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We describe an algorithm for computing the separating common tangents of twosimple polygons using linear time and only constant workspace. A tangent of apolygon is a line touching the polygon such that all of the polygon lies to thesame side of the line. A separating common tangent of two polygons is a tangentof both polygons where the polygons are lying on different sides of thetangent. Each polygon is given as a read-only array of its corners. If aseparating common tangent does not exist, the algorithm reports that.Otherwise, two corners defining a separating common tangent are returned. Thealgorithm is simple and implies an optimal algorithm for deciding if the convexhulls of two polygons are disjoint or not. This was not known to be possible inlinear time and constant workspace prior to this paper.  An outer common tangent is a tangent of both polygons where the polygons areon the same side of the tangent. In the case where the convex hulls of thepolygons are disjoint, we give an algorithm for computing the outer commontangents in linear time using constant workspace.

An Optimal Algorithm for the Separating Common Tangents of two Polygons