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cspice_recpgr

Table of contents
Abstract
I/O
Parameters
Examples
Particulars
Exceptions
Files
Restrictions
Required_Reading
Literature_References
Author_and_Institution
Version
Index_Entries

Abstract


   CSPICE_RECPGR converts rectangular coordinates to
   planetographic coordinates.

I/O


   Given:

      body     the body name with which the planetographic coordinate
               system is associated.

               [1,c1] = size(body); char = class(body)

                  or

               [1,1] = size(body); cell = class(body)

               Optionally, you may supply the integer ID code for the
               object as an integer string, i.e. both 'MOON' and '301' are
               legitimate strings that indicate the Moon is the target body.

      rectan   the array(s) containing the rectangular coordinates of the
               position or set of positions.

               [3,n] = size(rectan); double = class(rectan)

       re      the value describing equatorial radius of the body
               of interest.

               [1,1] = size(re); double = class(re)

       f       the value describing flattening coefficient of the body,
               a dimensionless value defined as:

                    equatorial_radius - polar_radius
                    --------------------------------
                           equatorial_radius

               [1,1] = size(f); double = class(f)

   the call:

      [lon, lat, alt] = cspice_recpgr( body, rectan, re, f )

   returns:

       lon     the value(s) describing the planetographic longitude of the
               input point.

               [1,n] = size(lon); double = class(lon)

               This is the angle between the prime meridian and the meridian
               containing `rectan'. For bodies having prograde (aka
               direct) rotation, the direction of increasing
               longitude is positive west: from the +X axis of the
               rectangular coordinate system toward the -Y axis.
               For bodies having retrograde rotation, the direction
               of increasing longitude is positive east: from the +X
               axis toward the +Y axis.

               The earth, moon, and sun are exceptions: planetographic
               longitude is measured positive east for these bodies.

               The default interpretation of longitude by this
               and the other planetographic coordinate conversion
               routines can be overridden; see the discussion in
               -Particulars below for details.

               `lon' is output in radians. The nominal range of `lon' is
               given by:

                  0  <  lon  <  2*pi
                     -

               However, round-off error could cause `lon' to equal 2*pi.

       lat     the value(s) describing the planetographic latitude of the
               input point.

               [1,n] = size(lat); double = class(lat)

               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
               planetographic latitude is that of the closest point
               to P on the spheroid.

               `lat' is output in radians. The range of `lat' is given
               by:

                  -pi/2  <  lat  <  pi/2
                         -       -

       alt     the value(s) describing the altitude above the
               reference spheroid.

               [1,n] = size(alt); double = class(alt)

               `lon', `lat', and `alt' return with the same vectorization
               measure, N, as `rectan'.

Parameters


   None.

Examples


   Any numerical results shown for these examples may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.

   1) Find the planetographic coordinates of the point having Mars
      rectangular coordinates:

         X (km) =      0.0
         Y (km) =  -2620.678914818178
         Z (km) =   2592.408908856967

      (These input values have been chosen to create "simple" output
      values.)

      Use the PCK kernel below to load the required triaxial
      ellipsoidal shape model and orientation data for Mars.

         pck00008.tpc


      Example code begins here.


      %
      % Example 1: convert a single set of bodyfixed
      %            coordinates to planetographic
      %            coordinates.
      function recpgr_ex1()

         %
         % Load a PCK file containing a triaxial
         % ellipsoidal shape model and orientation
         % data for Mars.
         %
         cspice_furnsh( 'pck00008.tpc' )

         %
         % Look up the radii for Mars.  Although we
         % omit it here, we could check the kernel pool
         % to make sure the variable BODY499_RADII
         % has three elements and numeric data type.
         % If the variable is not present in the kernel
         % pool, cspice_bodvrd will signal an error.
         %
         body = 'MARS';
         radii = cspice_bodvrd( body, 'RADII', 3 );

         %
         %
         % Calculate the flatness coefficient. Set a bodyfixed
         % position vector, `x'.
         %
         re   = radii(1);
         rp   = radii(3);
         flat = ( re - rp ) / re;
         x    = [ 0.0,
                 -2620.678914818178,
                  2592.408908856967 ];

         %
         % Do the conversion.
         %
         [lon, lat, alt] = cspice_recpgr( body, x, re, flat );

         %
         % Output.
         %
         disp( 'Rectangular coordinates in km (x, y, z)' )
         fprintf( '%9.3f   %9.3f   %9.3f\n', x' )

         disp( 'Planetographic coordinates in degs and km (lon, lat, alt)' )
         fprintf( '%9.3f   %9.3f   %9.3f\n', lon *cspice_dpr() ...
                                           , lat *cspice_dpr() ...
                                           , alt               )

         %
         % It's always good form to unload kernels after use,
         % particularly in MATLAB due to data persistence.
         %
         cspice_kclear


      When this program was executed on a Mac/Intel/Octave6.x/64-bit
      platform, the output was:


      Rectangular coordinates in km (x, y, z)
          0.000   -2620.679    2592.409
      Planetographic coordinates in degs and km (lon, lat, alt)
         90.000      45.000     300.000


   2) Create a table showing a variety of rectangular coordinates
      and the corresponding Mars planetographic coordinates. The
      values are computed using the reference spheroid having radii

         Equatorial radius:    3396.190
         Polar radius:         3376.200

      Note: the values shown above may not be current or suitable
            for your application.


      Corresponding rectangular and planetographic coordinates are
      listed to three decimal places.

      Use the PCK file from example 1 above.


      Example code begins here.


      %
      % Example 2: convert a vectorized set of bodyfixed coordinates
      %            to planetographic coordinates
      %

      function recpgr_ex2()
         %
         % Load a PCK file containing a triaxial
         % ellipsoidal shape model and orientation
         % data for Mars.
         %
         cspice_furnsh( 'pck00008.tpc' )

         %
         % Look up the radii for Mars.  Although we
         % omit it here, we could check the kernel pool
         % to make sure the variable BODY499_RADII
         % has three elements and numeric data type.
         % If the variable is not present in the kernel
         % pool, cspice_bodvrd will signal an error.
         %
         body = 'MARS';
         radii = cspice_bodvrd( body, 'RADII', 3 );

         %
         %
         % Calculate the flatness coefficient. Set a bodyfixed
         % position vector, `x'.
         %
         re   = radii(1);
         rp   = radii(3);
         flat = ( re - rp ) / re;
         x    = [ 0.0,
                 -2620.678914818178,
                  2592.408908856967 ];

         %
         % Define an array of body-fixed 3x1 arrays.
         %
         x = [ [  3396.190;  0.000   ;  0.000    ], ...
               [ -3396.190;  0.000   ;  0.000    ], ...
               [ -3406.190;  0.000   ;  0.000    ], ...
               [ -3406.190;  0.000   ;  0.000    ], ...
               [  0.000   ; -3396.190;  0.000    ], ...
               [  0.000   ;  3396.190;  0.000    ], ...
               [  0.000   ;  0.000   ;  3376.200 ], ...
               [  0.000   ;  0.000   ; -3376.200 ], ...
               [  0.000   ;  0.000   ;   0.000   ] ];

         %
         % Using the same Mars parameters, convert the 3-vectors to
         % planetographic.
         %
         [ lon, lat, alt] = cspice_recpgr( body, x, re, flat );

         disp( ['rectan(1)   rectan(2)   rectan(3)' ...
                '         lon         lat         alt'] )

         disp( ['---------------------------------' ...
                '------------------------------------'] )

         %
         % Create an array of values for output.
         %
         output = [  x(1,:);         x(2,:);         x(3,:); ...
                     lon*cspice_dpr; lat*cspice_dpr; alt ];

         txt = sprintf( '%9.3f   %9.3f   %9.3f   %9.3f   %9.3f   %9.3f\n', ...
                                                                     output);
         disp( txt )

         %
         % It's always good form to unload kernels after use,
         % particularly in MATLAB due to data persistence.
         %
         cspice_kclear


      When this program was executed on a Mac/Intel/Octave6.x/64-bit
      platform, the output was:


      rectan(1)   rectan(2)   rectan(3)         lon         lat         alt
      ---------------------------------------------------------------------
       3396.190       0.000       0.000       0.000       0.000       0.000
      -3396.190       0.000       0.000     180.000       0.000       0.000
      -3406.190       0.000       0.000     180.000       0.000      10.000
      -3406.190       0.000       0.000     180.000       0.000      10.000
          0.000   -3396.190       0.000      90.000       0.000       0.000
          0.000    3396.190       0.000     270.000       0.000       0.000
          0.000       0.000    3376.200       0.000      90.000       0.000
          0.000       0.000   -3376.200       0.000     -90.000       0.000
          0.000       0.000       0.000       0.000      90.000   -3376.200


   3) Below we show the analogous relationships for the earth,
      using the reference ellipsoid radii

         Equatorial radius:    6378.140
         Polar radius:         6356.750

      Note the change in longitudes for points on the +/- Y axis
      for the earth vs the Mars values.

      rectan(1)   rectan(2)   rectan(3)         lon         lat         alt
      ---------------------------------------------------------------------
       6378.140       0.000       0.000       0.000       0.000       0.000
      -6378.140       0.000       0.000     180.000       0.000       0.000
      -6388.140       0.000       0.000     180.000       0.000      10.000
      -6368.140       0.000       0.000     180.000       0.000     -10.000
          0.000   -6378.140       0.000     270.000       0.000       0.000
          0.000    6378.140       0.000      90.000       0.000       0.000
          0.000       0.000    6356.750       0.000      90.000       0.000
          0.000       0.000   -6356.750       0.000     -90.000       0.000
          0.000       0.000       0.000       0.000      90.000   -6356.750

Particulars


   Given the body-fixed rectangular coordinates of a point, this
   routine returns the planetographic coordinates of the point. The
   body-fixed rectangular frame is that having the X-axis pass
   through the 0 degree latitude 0 degree longitude direction, the
   Z-axis pass through the 90 degree latitude direction, and the
   Y-axis equal to the cross product of the unit Z-axis and X-axis
   vectors.

   The planetographic definition of latitude is identical to the
   planetodetic (also called "geodetic" in SPICE documentation)
   definition. In the planetographic coordinate system, latitude is
   defined using a reference spheroid. The spheroid is
   characterized by an equatorial radius and a polar radius. For a
   point P on the spheroid, latitude is defined as the angle between
   the X-Y plane and the outward surface normal at P. For a point P
   off the spheroid, latitude is defined as the latitude of the
   nearest point to P on the spheroid. Note if P is an interior
   point, for example, if P is at the center of the spheroid, there
   may not be a unique nearest point to P.

   In the planetographic coordinate system, longitude is defined
   using the spin sense of the body. Longitude is positive to the
   west if the spin is prograde and positive to the east if the spin
   is retrograde. The spin sense is given by the sign of the first
   degree term of the time-dependent polynomial for the body's prime
   meridian Euler angle "W": the spin is retrograde if this term is
   negative and prograde otherwise. For the sun, planets, most
   natural satellites, and selected asteroids, the polynomial
   expression for W may be found in a SPICE PCK kernel.

   The earth, moon, and sun are exceptions: planetographic longitude
   is measured positive east for these bodies.

   If you wish to override the default sense of positive longitude
   for a particular body, you can do so by defining the kernel
   variable

      BODY<body ID>_PGR_POSITIVE_LON

   where <body ID> represents the NAIF ID code of the body. This
   variable may be assigned either of the values

      'WEST'
      'EAST'

   For example, you can have this routine treat the longitude
   of the earth as increasing to the west using the kernel
   variable assignment

      BODY399_PGR_POSITIVE_LON = 'WEST'

   Normally such assignments are made by placing them in a text
   kernel and loading that kernel via cspice_furnsh.

   The definition of this kernel variable controls the behavior of
   the Mice planetographic routines

      cspice_pgrrec
      cspice_recpgr
      cspice_dpgrdr
      cspice_drdpgr

   It does not affect the other Mice coordinate conversion
   routines.

Exceptions


   1)  If the body name `body' cannot be mapped to a NAIF ID code, and
       if `body' is not a string representation of an integer, the
       error SPICE(IDCODENOTFOUND) is signaled by a routine in the
       call tree of this routine.

   2)  If the kernel variable

          BODY<ID code>_PGR_POSITIVE_LON

       is present in the kernel pool but has a value other than one
       of

           'EAST'
           'WEST'

       the error SPICE(INVALIDOPTION) is signaled by a routine in the
       call tree of this routine. Case and blanks are ignored when
       these values are interpreted.

   3)  If polynomial coefficients for the prime meridian of `body' are
       not available in the kernel pool, and if the kernel variable
       BODY<ID code>_PGR_POSITIVE_LON is not present in the kernel
       pool, the error SPICE(MISSINGDATA) is signaled by a routine in
       the call tree of this routine.

   4)  If the equatorial radius is non-positive, the error
       SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call
       tree of this routine.

   5)  If the flattening coefficient is greater than or equal to one,
       the error SPICE(VALUEOUTOFRANGE) is signaled by a routine in
       the call tree of this routine.

   6)  For points inside the reference ellipsoid, the nearest point
       on the ellipsoid to `rectan' may not be unique, so latitude may
       not be well-defined.

   7)  If any of the input arguments, `body', `rectan', `re' or `f',
       is undefined, an error is signaled by the Matlab error
       handling system.

   8)  If any of the input arguments, `body', `rectan', `re' or `f',
       is not of the expected type, or it does not have the expected
       dimensions and size, an error is signaled by the Mice
       interface.

Files


   This routine expects a kernel variable giving BODY's prime
   meridian angle as a function of time to be available in the
   kernel pool. Normally this item is provided by loading a PCK
   file. The required kernel variable is named

      BODY<body ID>_PM

   where <body ID> represents a string containing the NAIF integer
   ID code for `body'. For example, if `body' is 'JUPITER', then
   the name of the kernel variable containing the prime meridian
   angle coefficients is

      BODY599_PM

   The optional kernel variable

      BODY<body ID>_PGR_POSITIVE_LON

   also is normally defined via loading a text kernel. When this
   variable is present in the kernel pool, the prime meridian
   coefficients for `body' are not required by this routine. See the
   -Particulars section for details.

Restrictions


   None.

Required_Reading


   KERNEL.REQ
   MICE.REQ
   NAIF_IDS.REQ
   PCK.REQ

Literature_References


   None.

Author_and_Institution


   J. Diaz del Rio     (ODC Space)
   E.D. Wright         (JPL)

Version


   -Mice Version 1.1.0, 24-AUG-2021 (EDW) (JDR)

       Added -Parameters, -Exceptions, -Files, -Restrictions,
       -Literature_References and -Author_and_Institution sections. Fixed
       typos in header. Completed list of Mice planetographic routines in
       -Particulars section. Extended Required Reading document list.

       Edited the header to comply with NAIF standard.
       Split the existing code example into two separate examples and
       added example 3.

       Eliminated use of "lasterror" in rethrow.

       Removed reference to the function's corresponding CSPICE header from
       -Required_Reading section.

   -Mice Version 1.0.2, 01-DEC-2014 (EDW)

       Edited -I/O section to conform to NAIF standard for Mice
       documentation.

   -Mice Version 1.0.1, 30-DEC-2008 (EDW)

       Corrected misspellings.

   -Mice Version 1.0.0, 22-JAN-2008 (EDW)

Index_Entries


   convert rectangular to planetographic coordinates


Fri Dec 31 18:44:26 2021