Procedure

   SpiceDouble vrel_c ( ConstSpiceDouble v1[3],
                        ConstSpiceDouble v2[3]  )

Abstract

   Return the relative difference between two 3-dimensional vectors.

Required_Reading

   None.

Keywords

   MATH
   VECTOR

Brief_I/O

   Variable  I/O  Description
   --------  ---  --------------------------------------------------
    v1,v2     I   Input vectors.

Detailed_Input

    v1, v2        are two 3-dimensional vectors for which the
                  relative difference is to be computed.

Detailed_Output

    vrel_c        the relative difference between V1 and V2.
                  It is defined as:
                                              || v1 - v2 ||
                            vrel_c   =   ----------------------
                                       max ( ||v1||, ||v2|| )

                  where || x || indicates the Euclidean norm of
                  the vector x ( ||x|| = sqrt( x . x ) ).

                  vrel_c assumes values in the range [0,2]. If both
                  v1 and v2 are zero vectors then vrel_c is defined
                  to be zero.

Parameters

   None.

Exceptions

   Error free.

   If both v1 and v2 are zero vectors then vrel_c is defined
   to be zero.

Files

   None.

Particulars

   This function computes the relative difference between two
   3-dimensional vectors as defined above.

   The function vrelg_c may be used to find the relative difference
   for two vectors of general dimension.

Examples

   This example code fragment computes the relative difference
   between the geometric and light time corrected state of Io
   with respect to Voyager 2 at a given UTC time.

         #include "SpiceUsr.h"
               .
               .
               .
         /.
         The NAIF integer code for Io is 501 and the code for
         Voyager 2 is -32.
         ./

         #define           IO    501
         #define           VG2   -32


         /.
         Local variables
         ./
         SpiceDouble       state [ 6 ];
         SpiceDouble       pos1  [ 3 ];
         SpiceDouble       pos2  [ 3 ];
         SpiceDouble       diff;
         SpiceDouble       lt;
         SpiceDouble       et;

         SpiceChar       * utc = "1979 JUN 25 12:00:00";

         /.
         Load the sample SPK ephemeris file.
        ./
         furnsh_c ( "VG2_JUP.BSP" );


         /.
         Convert the UTC time string to ephemeris time.
         ./
         utc2et_c ( utc, &et );


         /.
         First calculate the geometric state and then the light
         time corrected state.
         ./
         spkez_c ( IO, et, "J2000", "none", VG2, state, &lt );

         vequ_c  ( state, pos1 );

         spkez_c ( IO, et, "J2000", "lt", VG2, state, &lt );

         vequ_c  ( state, pos2 );

         /.
         Call vrel_c to find the relative difference between the
         two states.
         ./
         diff = vrel_c ( pos1, pos2 );

         .
         .
         .

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

   J.M. Lynch     (JPL)
   E.D. Wright    (JPL)

Version

   -CSPICE Version 1.1.0, 28-AUG-2001 (NJB)
     
      Include interface macro definition file SpiceZim.h. 

   -CSPICE Version 1.0.1, 13-APR-2000 (NJB) 
   
      Made some minor updates and corrections in the code example.
      
   -CSPICE Version 1.0.0, 6-JUL-1999

Index_Entries

   relative difference of 3-dimensional vectors

Link to routine vrel_c source file vrel_c.c