reference meridian, and an angle
       from the z-axis.
#### 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) Co-latitude is obtained by subtracting latitude from halfpi_c
          Radius and longitude mean the same thing in both latitudinal
          and spherical coordinates. The table below lists `lat' and
          corresponding `colat' in terms of degrees.

               LAT     COLAT
              -----    -----
                 0        90
                20        70
                45        45
               -30       120
                90         0
               -45       135

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

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

             KPL/MK

             File name: latsph_ex2.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 latsph_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables
             ./
             SpiceDouble          colat;
             SpiceDouble          et;
             SpiceDouble          lat;
             SpiceDouble          lon;
             SpiceDouble          lt;
             SpiceDouble          pos    [3];
             SpiceDouble          r;
             SpiceDouble          radius;
             SpiceDouble          rectan [3];
             SpiceDouble          slon;

             /.
             Load SPK and LSK kernels, use a meta kernel for
             convenience.
             ./
             furnsh_c ( "latsph_ex2.tm" );

             /.
             Look up the geometric state of the Moon as seen from
             the Earth at 2017 Mar 20, relative to the J2000
             reference frame.
             ./
             str2et_c ( "2017 Mar 20", &et );

             spkpos_c ( "Moon", et, "J2000", "NONE", "Earth", pos, &lt );

             /.
             Convert the position vector `pos' to latitudinal
             coordinates.
             ./
             reclat_c ( pos, &radius, &lon, &lat );

             /.
             Convert the latitudinal coordinates to spherical.
             ./
             latsph_c ( radius, lon, lat, &r, &colat, &slon );

             /.
             Convert the spherical coordinates to rectangular.
             ./
             sphrec_c ( r, colat, slon, rectan );

             printf( " \n" );
             printf( "Original rectangular coordinates:\n" );
             printf( " \n" );
             printf( " X           (km):  %19.8f\n", pos[0] );
             printf( " Y           (km):  %19.8f\n", pos[1] );
             printf( " Z           (km):  %19.8f\n", pos[2] );
             printf( " \n" );
             printf( "Latitudinal coordinates:\n" );
             printf( " \n" );
             printf( " Radius      (km):  %19.8f\n", radius );
             printf( " Longitude  (deg):  %19.8f\n", lon*dpr_c ( ) );
             printf( " Latitude   (deg):  %19.8f\n", lat*dpr_c ( ) );
             printf( " \n" );
             printf( "Spherical coordinates:\n" );
             printf( " \n" );
             printf( " Radius      (km):  %19.8f\n", r );
             printf( " Colatitude (deg):  %19.8f\n", colat*dpr_c ( ) );
             printf( " Longitude  (deg):  %19.8f\n", slon*dpr_c ( ) );
             printf( " \n" );
             printf( "Rectangular coordinates from sphrec_c:\n" );
             printf( " \n" );
             printf( " X           (km):  %19.8f\n", rectan[0] );
             printf( " Y           (km):  %19.8f\n", rectan[1] );
             printf( " Z           (km):  %19.8f\n", rectan[2] );
             printf( " \n" );

             return ( 0 );
          }

          When this program was executed on a Mac/Intel/cc/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

          Spherical coordinates:

           Radius      (km):      403626.33912495
           Colatitude (deg):         108.26566077
           Longitude  (deg):         -98.34959789

          Rectangular coordinates from sphrec_c:

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

       3) Create a table showing a variety of latitudinal coordinates
          and the corresponding spherical coordinates.

          Corresponding latitudinal and spherical coordinates are
          listed to three decimal places. Input and output angles are
          in degrees.

          Example code begins here.

          /.
             Program latsph_ex3
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local parameters.
             ./
             #define NREC         11

             /.
             Local variables.
             ./
             SpiceDouble          colat;
             SpiceDouble          r;
             SpiceDouble          rlat;
             SpiceDouble          rlon;
             SpiceDouble          slon;

             SpiceInt             i;

             /.
             Define the input latitudinal coordinates. Angles in
             degrees.
             ./

             SpiceDouble          radius [NREC] = {  0.0,  1.0,    1.0,
                                                     1.0,  1.4142, 1.0,
                                                     1.0,  1.0,    1.4142,
                                                     1.0,  0.0            };

             SpiceDouble          lon    [NREC] = {  0.0,   0.0,  90.0,
                                                     0.0, 180.0, -90.0,
                                                     0.0,  45.0, 180.0,
                                                   180.0,  33.0        };

             SpiceDouble          lat    [NREC] = { 90.0,  0.0,   0.0,
                                                    90.0, 45.0,   0.0,
                                                   -90.0,  0.0, -45.0,
                                                    90.0,  0.0        };

             /.
             Print the banner.
             ./
             printf( "  radius    lon      lat       r      colat     slon\n" );
             printf( " -------  -------  -------  -------  -------  ------- \n" );

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

                rlon = lon[i] * rpd_c ( );
                rlat = lat[i] * rpd_c ( );

                latsph_c ( radius[i], rlon, rlat, &r, &colat, &slon );

                printf( "%8.3f %8.3f %8.3f ", radius[i], lon[i], lat[i] );
                printf( "%8.3f %8.3f %8.3f\n",
                        r, colat * dpr_c ( ), slon * dpr_c ( ) );

             }

             return ( 0 );
          }

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

            radius    lon      lat       r      colat     slon
           -------  -------  -------  -------  -------  -------
             0.000    0.000   90.000    0.000    0.000    0.000
             1.000    0.000    0.000    1.000   90.000    0.000
             1.000   90.000    0.000    1.000   90.000   90.000
             1.000    0.000   90.000    1.000    0.000    0.000
             1.414  180.000   45.000    1.414   45.000  180.000
             1.000  -90.000    0.000    1.000   90.000  -90.000
             1.000    0.000  -90.000    1.000  180.000    0.000
             1.000   45.000    0.000    1.000   90.000   45.000
             1.414  180.000  -45.000    1.414  135.000  180.000
             1.000  180.000   90.000    1.000    0.000  180.000
             0.000   33.000    0.000    0.000   90.000   33.000
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       J. Diaz del Rio     (ODC Space)
       B.V. Semenov        (JPL)
       W.L. Taber          (JPL)
       E.D. Wright         (JPL)
#### Version
       -CSPICE Version 1.1.0, 13-AUG-2021 (JDR)

           Changed the output argument name "lons" to "slon" for
           consistency with other routines.

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

       -CSPICE Version 1.0.2, 26-JUL-2016 (BVS)

           Minor headers edits.

       -CSPICE Version 1.0.1, 13-DEC-2005 (EDW)

           Corrected typo in -Detailed_Output, substituted
           "colat" for "lat."

       -CSPICE Version 1.0.0, 08-FEB-1998 (EDW) (WLT)
#### Index_Entries
       latitudinal to spherical coordinates
#### Link to routine latsph_c source file latsph_c.c

    Fri Dec 31 18:41:08 2021