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Separability of pairs of polygons through single translations‡

Published online by Cambridge University Press:  09 March 2009

Jörg-Rüdiger Sack  and
Godfried T. Toussaint
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Summary

Let P = {p1, …,pn} and Q = {q1,…,qm} be two simple polygons in the plane with non-intersecting interiors, the vertices of which are specified by their cartesian coordinates in order. The translation separability query asks whether there exists a direction in which P can be translated by an arbitrary distance without colliding with Q. It is shown that all directions that admit such a motion can be computed in O(nlogm) time, where n > m, thus improving the previous complexity of O(nm) established for this problem. In designing this algorithm a polygon partitioning technique is introduced that may find application in other geometric problems.

The algorithm presented in this paper solves a simplified version of the grasping problem in robotics. Given a description of a robot hand and a set of objects to be manipulated, the robot must determine which objects can be grasped. The solution given here assumes a two-dimensional world, a hand without an arm, and grasping under translation only.

Type
Article
Information
Robotica , Volume 5 , Issue 1 , January 1987 , pp. 55 - 63
Copyright
Copyright © Cambridge University Press 1987

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