Reachable grasps on a polygon: The convex rope algorithm

We describe an algorithm which finds the externally visible vertices of a polygon, and which generates a new geometric construction we call the convex ropes of each visible vertex. The convex ropes give the range of angles from which each vertex is visible, and give all the pairs of vertices which are reachable by a straight robot finger. All of the convex ropes can be found in expected time order n, where n is the number of vertices of the polygon. We discuss the application of this geometric construction to automated grasp planning. The algorithm may also be useful in image interpretation and graphics where efficient computation of visible points is important. The direct application of the algorithm is restricted to two dimensions since sequential ordering of vertices is required. Extention to three dimensions would rely on well chosen intersecting or projective planes.