A tight bound for point guards in piecewise convex art galleries

We consider the problem of guarding curvilinear art galleries. A closed arc a joining two points, p and q, in the plane is called a convex arc if the curve obtained by joining a with the line segment pq encloses a convex set. A piece-wise convex polygon P with vertices v0, . . . , vn−1 is the region bounded by a set {a0, . . . , an−1} of n convex arcs with pairwise disjoint interiors such that ai joins vi to vi+1, addition taken mod n, each of them convex with respect to the interior of P . A piece-wise convex art gallery is the connected region bounded by a piece-wise convex polygon. We show that dn2 e point guards are always sufficient in order to guard a piece-wise convex art gallery. This bound is best possible.