Procedure

   vlcom_c ( Vector linear combination, 3 dimensions ) 

   void vlcom_c ( SpiceDouble        a,
                  ConstSpiceDouble   v1[3],
                  SpiceDouble        b,
                  ConstSpiceDouble   v2[3],
                  SpiceDouble        sum[3] )

Abstract

   Compute a vector linear combination of two double precision,
   3-dimensional vectors.

Required_Reading

   None.

Keywords

   VECTOR

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   a          I   Coefficient of `v1'.
   v1         I   Vector in 3-space.
   b          I   Coefficient of `v2'.
   v2         I   Vector in 3-space.
   sum        O   Linear vector combination a*v1 + b*v2.

Detailed_Input

   a           is the double precision scalar variable that multiplies
               `v1'.

   v1          is an arbitrary, double precision 3-dimensional vector.

   b           is the double precision scalar variable that multiplies
               `v2'.

   v2          is an arbitrary, double precision 3-dimensional vector.

Detailed_Output

   sum         is the double precision 3-dimensional vector which
               contains the linear combination

                  a * v1 + b * v2

Parameters

   None.

Exceptions

   Error free.

Files

   None.

Particulars

   The code reflects precisely the following mathematical expression

      For each value of the index `i', from 0 to 2:

         sum[i] = a*v1[i] + b*v2[i]

   No error checking is performed to guard against numeric overflow.

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) Suppose you want to generate a sequence of points representing
      an elliptical footprint, from the known semi-major
      and semi-minor axes.


      Example code begins here.


      /.
         Program vlcom_ex1
      ./
      #include <math.h>
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

         /.
         Local variables.
         ./
         SpiceDouble          step;
         SpiceDouble          theta;
         SpiceDouble          vector [3];

         SpiceInt             i;

         /.
         Let `smajor' and `sminor' be the two known semi-major and
         semi-minor axes of our elliptical footprint.
         ./
         SpiceDouble          smajor [3] = { 0.070115, 0.0,        0.0 };

         SpiceDouble          sminor [3] = { 0.0,       0.035014,  0.0 };

         /.
         Compute the vectors of interest and display them
         ./
         theta = 0.0;
         step  = twopi_c() / 16;

         for ( i = 0; i < 16; i++ )
         {

            vlcom_c ( cos(theta), smajor, sin(theta), sminor, vector );

            printf( "%2d: %9.6f %9.6f %9.6f\n",
                    i, vector[0], vector[1], vector[2] );

            theta = theta + step;

         }

         return ( 0 );
      }


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


       0:  0.070115  0.000000  0.000000
       1:  0.064778  0.013399  0.000000
       2:  0.049579  0.024759  0.000000
       3:  0.026832  0.032349  0.000000
       4:  0.000000  0.035014  0.000000
       5: -0.026832  0.032349  0.000000
       6: -0.049579  0.024759  0.000000
       7: -0.064778  0.013399  0.000000
       8: -0.070115  0.000000  0.000000
       9: -0.064778 -0.013399 -0.000000
      10: -0.049579 -0.024759 -0.000000
      11: -0.026832 -0.032349 -0.000000
      12: -0.000000 -0.035014 -0.000000
      13:  0.026832 -0.032349  0.000000
      14:  0.049579 -0.024759  0.000000
      15:  0.064778 -0.013399  0.000000


   2) As a second example, suppose that U and V are orthonormal
      vectors that form a basis of a plane. Moreover suppose that we
      wish to project a vector X onto this plane.


      Example code begins here.


      /.
         Program vlcom_ex2
      ./
      #include <math.h>
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

         /.
         Local variables.
         ./
         SpiceDouble          puv    [3];
         SpiceDouble          v      [3];

         /.
         Let `x' be an arbitrary 3-vector
         ./
         SpiceDouble          x      [3] = { 4.0, 35.0, -5.0 };

         /.
         Let `u' and `v' be orthonormal 3-vectors spanning the
         plane of interest.
         ./
         SpiceDouble          u      [3] = { 0.0,  0.0,  1.0 };

         v[0] =  sqrt(2.0)/2.0;
         v[1] = -sqrt(2.0)/2.0;
         v[2] =  0.0;

         /.
         Compute the projection of `x' onto this 2-dimensional
         plane in 3-space.
         ./
         vlcom_c ( vdot_c ( x, u ), u, vdot_c ( x, v ), v, puv );

         /.
         Display the results.
         ./
         printf( "Input vector             :  %5.1f %5.1f %5.1f\n",
                                                   x[0], x[1], x[2] );
         printf( "Projection into 2-d plane:  %5.1f %5.1f %5.1f\n",
                                             puv[0], puv[1], puv[2] );

         return ( 0 );
      }


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


      Input vector             :    4.0  35.0  -5.0
      Projection into 2-d plane:  -15.5  15.5  -5.0

Restrictions

   1)  No error checking is performed to guard against numeric
       overflow or underflow. The user is responsible for insuring
       that the input values are reasonable.

Literature_References

   None.

Author_and_Institution

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

Version

   -CSPICE Version 1.1.1, 13-AUG-2021 (JDR)

       Edited the header to comply with NAIF standard. Added complete
       code example.

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

       Made input vectors const.

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

Index_Entries

   linear combination of two 3-dimensional vectors