Procedure

   twovec_c ( Two vectors defining an orthonormal frame ) 

   void twovec_c ( ConstSpiceDouble    axdef  [3],
                   SpiceInt            indexa,
                   ConstSpiceDouble    plndef [3],
                   SpiceInt            indexp,
                   SpiceDouble         mout   [3][3] )

Abstract

   Find the transformation to the right-handed frame having a
   given vector as a specified axis and having a second given
   vector lying in a specified coordinate plane.

Required_Reading

   None.

Keywords

   AXES
   FRAME
   ROTATION
   TRANSFORMATION

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   axdef      I   Vector defining a principal axis.
   indexa     I   Principal axis number of `axdef' (x=1, y=2, z=3).
   plndef     I   Vector defining (with `axdef') a principal plane.
   indexp     I   Second axis number (with `indexa') of principal
                  plane.
   mout       O   Output rotation matrix.

Detailed_Input

   axdef       is a vector defining one of the principal axes of a
               coordinate frame.

   indexa      is a number that determines which of the three
               coordinate axes contains `axdef'.

               If `indexa' is 1 then `axdef' defines the X axis of the
               coordinate frame.

               If `indexa' is 2 then `axdef' defines the Y axis of the
               coordinate frame.

               If `indexa' is 3 then `axdef' defines the Z axis of the
               coordinate frame.

   plndef      is a vector defining (with `axdef') a principal plane of
               the coordinate frame. `axdef' and `plndef' must be
               linearly independent.

   indexp      is the second axis of the principal frame determined by
               `axdef' and `plndef'.  `indexa', `indexp' must be different
               and be integers from 1 to 3.

               If `indexp' is 1, the second axis of the principal
               plane is the X-axis.

               If `indexp' is 2, the second axis of the principal
               plane is the Y-axis.

               If `indexp' is 3, the second axis of the principal plane
               is the Z-axis.

Detailed_Output

   mout        is a rotation matrix that transforms coordinates given
               in the input frame to the frame determined by `axdef',
               `plndef', `indexa' and `indexp'.

Parameters

   None.

Exceptions

   1)  If `indexa' or `indexp' is not in the set {1,2,3}, the error
       SPICE(BADINDEX) is signaled by a routine in the call tree of
       this routine.

   2)  If `indexa' and `indexp' are the same, the error
       SPICE(UNDEFINEDFRAME) is signaled by a routine in the call
       tree of this routine.

   3)  If the cross product of the vectors `axdef' and `plndef' is zero,
       the error SPICE(DEPENDENTVECTORS) is signaled by a routine in
       the call tree of this routine.

Files

   None.

Particulars

   Given two linearly independent vectors there is a unique
   right-handed coordinate frame having:

      `axdef' lying along the `indexa' axis.

      `plndef' lying in the indexa-indexp coordinate plane.

   This routine determines the transformation matrix that transforms
   from coordinates used to represent the input vectors to the
   the system determined by `axdef' and `plndef'. Thus a vector
   (x,y,z) in the input coordinate system will have coordinates

                   t
      mout* (x,y,z)

   in the frame determined by `axdef' and `plndef'.

Examples

   The rotation matrix ticc from inertial to Sun-Canopus
   (celestial) coordinates is found by the call

      twovec_c ( Sun_vector, 3, Canopus_vector, 1, ticc );

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

   N.J. Bachman        (JPL)
   J. Diaz del Rio     (ODC Space)
   W.M. Owen           (JPL)
   W.L. Taber          (JPL)

Version

   -CSPICE Version 1.0.1, 13-AUG-2021 (JDR)

       Edited the header to comply with NAIF standard.

   -CSPICE Version 1.0.0, 22-OCT-1998 (NJB)

       Made input matrices const.

   -CSPICE Version 1.0.0, 02-MAR-1998 (WLT) (WMO)

Index_Entries

   define an orthonormal frame from two vectors