WADS 1991: Algorithms and Data Structures pp 214-227

# Immobilizing a polytope

• Jurek Czyzowicz
• Ivan Stojmenovic
• Jorge Urrutia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)

## Abstract

We say that a polygon P is immobilized by a set of points I on its boundary if any rigid motion of P in the plane causes at least one point of I to penetrate the interior of P. Three immobilization points are always sufficient for a polygon with vertices in general positions, but four points are necessary for some polygons with parallel edges. An O(n log n) algorithm that finds a set of 3 points that immobilize a given polygon with vertices in general positions is suggested. The algorithm becomes linear for convex polygons. Some results are generalized for d-dimensional polytopes, where 2d points are always sufficient and sometimes necessary to immobilize. When the polytope has vertices in general position d+1 points are sufficient to immobilize.

## Keywords

Interior Point General Position Voronoi Diagram Convex Polygon Rigid Motion
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Jurek Czyzowicz
• 1
• Ivan Stojmenovic
• 2
• Jorge Urrutia
• 2
1. 1.Departement d'InformatiqueUniversité du Québec à HullHullCanada
2. 2.Computer Science DepartmentUniversity of OttawaOttawaCanada