K-star-shaped Polygons
نویسندگان
چکیده
We introduce k-star-shaped polygons, polygons for which there exists at least one point x such that for any point y of the polygon, segment xy crosses the polygon’s boundary at most k times. The set of all such points x is called the k-kernel of the polygon. We show that the maximum complexity (number of vertices) of the k-kernel of an n-vertex polygon is Θ(n) if k = 2 and Θ(n) if k ≥ 4. We give an algorithm for constructing the k-kernel that is optimal for high complexity kkernels. Finally, we show how k-convex polygons can be recognized in O(n ·min(1+k, log n)) time and O(n) space.
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