Abstract

   CSPICE_HALFPI returns the double precision value of the constant pi/2.0.

I/O

   The call:

      [halfpi] = cspice_halfpi

   returns:

      halfpi   half the value of pi (the ratio of a circle's circumference
               to its diameter), determined by the acos function.

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

               That is,

                     halfpi = acos ( -1.0 ) * 0.5;

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) The following code example returns the double precision value of
      the constant pi/2.0 and prints it out.

      Example code begins here.


      function halfpi_ex1()

         %
         % Print the double precision value of pi/2.0
         %
         fprintf( 'Half pi: %25.22f\n', cspice_halfpi )


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


      Half pi:  1.5707963267948965579990


   2) Compute the transformation from inertial to body fixed
      coordinates, given the directions of the north pole and prime
      meridian of the body.

      When using the following values for Pluto, extracted from the
      PCK kernel pck00010.tpc:

         Right ascension (deg): 132.993
         Declination     (deg):  -6.163
         Prime meridian  (deg): 302.695

      at ephemeris epoch 2000 Jan 1 12:00:00 TDB, the result should
      match that obtained using the following call:

         [tipm] = cspice_pxform ( "J2000", "IAU_PLUTO", 0.0 );

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

         pck00010.tpc


      Example code begins here.


      function halfpi_ex2()

         %
         % Load the PCK.
         %
         cspice_furnsh( 'pck00010.tpc' );

         %
         % Compute the transformation from inertial to body
         % fixed coordinates, given the directions of the north
         % pole and prime meridian of the body.
         %

         %
         % Assign the values for Pluto, in radians.
         %
         ra  = 132.993 * cspice_rpd;
         dec =  -6.163 * cspice_rpd;
         w   = 302.695 * cspice_rpd;

         %
         % The transformation is defined by the compound
         % rotation
         %
         %   [W] [pi/2 - Dec] [RA + pi/2]
         %      3            1           3
         %
         [tipm] = cspice_rotate( ra + cspice_halfpi, 3 );
         [tipm] = cspice_rotmat( tipm, cspice_halfpi - dec, 1 );
         [tipm] = cspice_rotmat( tipm, w, 3 );

         %
         % Print the results
         %
         fprintf( 'Rotation matrix, from pole direction and prime\n' )
         fprintf( 'meridian:\n' )
         fprintf( '    %11.5f  %11.5f  %11.5f\n', ...
                                     tipm(1,1), tipm(1,2), tipm(1,3) )
         fprintf( '    %11.5f  %11.5f  %11.5f\n', ...
                                     tipm(2,1), tipm(2,2), tipm(2,3) )
         fprintf( '    %11.5f  %11.5f  %11.5f\n', ...
                                     tipm(3,1), tipm(3,2), tipm(3,3) )

         %
         % Use pxform_c to obtain the same transformation.
         %
         [tipm] = cspice_pxform( 'J2000', 'IAU_PLUTO', 0.0 );
         fprintf( '\n' )
         fprintf( 'Rotation matrix, from pxform_c:\n' )
         fprintf( '    %11.5f  %11.5f  %11.5f\n', ...
                                     tipm(1,1), tipm(1,2), tipm(1,3) )
         fprintf( '    %11.5f  %11.5f  %11.5f\n', ...
                                     tipm(2,1), tipm(2,2), tipm(2,3) )
         fprintf( '    %11.5f  %11.5f  %11.5f\n', ...
                                     tipm(3,1), tipm(3,2), tipm(3,3) )

         %
         % 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:


      Rotation matrix, from pole direction and prime
      meridian:
             -0.33349     -0.43443     -0.83669
             -0.65509     -0.53145      0.53704
             -0.67797      0.72721     -0.10736

      Rotation matrix, from pxform_c:
             -0.33349     -0.43443     -0.83669
             -0.65509     -0.53145      0.53704
             -0.67797      0.72721     -0.10736

Particulars

   The first time the function is referenced, the value is computed
   as shown above. The value is saved, and returned directly upon
   subsequent reference.

Exceptions

   Error free.

Files

   None.

Restrictions

   None.

Required_Reading

   MICE.REQ

Literature_References

   None.

Author_and_Institution

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

Version

   -Mice Version 1.1.0, 25-AUG-2021 (EDW) (JDR)

       Edited the header to comply with NAIF standard: created
       a complete example using the existing code fragments and added
       example's problem statement. Added example #2.

       Changed output argument name "return_val" to "halfpi" to comply with
       NAIF standard.

       Added -Parameters, -Particulars, -Exceptions, -Files, -Restrictions,
       -Literature_References and -Author_and_Institution sections.

       Eliminated use of "lasterror" in rethrow.

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

   -Mice Version 1.0.0, 22-NOV-2005 (EDW)

Index_Entries

   half the value of pi