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Index Page recsph_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

       recsph_c ( Rectangular to spherical coordinates )

       void recsph_c ( ConstSpiceDouble     rectan[3],
                       SpiceDouble        * r,
                       SpiceDouble        * colat,
                       SpiceDouble        * slon      )

#### Abstract

       Convert from rectangular coordinates to spherical coordinates.

#### Required_Reading

       None.

#### Keywords

       CONVERSION
       COORDINATES

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       rectan     I   Rectangular coordinates of a point.
       r          O   Distance of the point from the origin.
       colat      O   Angle of the point from the Z-axis in radians
       slon       O   Longitude of the point in radians.

#### Detailed_Input

       rectan      are the rectangular coordinates of a point.

#### Detailed_Output

       r           is the distance of the point from the origin.

       colat       is the angle between the point and the positive z-axis in
                   radians. The range of `colat' is [0, pi].

       slon        is the longitude of the point in radians. This is the
                   angle between the positive X-axis and the orthogonal
                   projection of the point onto the XY plane. `slon'
                   increases in the counterclockwise sense about the
                   positive Z-axis. The range of `slon' is [-pi, pi].

#### Parameters

       None.

#### Exceptions

       Error free.

#### Files

       None.

#### Particulars

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

       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) Compute the spherical 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: recsph_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 recsph_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

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

             /.
             Load SPK and LSK kernels, use a meta kernel for
             convenience.
             ./
             furnsh_c ( "recsph_ex1.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 spherical
             coordinates.
             ./
             recsph_c ( pos, &radius, &colat, &slon );

             /.
             Convert the spherical coordinates to rectangular.
             ./
             sphrec_c ( radius, 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( "Spherical coordinates:\n" );
             printf( " \n" );
             printf( " Radius      (km):  %19.8f\n", radius );
             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

          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

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

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

          Example code begins here.

          /.
             Program recsph_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local parameters.
             ./
             #define NREC         11

             /.
             Local variables.
             ./
             SpiceDouble          colat;
             SpiceDouble          radius;
             SpiceDouble          slon;

             SpiceInt             i;

             /.
             Define the input rectangular coordinates.
             ./
             SpiceDouble          rectan [NREC][3] = {
                                       { 0.0,         0.0,         0.0},
                                       { 1.0,         0.0,         0.0},
                                       { 0.0,         1.0,         0.0},
                                       { 0.0,         0.0,         1.0},
                                       {-1.0,         0.0,         0.0},
                                       { 0.0,        -1.0,         0.0},
                                       { 0.0,         0.0,        -1.0},
                                       { 1.0,         1.0,         0.0},
                                       { 1.0,         0.0,         1.0},
                                       { 0.0,         1.0,         1.0},
                                       { 1.0,         1.0,         1.0} };

             /.
             Print the banner.
             ./
             printf( " rect[0]  rect[1]  rect[2]   radius   colat     slon\n" );
             printf( " -------  -------  -------  -------  -------  -------\n" );

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

                recsph_c ( rectan[i], &radius, &colat, &slon );

                printf( "%8.3f %8.3f %8.3f ", rectan[i][0], rectan[i][1],
                                              rectan[i][2]               );
                printf( "%8.3f %8.3f %8.3f\n", radius, colat * dpr_c(),
                                                        slon * dpr_c() );

             }

             return ( 0 );
          }

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

           rect[0]  rect[1]  rect[2]   radius   colat     slon
           -------  -------  -------  -------  -------  -------
             0.000    0.000    0.000    0.000    0.000    0.000
             1.000    0.000    0.000    1.000   90.000    0.000
             0.000    1.000    0.000    1.000   90.000   90.000
             0.000    0.000    1.000    1.000    0.000    0.000
            -1.000    0.000    0.000    1.000   90.000  180.000
             0.000   -1.000    0.000    1.000   90.000  -90.000
             0.000    0.000   -1.000    1.000  180.000    0.000
             1.000    1.000    0.000    1.414   90.000   45.000
             1.000    0.000    1.000    1.414   45.000    0.000
             0.000    1.000    1.000    1.414   45.000   90.000
             1.000    1.000    1.000    1.732   54.736   45.000

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       B.V. Semenov        (JPL)
       W.L. Taber          (JPL)
       E.D. Wright         (JPL)

#### Version

       -CSPICE Version 1.2.0, 10-AUG-2021 (JDR)

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

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

       -CSPICE Version 1.1.2, 26-JUL-2016 (BVS)

           Minor headers edits.

       -CSPICE Version 1.1.1, 07-JAN-2002 (NJB) (EDW)

           Fixed description of slon in -Brief_I/O and Detailed_I/O
           header sections.

       -CSPICE Version 1.1.0, 22-OCT-1998 (NJB)

           Made input coordinate array const.

       -CSPICE Version 1.0.0, 08-FEB-1998 (EDW) (WLT)

#### Index_Entries

       rectangular to spherical coordinates

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

    Fri Dec 31 18:41:11 2021