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QTANG

QTANG

Name


  QTANG

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


  Find rotation angle(s) of unit quaternion

Major Topics


  Geometry

Calling Sequence


  PHI = QTANG(Q)

Description



  The function QTANG accepts a unit quaternion Q and returns the
  rotation angle PHI of the quaternion.
  Use QTAXIS and QTANG to extract the properties of an existing
  quaternion. Use QTCOMPOSE to combine a rotation axis and angle
  into a new 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



  For a single quaternion, returns the scalar quaternion rotation
  angle in radians. For N quaternions, returns an N-vector of
  rotation angles.

Keyword Parameters



  NONE

Example



  IDL> print, qtang(qtcompose([0d,1,0], !dpi/4))
        0.78539816
  Prints the angle part of the quaternion composed of a rotation of
  !dpi/4 radians around the axis [0,1,0]

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: qtang.pro,v 1.6 2008/12/14 20:00:31 craigm Exp $



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