The Fortress Problem in Terms of the Number of Reflex and Convex Vertices. A 3D objects scanning application

This work focuses on the visibility of exterior of a polygon. We show a lower bound for the Fortress Problem applied to polygons P having n vertices in terms of the number of reflex vertices, the number of convex vertices and the number of pockets that are found when the convex hull is made on P. The results are related to the task of the geometric data acquisition for architectural surveys through techniques such as laser scanner.