  We study a turn-based game in a simply connected polygonal environment $Q$
between a pursuer $P$ and an adversarial evader $E$. Both players can move in a
straight line to any point within unit distance during their turn. The pursuer
$P$ wins by capturing the evader, meaning that their distance satisfies $d(P,
E) \leq 1$, while the evader wins by eluding capture forever. Both players have
a map of the environment, but they have different sensing capabilities. The
evader $E$ always knows the location of $P$. Meanwhile, $P$ only has
line-of-sight visibility: $P$ observes the evader's position only when the line
segment connecting them lies entirely within the polygon. Therefore $P$ must
search for $E$ when the evader is hidden from view.
  We provide a winning strategy for $P$ in two families of polygons: monotone
polygons and scallop polygons. In both families, a straight line $L$ can be
moved continuously over $Q$ so that (1) $L \cap Q$ is a line segment and (2)
every point on the boundary $\partial Q$ is swept exactly once. These are both
subfamilies of strictly sweepable polygons. The sweeping motion for a monotone
polygon is a single translation, and the sweeping motion for a scallop polygon
is a single rotation. Our algorithms use rook's strategy during its pursuit
phase, rather than the well-known lion's strategy. The rook's strategy is
crucial for obtaining a capture time that is linear in the area of $Q$. For
both monotone and scallop polygons, our algorithm has a capture time of $O(n(Q)
+ \mbox{area}(Q))$, where $n(Q)$ is the number of polygon vertices.
