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QTINV

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

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.

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.

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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