Structured visibility profiles with applications to problems in simple polygons (extended abstract)

A number of problems in computational geometry involving simple polygons can be solved in linear time once the polygon has been triangulated. Since the worst-case time bound for triangulating a general simple polygon is currently super-linear, these algorithms are not linear time in the worst case. In this paper we define the structured visibility profile of a polygonal path and show how to compute it in linear time. We apply this result to solve many problems in linear time that previously required triangulation. Our list of problems includes: translation separability of two simple polygons, computing the weak visibility region for a segment within a simple polygon, finding shortest monotone paths in a simple polygon, ray shooting from an edge, and the convex rope problem.