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QTMULTN

QTMULTN

Name


  QTMULTN

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


  Multiply several quaternions

Major Topics


  Geometry

Calling Sequence


  QRESULT = QTMULTN(Q1, Q2, ..., [/INV1, /INV2, ...] )

Description



  The function QTMULTN performs multiplication of quaternions.
  It is a convenience routine to simplify the multiplication
  of a chain of several quaternions.
 
  For example,
    QTMULTN(Q1,Q2,Q3,/INV3,Q4)
  is the same as,
    QTMULT(Q1,QTMULT(Q2,QTMULT(QTINV(Q3),Q4)))
  Up to eight quaternions may be multiplied with this routine.
  As for QTMULT(), Qn may be 'vectors' of quaternions, if the Qn are
  4xN arrays. In that case the input arrays must be of the same
  dimension.
  Note that quaternion multiplication is not commutative.
  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



  Qn - array of one or more unit quaternions, the nth operand in the
      multiplication. For a single quaternion, Qn should be a
      4-vector. For N quaternions, Qn should be a 4xN array.
      If INVn is set, then the inverse of Qn is used.
  INVn - if set, use QTINV(Qn) in place of Qn.

Returns



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

Keyword Parameters



  NONE

Example



  Q1 = qtcompose([0,0,1], 32d*!dpi/180d)
  Q2 = qtcompose([1,0,0], 116d*!dpi/180d)
  IDL> print, qtmult(q1, q2)
        0.81519615 0.23375373 0.14606554 0.50939109
  Form a rotation quaternion of 32 degrees around the Z axis, and
  116 degrees around the X axis, then multiply the two quaternions.
 

See Also


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

Modification History


  Written, 30 Aug 2007, CM
  $Id: qtmultn.pro,v 1.2 2008/12/14 20:00:31 craigm Exp $



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