# A fast algorithm for polygon containment by translation

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## Abstract

The polygon containment problem is the problem of deciding whether one polygon, *C*, can be translated to fit within another polygon *N*. We present an algorithm that runs in time *O* (*cn* log *cn*) to solve this problem, in the case that the polygon *C* is convex. Here *c* is the number of bounding edges of *C*, and *n* is the number of bounding edges of *N*. The algorithm actually computes the feasible region, that is, a description of the set of all placements of *C* inside *N*. The algorithm is close to optimal in that the feasible region may have *O* (*cn*) vertices.

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© Springer-Verlag Berlin Heidelberg 1985