What is the 3D rotation equivalent of integrating (or a simpler version of the problem, simply evaluating or enumerating) all the values?
For example in one dimension we have the possibility of an improper integral that covers an infinite range of values, the result can be finite. $\int_{0}^{\infty} \frac{dx}{(x+1)\sqrt{x}} = \pi$
What if instead the domain is a rotation value? Expressed as Euler angles or rotation matrices or quaternions.
Is this possible? How could I approach it? Suppose I want to compute $\int_{rotations}w(q)\ dq$ where I have reason to suspect that the answer is not infinite...
This is weird, also because it is very nontrivial to even try to define a subset of the SO(3) space, whereas that is quite natural to do with a normal integral.
Maybe something can be done with spherical harmonics...