Index of Functions: A B C D E F G H I J K L M N O P Q R S T U V W X
Index Page vrotv_c

Table of contents

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

       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

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

    Fri Dec 31 18:41:15 2021