Approximate Shortest Routes for Frontier Visibility under Limited Visibility

Consider a simple polygon P and a point s on the frontier ∂P of P . For any real δ > 0 there exists a shortest path ρ inside of P such that s is on the path ρ, and for each point p in ∂P , there exists a point q in ρ at Euclidean distance less than or equal δ to p such that the line segment pq is in P . Such an optimum path ρ is called a shortest route for ∂P visibility under δ-visibility that starts at point s on ∂P . We provide an approximation algorithm (which belongs to the class of rubberband algorithms) for finding such a path ρ in O(n) run time, where n is the number of vertices of a given simple polygon P . The run time does not depend on δ or on the start point s.