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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_PGRREC converts planetographic coordinates to
   rectangular coordinates.

I/O


   Given:

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

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

       lon    the planetographic longitude of the input point. This is the
             angle between the prime meridian and the meridian containing the
             input point. 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.

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

             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 measured in radians. On input, the range
             of longitude is unrestricted.

       lat    the planetographic latitude of the input point.  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.

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

             'lat' is measured in radians.  On input, the
             range of latitude is unrestricted.

       alt    the altitude above the reference spheroid.

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

             Units of 'alt' must match those of  're'.

       re    equatorial radius of the body of interest.

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

       f     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:

      rectan = cspice_pgrrec( body, lon, lat, alt, re, f)

   returns:

      rectan   the rectangular body-fixed coordinates of the position or set
               of positions.

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

               'rectan' returns with the same units associated with
               'alt' and 're'.

               'rectan' returns with the same vectorization measure
                (N) as 'lon', 'lat', and 'alt'.

Examples


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

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

      %
      % Example 1: convert a single set of planetographic
      %            coordinates to rectangular bodyfixed
      %            coordinates.
      %
      % 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;

      % Set a longitude, latitude, altitude position.
      % Note that we must provide longitude and
      % latitude in radians.
      %
      lon  = 90. * cspice_rpd;
      lat  = 45.  * cspice_rpd;
      alt  = 3.d2;

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

      %
      % Output.
      %
      disp( 'Scalar:' )
      disp(' ')

      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               )
      disp(' ')


      %
      % Example 2: convert a vectorized set of planetographic coordinates
      %            to rectangular bodyfixed coordinates.
      %
      % Define 1xN arrays of longitudes, latitudes, and altitudes.
      %
      lon = [ 0.,   ...
              180., ...
              180., ...
              180., ...
              90.,  ...
              270., ...
              0.,   ...
              0.,   ...
              0. ];

      lat = [ 0.,  ...
              0.,  ...
              0.,  ...
              0.,  ...
              0.,  ...
              0.,  ...
              90., ...
             -90., ...
              90. ];

      alt = [ 0., ...
              0., ...
              10., ...
              10., ...
              0., ...
              0., ...
              0., ...
              0., ...
             -3376.200 ];

      %
      % Convert angular measures to radians.
      %
      lon = lon*cspice_rpd;
      lat = lat*cspice_rpd;

      %
      % Using the same Mars parameters, convert the 'lon', 'lat', 'alt'
      % vectors to bodyfixed rectangular coordinates.
      %
      x = cspice_pgrrec( body, lon, lat, alt, re, flat);

      disp('Vector:')
      disp(' ')

      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

   MATLAB outputs:

      Scalar:

      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

      Vector:

      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

Particulars


   Given the planetographic coordinates of a point, this routine
   returns the body-fixed rectangular 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 CSPICE planetographic routines

      cspice_pgrrec
      cspice_recpgr

Required Reading


   For important details concerning this module's function, please refer to
   the CSPICE routine pgrrec_c.

   MICE.REQ

Version


   -Mice Version 1.0.1, 12-MAR-2012, EDW (JPL), SCK (JPL)

      Corrected misspellings.

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

Index_Entries


   convert planetographic to rectangular coordinates


Wed Apr  5 18:00:33 2017