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We provide a remarkably simple algorithm to compute all (at most four) commontangents of two disjoint simple polygons. Given each polygon as a read-onlyarray of its corners in cyclic order, the algorithm runs in linear time andconstant workspace and is the first to achieve the two complexity boundssimultaneously. The set of common tangents provides basic information about theconvex hulls of the polygons---whether they are nested, overlapping, ordisjoint---and our algorithm thus also decides this relationship.

Common tangents of two disjoint polygons in linear time and constant workspace