[Numpy-discussion] Quaternion dtype for NumPy - initial implementation available

[Charles R Harris]

On Thu, Jul 28, 2011 at 8:48 PM, Robert Love <rblove_lists at comcast.net>wrote:

>
> On Jul 28, 2011, at 7:42 AM, Martin Ling wrote:
>
> > On Wed, Jul 27, 2011 at 10:29:08PM -0500, Robert Love wrote:
> >>
> >> To use quaternions I find I often need conversion to/from matrices and
> >> to/from Euler angles.  Will you add that functionality?
> >
> > Yes, I intend to. Note that these conversions are already available in
> > the standalone (non-dtype) implementation in imusim.maths.quaternions:
> >
> >
> http://www.imusim.org/docs/api/imusim.maths.quaternions.Quaternion-class.html#setFromEuler
> >
> http://www.imusim.org/docs/api/imusim.maths.quaternions.Quaternion-class.html#toEuler
> >
> http://www.imusim.org/docs/api/imusim.maths.quaternions.Quaternion-class.html#setFromMatrix
> >
> http://www.imusim.org/docs/api/imusim.maths.quaternions.Quaternion-class.html#toMatrix
> >
> > I should do a new release though - the Euler methods there only support
> > ZYX and ZXY order conversions, my development version supports any order.
> >
> >> Will you handle the left versor and right versor versions?
> >
> > I don't know what this means. Please enlighten me and I'll be happy to
> > try! I thought a 'right versor' was a unit quaternion representing an
> > angle of 90 degrees (as in 'right angle') - I don't see what a 'left'
> > one would be.
> >
>
> Quaternions have a "handedness" or a sign convention.  The recently
> departed Space Shuttle used a Left versor convention while most things,
> including Space Station, use the right versor convention, in their flight
> software.  Made for frequent confusion.
>
> Let me see if I can illustrate by showing the functions I use for
> converting a matrix to a quaternion.
>
>
> def Quaternion_Of(m):
>    """
>    Returns a quaternion in the right versor sense.
>    """
>
>    q = N.zeros(4,float)
>
>    q[0] = 0.5*sqrt(1.0 + m[0,0] + m[1,1] + m[2,2])
>
>    q04_inv = 1.0/(4.0*q[0])
>    q[1] = (m[1,2] - m[2,1])*q04_inv
>    q[2] = (m[2,0] - m[0,2])*q04_inv
>    q[3] = (m[0,1] - m[1,0])*q04_inv
>
>    return q
>
>
>
> def Quaternion_Of(m):
>    """
>    Returns a quaternion in the left versor sense.
>    """
>
>    q = N.zeros(4,float)
>
>    q[0] = 0.5*sqrt(1.0 + m[0,0] + m[1,1] + m[2,2])
>
>    q04_inv = 1.0/(4.0*q[0])
>    q[1] = (m[2,1] - m[1,2])*q04_inv
>    q[2] = (m[0,2] - m[2,0])*q04_inv
>    q[3] = (m[1,0] - m[0,1])*q04_inv
>
>    return q
>
>
> Or transforming a vector using the different conventions.
>
>
> def Transform(q,v):
>    """
>    Returns the vector part of q*vq which transforms v from one
>    coordinate system to another.  Right Versor
>    """
>    u = Q.Vector_Part(q)
>    return 2.0*(q[0]*N.cross(v,u) +
>                N.dot(v,u)*u +
>                (q[0]*q[0] - 0.5)*v)
>
>
> def Transform(q,v):
>    """
>    Returns the vector part of q*vq which transforms v from one
>    coordinate system to another.  Left Versor
>    """
>    u = Q.Vector_Part(q)
>    return 2.0*(q[0]*N.cross(u,v) +
>                N.dot(u,v)*u +
>                (q[0]*q[0] - 0.5)*v)
>
>
>
>
>
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