EFFICIENT ALGORITHMS FOR SOLVING DIAGONAL VISIBILITY PROBLEMS IN A SIMPLE POLYGON

Abstract

A diagonal guard is a guard capable of moving along an edge or an internal diagonal in a polygon. A polygon which can be guarded by a diagonal guard is called diagonal-visible. We consider the following three problems concerning the diagonal visibility in a polygon P. First, determine whether or not a guard diagonal exists in P, i.e., P is diagonal-visible. Second, compute all guard diagonals of P. Third, given a query diagonal, determine whether or not it is a guard diagonal. For these problems, we construct a data structure for keeping all guard diagonals in O (n log n) time and O(n) space. Using this data structure, we show that these problems can be solved in O(n log n), O(n log n + k), and O(1) time, respectively, where k is the number of guard diagonals.