Procedure

   rotvec_c ( Transform a vector via a rotation ) 

   void rotvec_c ( ConstSpiceDouble  v1    [3],
                   SpiceDouble       angle,
                   SpiceInt          iaxis,
                   SpiceDouble       vout  [3] )

Abstract

   Transform a vector to a new coordinate system rotated by `angle'
   radians about axis `iaxis'. This transformation rotates `v1' by
   -angle radians about the specified axis.

Required_Reading

   None.

Keywords

   ROTATION
   VECTOR

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   v1         I   Vector whose coordinate system is to be rotated.
   angle      I   Angle of rotation in radians.
   iaxis      I   Axis of rotation (X=1, Y=2, Z=3).
   vout       O   Resulting vector expressed in the new coordinate
                  system.

Detailed_Input

   v1          is a vector (typically representing a vector fixed
               in inertial space) which is to be expressed in another
               coordinate system. The vector remains fixed but the
               coordinate system changes.

   angle       is an angle given in radians, through which the rotation
               is performed.

   iaxis       is the index of the axis of rotation. The X, Y, and Z
               axes have indices 1, 2 and 3 respectively.

Detailed_Output

   vout        is the vector expressed in the new coordinate system
               specified by the angle of rotation and axis. If

                  m = [angle]
                             iaxis

               represents the rotation matrix described by the `angle'
               and `iaxis', (refer to the routine rotate_c) then

                  vout =  m * v1  = [angle]      * v1
                                           iaxis

Parameters

   None.

Exceptions

   Error free.

   1)  If the `iaxis' index is not in the range 1 to 3, it will be
       treated the same as that integer 1, 2, or 3 that is congruent
       to it mod 3.

Files

   None.

Particulars

   A rotation about the first, i.e. X-axis, is described by

      .-                              -.
      |   1       0            0       |
      |   0   cos(theta)   sin(theta)  |
      |   0  -sin(theta)   cos(theta)  |
      `-                              -'

   A rotation about the second, i.e. Y-axis, is described by

      .-                              -.
      |   cos(theta)   0  -sin(theta)  |
      |       0        1       0       |
      |   sin(theta)   1   cos(theta)  |
      `-                              -'

   A rotation about the third, i.e. Z-axis, is described by

      .-                              -.
      |   cos(theta)   sin(theta)   0  |
      |  -sin(theta)   cos(theta)   0  |
      |       0            0        1  |
      `-                              -'

   rotvec_c decides which form is appropriate according to the value
   of `iaxis' and applies the rotation to the input vector.

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) Apply a rotation of -45.0 degrees about the +Z axis to
      a 3 dimensional vector.

      Example code begins here.


      /.
         Program rotvec_ex1
      ./
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

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

         SpiceInt             iaxis;

         /.
         Input values.
         ./
         SpiceDouble          v1     [3] = { 1.414, 0.0, 0.0 };

         angle = pi_c ( )/4;
         iaxis = 3;

         /.
         Rotate `v1' by `angle' radians about `iaxis'.
         ./
         rotvec_c ( v1, angle, iaxis, vout );

         printf( "Input vector  : %9.3f %9.3f %9.3f\n",
                                   v1[0], v1[1], v1[2] );
         printf( "Rotated vector: %9.3f %9.3f %9.3f\n",
                             vout[0], vout[1], vout[2] );

         return ( 0 );
      }


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


      Input vector  :     1.414     0.000     0.000
      Rotated vector:     1.000    -1.000     0.000

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

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

Version

   -CSPICE Version 1.1.2, 04-AUG-2021 (JDR)

       Edited the header to comply with NAIF standard.

       Created complete code example from existing code fragments.

   -CSPICE Version 1.1.1, 04-OCT-1999 (NJB)

       Procedure line and abstract and were changed to dispel the
       impression that the input vector is rotated by +angle
       radians about the specified axis.

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

       Made input vector const.

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

Index_Entries

   rotate a vector