RE: [Algorithms] Quaternions in IK

[Robert D. <RD...@ac...>]

> I did choose the wrong word with "unique".   Rather, I meant
> "analytic", or free of singularities, which would also imply
> one-to-one.  That is, I seek maximal neighborhoods of the identity
> that can be covered analtyically with an Euler-angle coordinate patch.
> 
> Surely, any sufficiently small neighborhood of the identity can be so
> covered (not uniquely, but in multiple ways).  How do I characterize a
> largest such neighborhood.  

If I understand you correctly, the answer I would expect is the
neighbourhood in which all 3 angles are within the range (-PI/2, PI/2) since
you only get singularities once one axis has been pushed onto another. The
problem with this of course is that it only gives you half the coverage.

Robert