Safety, coverage, and support functions

For cardinal hops of length $a$, one per interval $\delta$, or a wait, in two dimensions,

Their support functions are $(a/\delta ){\Vert n\Vert }_{\infty }$ and $(a/\delta ){\Vert n\Vert }_2$. The disk is not contained in the diamond: $(a/(\sqrt{2}\delta ),a/(\sqrt{2}\delta ))$ is a counterexample. Thus the diamond is safe but does not cover all physical directions.

If a constant physical velocity set $K_{\mathrm{phys}}$ contains $K_Q+\overline{B}(0,R_Q/t)$, then (eq:offset) certifies endpoint reachability within time $t$. It does not certify the intermediate implementation paths. For Target B, check the actual route velocities locally.