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

TL;DR

This paper presents a simple, efficient algorithm to compute all common tangents of two disjoint polygons in linear time and constant workspace, aiding in understanding their spatial relationship.

Contribution

It introduces the first algorithm that simultaneously achieves linear time complexity and constant workspace for finding common tangents of two polygons.

Findings

Computes all common tangents in linear time

Uses constant workspace for the algorithm

Decides the polygons' spatial relationship

Abstract

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