Cutting a Cornered Convex Polygon Out of a Circle
Syed Ishtiaque Ahmed, Md. Ashraful Islam, Masud Hasan · Journal of Computers · 2009
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(n3). Index Terms — algorithms, approximation algorithms, com-putational geometry, line cut, ray cut, polygon cutting, rotating calipers I.