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QTINV

QTINV

Name


  QTINV

Author


  Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
  craigm@lheamail.gsfc.nasa.gov
  UPDATED VERSIONs can be found on my WEB PAGE:
      http://cow.physics.wisc.edu/~craigm/idl/idl.html

Purpose


  Compute inverse of QUATERNION

Major Topics


  Geometry

Calling Sequence


  QINV = QTINV(Q)

Description



  The function QTINV computes the inverse of the quaternion Q. The
  inverse of a quaternion is equivalent to a rotation about the same
  axis but the opposite direction.
  The inverse is also defined mathematically such that
    QTMULT( Q, QTINV(Q) )
  becomes [0, 0, 0, 1], which is the identity quaternion.
  Conventions for storing quaternions vary in the literature and from
  library to library. This library uses the convention that the
  first three components of each quaternion are the 3-vector axis of
  rotation, and the 4th component is the rotation angle. Expressed
  in formulae, a single quaternion is given by:
    Q(0:2) = [VX, VY, VZ]*SIN(PHI/2)
    Q(3) = COS(PHI/2)
  where PHI is the rotation angle, and VAXIS = [VX, VY, VZ] is the
  rotation eigen axis expressed as a unit vector. This library
  accepts quaternions of both signs, but by preference returns
  quaternions with a positive 4th component.

Inputs



  Q - array of one or more unit quaternions. For a single
      quaternion, Q should be a 4-vector. For N quaternions, Q
      should be a 4xN array.

Returns



  The resulting inverse unit quaternions. For a single input
  quaternion, returns a 4-vector. For N input quaternions, returns
  N quaternions as a 4xN array.

Keyword Parameters



  NONE

Example



  IDL> print, qtcompose([0d,1,0], !dpi/4)
          0.0000000 0.38268343 0.0000000 0.92387953
  IDL> print, qtinv(qtcompose([0d,1,0], !dpi/4))
          0.0000000 0.38268343 0.0000000 -0.92387953
  Prints the quaternion composed of a rotation of !dpi/4 radians
  around the axis [0,1,0], then the inverse of the same quaternion.

See Also


  QTANG, QTAXIS, QTCOMPOSE, QTERP, QTEXP, QTFIND, QTINV, QTLOG,
  QTMAT, QTMULT, QTPOW, QTVROT

Modification History


  Written, July 2001, CM
  Documented, Dec 2001, CM
  Usage message, error checking, 15 Mar 2002, CM
  $Id: qtinv.pro,v 1.6 2002/05/09 23:03:27 craigm Exp $



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