Circular Separability of Polygons

TL;DR

This paper introduces efficient algorithms for determining circular separability of polygons and finding the largest inscribed circle within a convex polygon under specific constraints.

Contribution

It presents a linear-time algorithm for checking circular separability of polygons and computing the minimal separating circle, along with methods for constrained largest inscribed circle queries.

Findings

Linear-time algorithm for polygon separability

Algorithm for smallest separating circle

Method for largest constrained inscribed circle

Abstract

Two planar sets are circularly separable if there exists a circle enclosing one of the sets and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A linear-time algorithm is proposed to decide if two polygons are circularly separable. The algorithm outputs the smallest separating circle. The second problem asks for the largest circle included in a preprocessed, convex polygon, under some point and/or line constraints. The resulting circle must contain the query points and it must lie in the halfplanes delimited by the query lines.