Computational geometry: an introduction
Computational geometry: an introduction
Computational geometry.
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Given a simple polygon P (a polygon without self-intersections) in the plane represented by a list of vertices in the order that they appear on P, finding the convex hull of P requires Ω(N) time, where N is the number of vertices in P. This problem will be referred to as the CHSP (convex hull of a simple polygon) problem. Several O(N)-time algorithms for the CHSP problem have been proposed [1-5]. The algorithm by Sklansky [1] was shown by Bykat [6] that it does not always work, and the algorithm proposed by Shamos in [2] also fails in some special cases. The algorithm given by McCallum and Avis in [3] uses two stacks and is quite complicated. Graham & Yao [4], and Lee [5] independently developed simpler algorithms using one stack. Their algorithms are almost the same. In this paper, we present an algorithm based on the ones given in [4] and [5]. We show that our algorithm is not only conceptually much simpler than any of previously known algorithms, but also more efficient compared with the algorithms given in [4] and [5].