Before revision:  Here, we study watchman routes outside a convex polygon, i.e., in R^2\O, where O^2\setminus \Omega, where \Omega } is a convex polygon  .
After revision:  Here, we study watchman routes outside a convex polygon, i.e., in \mathbb{R^2\setminus \Omega, where \Omega } is a convex polygon .