Random rotation

[versatran01]

Is there a function that generates a random member of SO3?
Like something described in
Effective sampling and distance metrics for 3d rigid body path planning, J. Kuffner, ICRA 2004.

[strasdat]

There is a simple, well-known method to sample uniformly from a sphere:
Draw x_i from a normal distribution N(0,1), construct a=(x_0, x_1, x_2) and normalize this to vector axis := a/a.norm(). Obviously, if a=0 we need to discard the samples and try again.
[1, Muller, M. E. "A Note on a Method for Generating Points Uniformly on N-Dimensional Spheres." Comm. Assoc. Comput. Mach. 2, 19-20, Apr. 1959.]

Now, axis is our axis of rotation. In addition, we sample theta from (-p, pi] uniformly.
Then SO3::exp(theta * axis) should be a uniform sample on the manifold SO(3), if I'm not mistaken.

[versatran01]

Thanks for the answer. I was just wondering if you can add this to the interface?

[strasdat]

Will do.

[strasdat]

I implemented this for SO(2) and SO(3). See #114.