Grasping Non-stretchable Cloth Polygons

In this paper, we examine non-stretchable 2D polygonal cloth, and place bounds on the number of fingers needed to immobilize it. For any non-stretchable cloth polygon, it is always necessary to pin all the convex vertices. We show that for some shapes, more fingers are necessary. No more than one third of the concave vertices need to be pinned for simple polygons, and no more than one third of the concave vertices plus two fingers per hole are necessary for polygons with holes.