Two-Finger Caging of Nonconvex Polytopes

In general, any object can be restricted or caged within a bounded region if we evenly place a sufficient number of fingers around the object. This naive approach often leads to inefficient utilization of fingers because only two fingers are sufficient to cage most nonconvex objects. In this paper, we propose an algorithm that identifies all the caging sets, i.e., set of two-finger placements that cage a given polytope representing the object. Whether a finger placement could cage the object can be queried efficiently from a structure generated by the algorithm. We implemented and tested the algorithm in the case of 2-D and 3-D objects.