Re: [eigen] Rotations and unit vectors

[Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>]

On 07.05.2013 17:51, Andreas Keil wrote:
> I therefore vote for using a threshold like sqrt(eps) or even smaller in
> a debug assert. I would argue that this is the least Eigen should do to
> ensure that its AngleAxis and Quaternion classes represent what they are
> named after.

W.r.t the threshold I vote for not being too strict, to avoid breaking 
code, where low precision is sufficient.

W.r.t. Quaternion there is the problem that it is only somehow intended 
to be a unit quaternion but never explicitly named so.
There are also users who like to use non-unit Quaternions:
http://eigen.tuxfamily.org/bz/show_bug.cgi?id=560

If it actually was a unit quaternion, then normalize(), normalized(), 
norm() and squaredNorm() could be essentially 
NOPs/accessors/const-expressions, and inverse() would be just an alias 
for conjugate().

However, functions such as toRotationMatrix() or q * v give undefined 
(or unintended) behavior for non-unit quaternions).

I'd like to vote again for adding a new class UnitQuaternion which does 
run-time checks for unity (and exploits all reasonable optimizations) 
and either deprecate the current Quaternion class to introduce a new 
class GeneralQuaternion, which works as suggested in bug 560, or let the 
current Quaternion class behave like a general quaternion.
That also means that q*v shall return (q*[0;v]*q.conjugate()).vec() or 
should not be implemented at all.

Unfortunately, I think that deprecating/deleting/redefining Quaternion 
is a rather heavy step and at least deleting/redefining must wait until 
Eigen 4.0, to ensure API compatibility.



Christoph


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Dipl.-Inf., Dipl.-Math. Christoph Hertzberg
Cartesium 0.049
Universität Bremen
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