Some chain visibility problems in a simple polygon

In this paper, the notions of convex chain visibility and reflex chain visibility of a simple polygon P are introduced, and some optimal algorithms concerned with convex- and reflex-chain visibility problems are described. For a convex-chain visibility problem, two linear-time algorithms are exhibited for determining whether or not P is visible from a given convex chain; one is the turn-checking approach and the other is the decomposition approach based on checking edge visibilities. We also present a linear-time algorithm for finding, if any, all maximal convex chains of a given polygon P from which P is visible, where a maximal convex chain is a convex chain which does not properly include any other convex chains. It can be made by showing that there can be at most four visible maximal convex chains in P with an empty kernel. By similar arguments, we show that the same problems for reflex chain visibility can be easily solved in linear time.