Procedure

   vrotv_c ( Vector rotation about an axis ) 

   void vrotv_c ( ConstSpiceDouble  v     [3],
                  ConstSpiceDouble  axis  [3],
                  SpiceDouble       theta,
                  SpiceDouble       r     [3] )

Abstract

   Rotate a vector about a specified axis vector by a specified
   angle and return the rotated vector.

Required_Reading

   ROTATION

Keywords

   ROTATION
   VECTOR

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   v          I   Vector to be rotated.
   axis       I   Axis of the rotation.
   theta      I   Angle of rotation (radians).
   r          O   Result of rotating `v' about axis by `theta'.

Detailed_Input

   v           is a 3-dimensional vector to be rotated.

   axis        is the axis about which the rotation is to be
               performed.

   theta       is the angle through which `v' is to be rotated about
               axis.

Detailed_Output

   r           is the result of rotating `v' about `axis' by `theta'.
               If `axis' is the zero vector, r = v.

Parameters

   None.

Exceptions

   Error free.

   1)  If the input axis is the zero vector, `r' will be returned
       as `v'.

Files

   None.

Particulars

   This routine computes the result of rotating (in a right handed
   sense) the vector v about the axis represented by axis through
   an angle of theta radians.

   If w is a unit vector parallel to axis, then r is given by:

       r = v + ( 1 - cos(theta) ) (w X(w X v)) + sin(theta) (w X v)

   where "X" above denotes the vector cross product.

Examples

   If axis = ( 0, 0, 1 ) and theta = pi/2 then the following results
   for r will be obtained

           v                           r
      -------------             ----------------
      ( 1, 2, 3 )                ( -2, 1, 3 )
      ( 1, 0, 0 )                (  0, 1, 0 )
      ( 0, 1, 0 )                ( -1, 0, 0 )


   If axis = ( 0, 1, 0 ) and theta = pi/2 then the following results
   for r will be obtained

           v                           r
      -------------             ----------------
      ( 1, 2, 3 )                (  3, 2, -1 )
      ( 1, 0, 0 )                (  0, 0, -1 )
      ( 0, 1, 0 )                (  0, 1,  0 )


   If axis = ( 1, 1, 1 ) and theta = pi/2 then the following results
   for r will be obtained

           v                                     r
      -----------------------------      -----------------------------
      ( 1.0,     2.0,     3.0     )      ( 2.577.., 0.845.., 2.577.. )
      ( 2.577.., 0.845.., 2.577.. )      ( 3.0      2.0,     1.0     )
      ( 3.0      2.0,     1.0     )      ( 1.422.., 3.154.., 1.422.. )
      ( 1.422.., 3.154.., 1.422.. )      ( 1.0      2.0,     3.0     )

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

   N.J. Bachman        (JPL)
   J. Diaz del Rio     (ODC Space)
   H.A. Neilan         (JPL)
   W.L. Taber          (JPL)

Version

   -CSPICE Version 1.0.2, 05-JUL-2021 (JDR)

       Edited the header to comply with NAIF standard.

   -CSPICE Version 1.0.1, 05-FEB-2003 (NJB)

       Header examples were corrected. -Exceptions section filled in.
       Miscellaneous header corrections were made.

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

Index_Entries

   vector rotation about an axis