Procedure

   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) 
   H.A. Neilan     (JPL) 
   W.L. Taber      (JPL) 
 

Version

 
   -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)

Index_Entries

 
   vector rotation about an axis 
 

Link to routine vrotv_c source file vrotv_c.c