Cutting a Cornered Convex Polygon Out of a Circle

Abstract

The problem of cutting a convex polygon P out of a piece of planar material Q with minimum total cutting length is a well studied problem in computational geometry. Researchers studied several variations of the problem, such as P and Q are convex or non-convex polygons and the cuts are line cuts or ray cuts. In this paper we consider yet another variation of the problem where Q is a circle and P is a convex polygon such that P is bounded by a half circle of Q and all the cuts are line cuts. We give two algorithms for solving this problem. Our first algorithm is an O (log n ) -approximation algorithm with O ( n ) running time, where n is the number of edges of P . The second algorithm is a constant factor approximation algorithm with approximation ratio 6 . 48 and running time O ( n 3 ) .