Let's say I have a point cloud of $n$ points $P = \{p_1, p_2, \ldots, p_n\} \in \mathbb{R}^k$, where $k=2$ or $k=3$. Further, we can assume that the points are on a rigid body, but with some small amount of noise.
I have the locations of the points along with the instantaneous velocity of each of the points. However, I only have this one snapshot of the point cloud - I have no time series data.
Does there exist an efficient algorithm to extract the angular velocity of this point cloud? For the 3D case ideally I would like to extract these in terms of Euler Angles if possible (but would settle for another representation).