On Fri, Jul 29, 2011 at 2:52 PM, Charles R Harris <charlesr.har...@gmail.com > wrote:
> > > On Fri, Jul 29, 2011 at 11:07 AM, Martin Ling <martin-nu...@earth.li>wrote: > >> On Fri, Jul 29, 2011 at 09:14:00AM -0600, Charles R Harris wrote: >> > >> > Well, if the shuttle used a different definition then it was out >> there >> > somewhere. The history of quaternions is rather involved and mixed up >> with >> > vectors, so it may be the case that there were different conventions. >> >> My point is that these are conventions of co-ordinate frame, not of >> different representations of quaternions themselves. There's no two >> "handednesses" of quaternions to support. There are an infinte number of >> co-ordinate frames, and a quaternion can be interpreted as a rotation in >> any one of them. It's a matter of interpretation, not calculation. >> >> > It might also be that the difference was between vector and >> > coordinate rotations, but it is hard to tell without knowing how >> > the code actually made use of the results. >> >> Indeed, this is the other place the duality shows up. If q is the >> rotation of frame A relative to frame B, then a vector v in A appears >> in B as: >> >> v' = q * v * q.conjugate >> >> while a vector u in B appears in A as: >> >> u' = q.conjugate * u * q >> >> The former is often thought of as 'rotating the vector' versus the >> second as 'rotating the co-ordinate frame', but both are actually the >> same operation performed using a different choice of frames. >> >> > They are different, a vector is an element of a vector space independent of > coordinate frames, coordinate frames are a collection of functions from the > vector space to scalars. Operationally, rotating vectors is a map from the > vector space onto itself, however the coordinates happen to be the same > when the inverse rotation is applied to the coordinate frame, it's pretty > much the definition of coordinate rotation. But the concepts aren't the > same. The similarity between the operations is how covariant vectors got to > be called contravariant tensors, the early workers in the field dealt with > the coordinates. > > But that is all to the side ;) I'm wondering about the history of the > 'versor' object and in which fields it was used. > > Chuck > > I am starting to get very interested in this quaternion concept (and maybe how I could use it for mplot3d), but I have never come across it before (beyond the typical vector math that I am familiar with). Can anybody recommend a good introductory resource to get me up to speed? Thanks, Ben Root
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