This thesis considers the problems of chain visibility of a simple polygon P with n vertices: find the minimum visible chain of P and determine whether or not P is visible from a query chain.
A chain on the boundary of P is said to be visible if all points of P can be seen from it. And the minimum visible chain is defined to be the visible chain with the minimum number of edges.
After O(nlogn) preprocessing, problems are solved in additional linear and logarithmic time, respectively.