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Index Page halfpi_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

       halfpi_c ( Half the value of pi )

       SpiceDouble halfpi_c ( void )

#### Abstract

       Return half the value of pi (the ratio of the circumference of
       a circle to its diameter).

#### Required_Reading

       None.

#### Keywords

       CONSTANTS

#### Brief_I/O

       The function returns half the value of pi.

#### Detailed_Input

       None.

#### Detailed_Output

       The function returns half the value of pi (the ratio of
       a circle's circumference to its diameter), determined by
       the ACOS function. That is,

             halfpi_c = acos ( -1.0 ) * 0.50

#### Parameters

       None.

#### Exceptions

       Error free.

#### Files

       None.

#### 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.

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

          Example code begins here.

          /.
             Program halfpi_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main ()
          {
             /.
             Print the double precision value of pi/2.0
             ./
             printf( "Half pi: %25.22f\n", halfpi_c( ) );

             return ( 0 );
          }

          When this program was executed on a Mac/Intel/cc/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:

             pxform_c ( "J2000", "IAU_PLUTO", 0.0, tipm );

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

             pck00010.tpc

          Example code begins here.

          /.
             Program halfpi_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main ( )
          {
             /.
             Compute the transformation from inertial to body
             fixed coordinates, given the directions of the north
             pole and prime meridian of the body.

             Local variables.
             ./
             SpiceDouble   ra;
             SpiceDouble   dec;
             SpiceDouble   w;
             SpiceDouble   tipm [3][3];

             /.
             Load the PCK.
             ./
             furnsh_c ( "pck00010.tpc" );

             /.
             Assign the values for Pluto, in radians.
             ./
             ra  = 132.993 * rpd_c( );
             dec =  -6.163 * rpd_c( );
             w   = 302.695 * rpd_c( );

             /.
             The transformation is defined by the compound
             rotation

               [W] [pi/2 - Dec] [RA + pi/2]
                  3            1           3
             ./
             rotate_c (        ra + halfpi_c(), 3, tipm );
             rotmat_c ( tipm, halfpi_c() - dec, 1, tipm );
             rotmat_c ( tipm, w,                3, tipm );

             /.
             Print the results
             ./
             printf( "Rotation matrix, from pole direction "
                     "and prime\nmeridian:\n"                  );
             printf( "   %12.6f %12.6f %12.6f\n",
                            tipm[0][0], tipm[1][0], tipm[2][0] );
             printf( "   %12.6f %12.6f %12.6f\n",
                            tipm[0][1], tipm[1][1], tipm[2][1] );
             printf( "   %12.6f %12.6f %12.6f\n",
                            tipm[0][2], tipm[1][2], tipm[2][2] );

             /.
             Use pxform_c to obtain the same transformation.
             ./
             pxform_c ( "J2000", "IAU_PLUTO", 0.0, tipm );
             printf( "\nRotation matrix, from pxform_c:\n"     );
             printf( "   %12.6f %12.6f %12.6f\n",
                            tipm[0][0], tipm[1][0], tipm[2][0] );
             printf( "   %12.6f %12.6f %12.6f\n",
                            tipm[0][1], tipm[1][1], tipm[2][1] );
             printf( "   %12.6f %12.6f %12.6f\n",
                            tipm[0][2], tipm[1][2], tipm[2][2] );

             return ( 0 );
          }

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

          Rotation matrix, from pole direction and prime
          meridian:
                -0.333489    -0.655091    -0.677968
                -0.434428    -0.531449     0.727210
                -0.836694     0.537045    -0.107357

          Rotation matrix, from pxform_c:
                -0.333489    -0.655091    -0.677968
                -0.434428    -0.531449     0.727210
                -0.836694     0.537045    -0.107357

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

       -CSPICE Version 1.0.1, 13-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard. Created simple example
           for retrieving pi/2.0 value, and converted code fragment into full
           example code.

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

#### Index_Entries

       half the value of pi

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

    Fri Dec 31 18:41:08 2021