A method for computing a sequence of circumscribing polygons and its analysis

In this paper, we propose two methods for computing a sequence of circumscribing polygons for a simple polygon. These methods are based on the greedy method, and are called the naive method and pocket method. The computational complexity of the two methods is O(n²) time and O(n) space for a simple polygon with n vertexes. We applied two methods to sets of simple polygons. We measured the number of intersection checks of two line segments and the execution time of each methods.