On Thu, Jul 28, 2011 at 8:48 PM, Robert Love <rblove_li...@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) > > > > > > _______________________________________________ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion >
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