United Nations Educational, Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS A LINEAR TIME ALGORITHM FOR FINDING THE CONVEX ROPES BETWEEN TWO VERTICES OF A SIMPLE POLYGON WITHOUT TRIANGULATION
نویسندگان
چکیده
The convex rope problem, posed by Peshkin and Sanderson in IEEE J. Robotics Automat, 2 (1986) pp. 53-58, is to find the counterclockwise and clockwise convex ropes starting at the vertex a and ending at the vertex b of a simple polygon, where a is on the boundary of the convex hull of the polygon and b is visible from infinity. In this paper, we present a linear time algorithm for solving this problem without resorting to a linear-time triangulation algorithm and without resorting to a convex hull algorithm for the polygon. The counterclockwise (clockwise, respectively) convex rope consists of two polylines obtained in a basic incremental strategy described in convex hull algorithms for the polylines forming the polygon from a to b. MIRAMARE – TRIESTE June 2008 1 [email protected]
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