Computing All Immobilizing Grasps of a Simple Polygon with Few Contacts

: We study the output-sensitive computations of all the combinations of the edges and vertices of a simple polygon P that allow a form closure grasp with less than four point contacts. More specifically, we present an O(m 4 3 log 1 3 m + K)time algorithm to compute all K pairs of concave vertices, an O(n2 log2 n + K)-time and O(m2 log2 m + nm 2 3 log 4 3 m + K)-time algorithm to compute all K triples of one concave vertex and two edges, and two concave vertices and an edge respectively, where n is the number of edges, and m is the number of concave vertices of P. We also present an O(n2 log4 n + K)-time algorithm that enumerates all the edge triples with a second-order immobility grasp using Czyzowicz's conditions in [4].

• Type: Journal
• Year: 2006
• Where: ALGORITHMICA
• Authors: Jae-Sook Cheong, Herman J. Haverkort, A. Frank van der Stappen
• Keywords: ALGORITHMICA 2006, Form Closure, Output-sensitive Computations, Simple Polygon