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