Given a polygon $P$ and an angle $\theta$, what is the name of the domain obtained from the union of all the rotations of the polygon from 0 to $\theta$?
That is, if we call $R(\alpha, v_0)P$ the rotation of polygon $P$ around point $v_0$ and angle $\alpha$, What's the name of the domain
$$D = \bigcup_{\alpha \in [0,\theta]} R(\alpha, v_0)P$$
Clearly $D$ is a circular-arc polygon.
It sounds like a reachability problem, but I couldn't find a name for it.
Examples on triangles, $D$ is the union of the gray and the dark-yellow regions:
