Procedure

   unorm_c ( Unit vector and norm, 3 dimensional ) 

   void unorm_c ( ConstSpiceDouble     v1[3],
                  SpiceDouble          vout[3],
                  SpiceDouble        * vmag    )

Abstract

   Normalize a double precision 3-vector and return its magnitude.

Required_Reading

   None.

Keywords

   VECTOR

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   v1         I     Vector to be normalized.
   vout       O     Unit vector v1 / |v1|.
   vmag       O     Magnitude of v1, i.e. |v1|.

Detailed_Input

   v1          is an arbitrary 3-vector, including the
               zero vector.

Detailed_Output

   vout        is the unit vector in the direction  of `v1'. If `v1' is
               the zero vector, then `vout' will also be the zero
               vector.

   vmag        is the magnitude of `v1'.

Parameters

   None.

Exceptions

   Error free.

Files

   None.

Particulars

   unorm_c references a function called vnorm_c (which itself is
   numerically stable) to calculate the norm of the input vector `v1'.
   If the norm is equal to zero, then each component of the output
   vector `vout' is set to zero. Otherwise, `vout' is calculated by
   dividing `v1' by the norm.

Examples

   The numerical results shown for this example 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) Define a set of vectors and compute their corresponding unit
      vector and magnitude.


      Example code begins here.


      /.
         Program unorm_ex1
      ./
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

         /.
         Local parameters.
         ./
         #define SETSIZ       2

         /.
         Local variables.
         ./
         SpiceDouble          vmag;
         SpiceDouble          vout   [3];

         SpiceInt             i;

         /.
         Define the vector set.
         ./
         SpiceDouble          seta   [SETSIZ][3] = {
                                   {5.0,  12.0,  0.0},
                                   {1.e-7,  2.e-7, 2.e-7} };

         /.
         Calculate the unit vectors and magnitudes.
         ./
         for ( i = 0; i < SETSIZ; i++ )
         {

            unorm_c ( seta[i], vout, &vmag );

            printf( "Vector     :  %12.8f %12.8f %12.8f\n",
                         seta[i][0], seta[i][1], seta[i][2] );
            printf( "Unit vector:  %12.8f %12.8f %12.8f\n",
                                  vout[0], vout[1], vout[2] );
            printf( "Magnitude  :  %12.8f\n", vmag );
            printf( " \n" );

         }

         return ( 0 );
      }


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


      Vector     :    5.00000000  12.00000000   0.00000000
      Unit vector:    0.38461538   0.92307692   0.00000000
      Magnitude  :   13.00000000

      Vector     :    0.00000010   0.00000020   0.00000020
      Unit vector:    0.33333333   0.66666667   0.66666667
      Magnitude  :    0.00000030

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

   N.J. Bachman        (JPL)
   J. Diaz del Rio     (ODC Space)
   W.M. Owen           (JPL)
   W.L. Taber          (JPL)
   E.D. Wright         (JPL)

Version

   -CSPICE Version 1.1.1, 10-AUG-2021 (JDR)

       Updated the header to comply with NAIF standard. Added
       complete code example to -Examples section.

       Header sections have been reordered.

   -CSPICE Version 1.1.0, 22-OCT-1998 (NJB)

       Made input vector const.

   -CSPICE Version 1.0.0, 17-OCT-1997 (EDW) (WMO) (WLT)

Index_Entries

   3-dimensional unit vector and norm