Quantitative Steinitz's theorems with applications to multifingered grasping
David G. Kirkpatrick, Bud Mishra, Chee Keng Yap · 1990
We prove the following quantitative form of a classical theorem of Steinitz: Let m be sufficiently large.If the convex huh of a subset S of Euclidean d-space contains a unit bMl then there is a subset of S with at most m points whose convex huh contains a ball with the same center and having residual radius 1 -3dThe case m = 2d was first considered by B~r£ny, Katchalski and Pach (1982).We also show an upper bound on the achievable residual radius of This quantitative Steinitz's theorem has applications in computing the efficiency of closure grasps by an m-fingered robot hand.The theorem also raises some new problems in eom-putationM geometry; we present some efficient algorithms for these problems, especially in the plane.