Re: [Algorithms] Quaternions in IK

[<ro...@do...>]

Robert Dibley  wrote:

>> In the rotation group SO(3), how can one characterize a maximal
>> neighborhood of the identity that has a unique analytic Euler
>> angle parametrization?
>
>My days of really understanding mathematical phraseology are long past I'm
>afraid, but surely there is no case which has a unique Euler representation,
>given that even the identity matrix has two representations in any given
>axis sequence.
>

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.