Art gallery theorems and algorithms
Art gallery theorems and algorithms
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Constructing stable force-closure grasps
ACM '86 Proceedings of 1986 ACM Fall joint computer conference
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Capturing a Convex Object With Three Discs
IEEE Transactions on Robotics
A geometric approach to robotic laundry folding
International Journal of Robotics Research
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In this paper, we examine non-stretchable two-dimensional 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 of 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.