Procedure

   rotate_c ( Generate a rotation matrix ) 

   void rotate_c ( SpiceDouble     angle,
                   SpiceInt        iaxis,
                   SpiceDouble     mout[3][3] )

Abstract

   Calculate the 3x3 rotation matrix generated by a rotation
   of a specified angle about a specified axis. This rotation
   is thought of as rotating the coordinate system.

Required_Reading

   None.

Keywords

   MATRIX
   ROTATION

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   angle      I   Angle of rotation (radians).
   iaxis      I   Axis of rotation (X=1, Y=2, Z=3).
   mout       O   Resulting rotation matrix [angle]
                                                   iaxis

Detailed_Input

   angle       is the 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

   mout        is the rotation matrix which describes the rotation of the
               COORDINATE system through angle radians about the
               axis whose index is iaxis.

Parameters

   None.

Exceptions

   Error free.

   1)  If the axis 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)  0   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   |

   rotate_c decides which form is appropriate according to the value
   of IAXIS.

Examples

   If rotate_c is called from a C program as follows:

         rotate_c ( pi_c()/4, 3, mout );

   then mout will be given by

                | sqrt(2)/2   sqrt(2)/2   0  |
         mout = |-sqrt(2)/2   sqrt(2)/2   0  |
                |     0           0       1  |

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

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

Version

   -CSPICE Version 1.0.1, 04-AUG-2021 (JDR)

       Edited the header to comply with NAIF standard.

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

       Based on SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

Index_Entries

   generate a rotation matrix