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Index Page rotvec_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

       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

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

    Fri Dec 31 18:41:11 2021