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