A tight bound for point guards in piecewise convex art galleries

作者：Cano Javier^*; Toth Csaba D; Urrutia Jorge

来源：Computational Geometry-Theory and Applications, 2013, 46(8): 945-958.

DOI：10.1016/j.comgeo.2013.04.004

• Art gallery
• Visibility
• Splinegon

We consider the problem of guarding curvilinear art galleries. A Jordan arc a joining two points, p and q, in the plane is called a convex arc if the closed curve obtained by joining a with the line segment pq encloses a convex set. A piecewise convex art gallery A with n vertices is a simply connected region in the plane whose boundary consists of n convex arcs where A lies on the convex side of each arc. We show that inverted right perpendicularn/2inverted left perpendicular point guards are always sufficient and sometimes necessary to guard a piecewise convex art gallery with n vertices. We also give a shorter proof for the sufficiency of left perpendicular2n/3right perpendicular vertex guards, for n %26gt;= 2, which was first derived by Karavelas et al.

• 出版日期2013-10