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Index Page azlrec_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
       azlrec_c ( AZ/EL to rectangular coordinates )

       void azlrec_c ( SpiceDouble         range,
                       SpiceDouble         az,
                       SpiceDouble         el,
                       SpiceBoolean        azccw,
                       SpiceBoolean        elplsz,
                       SpiceDouble         rectan [3] )
#### Abstract
       Convert from range, azimuth and elevation of a point to
       rectangular coordinates.
#### Required_Reading
       None.
#### Keywords
       CONVERSION
       COORDINATES
#### Brief_I/O
       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       range      I   Distance of the point from the origin.
       az         I   Azimuth in radians.
       el         I   Elevation in radians.
       azccw      I   Flag indicating how azimuth is measured.
       elplsz     I   Flag indicating how elevation is measured.
       rectan     O   Rectangular coordinates of a point.
#### Detailed_Input
       range       is the distance of the point from the origin. The
                   input should be in terms of the same units in which
                   the output is desired.

                   Although negative values for `range' are allowed, its
                   use may lead to undesired results. See the -Exceptions
                   section for a discussion on this topic.

       az          is the azimuth of the point. This is the angle between
                   the projection onto the XY plane of the vector from
                   the origin to the point and the +X axis of the
                   reference frame. `az' is zero at the +X axis.

                   The way azimuth is measured depends on the value of
                   the logical flag `azccw'. See the descriptions of the
                   argument `azccw' for details.

                   The range (i.e., the set of allowed values) of `az' is
                   unrestricted. See the -Exceptions section for a
                   discussion on the `az' range.

                   Units are radians.

       el          is the elevation of the point. This is the angle
                   between the vector from the origin to the point and
                   the XY plane. `el' is zero at the XY plane.

                   The way elevation is measured depends on the value of
                   the logical flag `elplsz'. See the descriptions of the
                   argument `elplsz' for details.

                   The range (i.e., the set of allowed values) of `el' is
                   [-pi/2, pi/2], but no error checking is done to ensure
                   that `el' is within this range. See the -Exceptions
                   section for a discussion on the `el' range.

                   Units are radians.

       azccw       is a flag indicating how the azimuth is measured.

                   If `azccw' is SPICETRUE, the azimuth increases in the
                   counterclockwise direction; otherwise it increases
                   in the clockwise direction.

       elplsz      is a flag indicating how the elevation is measured.

                   If `elplsz' is SPICETRUE, the elevation increases from
                   the XY plane toward +Z; otherwise toward -Z.
#### Detailed_Output
       rectan      is an array containing the rectangular coordinates of
                   the point.

                   The units associated with the point are those
                   associated with the input `range'.
#### Parameters
       None.
#### Exceptions
       Error free.

       1)  If the value of the input argument `range' is negative
           the output rectangular coordinates will be negated, i.e.
           the resulting array will be of the same length
           but opposite direction to the one that would be obtained
           with a positive input argument `range' of value ||RANGE||.

       2)  If the value of the input argument `el' is outside the
           range [-pi/2, pi/2], the results may not be as
           expected.

       3)  If the value of the input argument `az' is outside the
           range [0, 2*pi], the value will be mapped to a value
           inside the range that differs from the input value by an
           integer multiple of 2*pi.
#### Files
       None.
#### Particulars
       This routine converts the azimuth, elevation, and range
       of a point into the associated rectangular coordinates.

       The input is defined by the distance from the center of
       the reference frame (range), the angle from a reference
       vector (azimuth), and the angle above the XY plane of the
       reference frame (elevation).

       The way azimuth and elevation are measured depends on the
       values given by the user to the `azccw' and `elplsz' logical
       flags. See the descriptions of these input arguments
       for details.
#### 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) Create four tables showing a variety of azimuth/elevation
          coordinates and the corresponding rectangular coordinates,
          resulting from the different choices of the `azccw' and `elplsz'
          flags.

          Corresponding azimuth/elevation and rectangular coordinates
          are listed to three decimal places. Input angles are in
          degrees.

          Example code begins here.

          /.
             Program azlrec_ex1
          ./
          #include <stdio.h>
          #include <string.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local parameters.
             ./
             #define NREC         11

             /.
             Local variables.
             ./
             SpiceChar            msg    [31];

             SpiceDouble          raz;
             SpiceDouble          rel;
             SpiceDouble          rectan [3];

             SpiceInt             i;
             SpiceInt             j;
             SpiceInt             n;

             /.
             Define the input azimuth/elevation coordinates and the
             different choices of the `azccw' and `elplsz' flags.
             ./
             SpiceDouble          range  [NREC] = { 0.0,   1.0,   1.0,   1.0,
                                                    1.0,   1.0,   1.0,   1.414,
                                                    1.414, 1.414, 1.732 };

             SpiceDouble          az     [NREC] = {   0.0,   0.0, 270.0,   0.0,
                                                    180.0,  90.0,   0.0, 315.0,
                                                      0.0, 270.0, 315.0 };

             SpiceDouble          el     [NREC] = {   0.0,   0.0,     0.0,
                                                    -90.0,   0.0,     0.0,
                                                     90.0,   0.0,   -45.0,
                                                    -45.0, -35.264,
                                                     };

             SpiceBoolean         azccw  [2] = { SPICEFALSE,  SPICETRUE };
             SpiceBoolean         elplsz [2] = { SPICEFALSE,  SPICETRUE };

             /.
             Create a table for each combination of `azccw' and `elplsz'.
             ./
             for ( i = 0; i < 2; i++ )
             {
                for ( j = 0; j < 2; j++ )
                {

                   /.
                   Display the flag settings.
                   ./
                   strncpy( msg, "AZCCW = #; ELPLSZ = #", 22 );
                   repml_c ( msg, "#", azccw[i], 'C', 31, msg );
                   repml_c ( msg, "#", elplsz[j], 'C', 31, msg );

                   printf( "\n" );
                   printf( "%s\n", msg );

                   /.
                   Print the banner.
                   ./
                   printf( "\n" );
                   printf( "   range      az       el    rect[0]  rect[1]  "
                           "rect[2]\n" );
                   printf( "  -------  -------  -------  -------  -------  "
                           "-------\n" );

                   /.
                   Do the conversion. Input angles in degrees.
                   ./
                   for ( n = 0; n < NREC; n++ )
                   {
                      raz = az[n] * rpd_c();
                      rel = el[n] * rpd_c();

                      azlrec_c ( range[n], raz,       rel,
                                 azccw[i], elplsz[j], rectan );

                      printf( "%9.3f %8.3f %8.3f %8.3f %8.3f %8.3f\n",
                              range[n],  az[n],     el[n],
                              rectan[0], rectan[1], rectan[2] );
                   }
                }
             }

             return ( 0 );
          }

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

          AZCCW = False; ELPLSZ = False

             range      az       el    rect[0]  rect[1]  rect[2]
            -------  -------  -------  -------  -------  -------
              0.000    0.000    0.000    0.000    0.000    0.000
              1.000    0.000    0.000    1.000    0.000    0.000
              1.000  270.000    0.000   -0.000    1.000    0.000
              1.000    0.000  -90.000    0.000    0.000    1.000
              1.000  180.000    0.000   -1.000   -0.000    0.000
              1.000   90.000    0.000    0.000   -1.000    0.000
              1.000    0.000   90.000    0.000    0.000   -1.000
              1.414  315.000    0.000    1.000    1.000    0.000
              1.414    0.000  -45.000    1.000    0.000    1.000
              1.414  270.000  -45.000   -0.000    1.000    1.000
              1.732  315.000  -35.264    1.000    1.000    1.000

          AZCCW = False; ELPLSZ = True

             range      az       el    rect[0]  rect[1]  rect[2]
            -------  -------  -------  -------  -------  -------
              0.000    0.000    0.000    0.000    0.000    0.000
              1.000    0.000    0.000    1.000    0.000    0.000
              1.000  270.000    0.000   -0.000    1.000    0.000
              1.000    0.000  -90.000    0.000    0.000   -1.000
              1.000  180.000    0.000   -1.000   -0.000    0.000
              1.000   90.000    0.000    0.000   -1.000    0.000
              1.000    0.000   90.000    0.000    0.000    1.000
              1.414  315.000    0.000    1.000    1.000    0.000
              1.414    0.000  -45.000    1.000    0.000   -1.000
              1.414  270.000  -45.000   -0.000    1.000   -1.000
              1.732  315.000  -35.264    1.000    1.000   -1.000

          AZCCW = True; ELPLSZ = False

             range      az       el    rect[0]  rect[1]  rect[2]
            -------  -------  -------  -------  -------  -------
              0.000    0.000    0.000    0.000    0.000    0.000
              1.000    0.000    0.000    1.000    0.000    0.000
              1.000  270.000    0.000   -0.000   -1.000    0.000
              1.000    0.000  -90.000    0.000    0.000    1.000
              1.000  180.000    0.000   -1.000    0.000    0.000
              1.000   90.000    0.000    0.000    1.000    0.000
              1.000    0.000   90.000    0.000    0.000   -1.000
              1.414  315.000    0.000    1.000   -1.000    0.000
              1.414    0.000  -45.000    1.000    0.000    1.000
              1.414  270.000  -45.000   -0.000   -1.000    1.000
              1.732  315.000  -35.264    1.000   -1.000    1.000

          AZCCW = True; ELPLSZ = True

             range      az       el    rect[0]  rect[1]  rect[2]
            -------  -------  -------  -------  -------  -------
              0.000    0.000    0.000    0.000    0.000    0.000
              1.000    0.000    0.000    1.000    0.000    0.000
              1.000  270.000    0.000   -0.000   -1.000    0.000
              1.000    0.000  -90.000    0.000    0.000   -1.000
              1.000  180.000    0.000   -1.000    0.000    0.000
              1.000   90.000    0.000    0.000    1.000    0.000
              1.000    0.000   90.000    0.000    0.000    1.000
              1.414  315.000    0.000    1.000   -1.000    0.000
              1.414    0.000  -45.000    1.000    0.000   -1.000
              1.414  270.000  -45.000   -0.000   -1.000   -1.000
              1.732  315.000  -35.264    1.000   -1.000   -1.000

       2) Compute the right ascension and declination of the pointing
          direction of DSS-14 station at a given epoch.

          Task Description
          ================

          In this example, we will obtain the right ascension and
          declination of the pointing direction of the DSS-14 station at
          a given epoch, by converting the station's pointing direction
          given in azimuth and elevation to rectangular coordinates
          in the station topocentric reference frame and applying a
          frame transformation from DSS-14_TOPO to J2000, in order to
          finally obtain the corresponding right ascension and
          declination of the pointing vector.

          In order to introduce the usage of the logical flags `azccw'
          and `elplsz', we will assume that the azimuth is measured
          counterclockwise and the elevation negative towards +Z
          axis of the DSS-14_TOPO reference frame.

          Kernels
          =======

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

             KPL/MK

             File name: azlrec_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
               ---------                        --------
               naif0011.tls                     Leapseconds
               earth_720101_070426.bpc          Earth historical
                                                binary PCK
               earth_topo_050714.tf             DSN station FK

             \begindata

             KERNELS_TO_LOAD = ( 'naif0011.tls',
                                 'earth_720101_070426.bpc',
                                 'earth_topo_050714.tf'     )

             \begintext

             End of meta-kernel.

          Example code begins here.

          /.
             Program azlrec_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local parameters
             ./
             #define META         "azlrec_ex2.tm"

             /.
             Local variables
             ./
             SpiceChar            msg    [41];
             SpiceChar          * obstim;
             SpiceChar          * ref;

             SpiceDouble          az;
             SpiceDouble          azr;
             SpiceDouble          dec;
             SpiceDouble          el;
             SpiceDouble          elr;
             SpiceDouble          et;
             SpiceDouble          jpos   [3];
             SpiceDouble          ptarg  [3];
             SpiceDouble          r;
             SpiceDouble          ra;
             SpiceDouble          range;
             SpiceDouble          rotate [3][3];

             SpiceBoolean         azccw;
             SpiceBoolean         elplsz;

             /.
             Load SPICE kernels.
             ./
             furnsh_c ( META );

             /.
             Convert the observation time to seconds past J2000 TDB.
             ./
             obstim = "2003 OCT 13 06:00:00.000000 UTC";

             str2et_c ( obstim, &et );

             /.
             Set the local topocentric frame
             ./
             ref    = "DSS-14_TOPO";

             /.
             Set the station's pointing direction in azimuth and
             elevation. Set arbitrarily the range to 1.0. Azimuth
             and elevation shall be given in radians. Azimuth
             increases counterclockwise and elevation is negative
             towards +Z (above the local horizon)
             ./
             az     =   75.00;
             el     =  -27.25;
             azr    =   az * rpd_c();
             elr    =   el * rpd_c();
             r      =    1.00;
             azccw  = SPICETRUE;
             elplsz = SPICEFALSE;

             /.
             Obtain the rectangular coordinates of the station's
             pointing direction.
             ./
             azlrec_c ( r, azr, elr, azccw, elplsz, ptarg );

             /.
             Transform the station's pointing vector from the
             local topocentric frame to J2000.
             ./
             pxform_c ( ref, "J2000", et, rotate );
             mxv_c ( rotate, ptarg, jpos );

             /.
             Compute the right ascension and declination.
             Express both angles in degrees.
             ./
             recrad_c ( jpos, &range, &ra, &dec );
             ra =   ra * dpr_c();
             dec =   dec * dpr_c();

             /.
             Display the computed pointing vector, the input
             data and resulting the angles.
             ./
             printf( "\n" );
             printf( "Pointing azimuth    (deg):  %14.8f\n", az );
             printf( "Pointing elevation  (deg):  %14.8f\n", el );

             repml_c ( "Azimuth counterclockwise?: #", "#", azccw, 'C', 41, msg );
             printf( "%s\n", msg );

             repml_c ( "Elevation positive +Z?   : #", "#", elplsz, 'C', 41,
                       msg );
             printf( "%s\n", msg );

             printf( "Observation epoch        : %s\n", obstim );
             printf( "\n" );
             printf( "Pointing direction (normalized):  \n" );
             printf( "   %14.8f %14.8f %14.8f\n", ptarg[0], ptarg[1], ptarg[2] );
             printf( "\n" );
             printf( "Pointing right ascension (deg):  %14.8f\n", ra );
             printf( "Pointing declination (deg):      %14.8f\n", dec );
             printf( "\n" );

             return ( 0 );
          }

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

          Pointing azimuth    (deg):     75.00000000
          Pointing elevation  (deg):    -27.25000000
          Azimuth counterclockwise?: True
          Elevation positive +Z?   : False
          Observation epoch        : 2003 OCT 13 06:00:00.000000 UTC

          Pointing direction (normalized):
                 0.23009457     0.85872462     0.45787392

          Pointing right ascension (deg):    280.06179939
          Pointing declination (deg):         26.92826084
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       J. Diaz del Rio     (ODC Space)
#### Version
       -CSPICE Version 1.0.0, 08-FEB-2021 (JDR)
#### Index_Entries
       range, az and el to rectangular coordinates
       range, azimuth and elevation to rectangular
       convert range, az and el to rectangular coordinates
       convert range, azimuth and elevation to rectangular
#### Link to routine azlrec_c source file azlrec_c.c

    Fri Dec 31 18:41:01 2021