# Translating polygons in the plane

## Abstract

Let P = (p_{1},...,p_{n}) and Q = (q_{1},...,q_{m}) be two simple polygons with non-intersecting interiors in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. It has been shown that this problem can be solved in time proportional to the number of vertices in P and Q. Here we present a new and efficient algorithm for determining all directions in which such movement is possible. In designing this algorithm a partitioning technique is developed which might find applications when solving other geometric problems. The algorithm utilizes several tools and concepts (e.g. convex hulls, point-location, weakly edge-visible polygons) from the area of computational geometry.

## Keywords

Computational Geometry Simple Polygon Convex Region Jordan Curve Theorem Reflex Vertex## Preview

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