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IJRR
2008

Caging Polygons with Two and Three Fingers

13 years 12 months ago
Caging Polygons with Two and Three Fingers
: We present algorithms for computing all placements of two and three fingers that cage a given polygonal object with n edges in the plane. A polygon is caged when it is impossible to take the polygon to infinity without penetrating one of the fingers. Using a classification into squeezing and stretching cagings, we provide an algorithm that reports all caging placements of two disc fingers in O(n2 log n) time. Our result extends and improves a recent solution for point fingers. In addition, we construct a data structure requiring O(n2 ) storage that can answer in O(log n) whether two fingers in a query placement cage the polygon. We also study caging with three point fingers. Given the placements of two so-called base fingers, we report all placements of the third finger so that the three fingers jointly cage the polygon. Using the fact that the boundary of the set of placements for the third finger consists of equilibrium grasps, we present an algorithm that reports all placements of...
Mostafa Vahedi, A. Frank van der Stappen
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2008
Where IJRR
Authors Mostafa Vahedi, A. Frank van der Stappen
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