---
title: Circular Separability of Polygons
url: https://www.emergentmind.com/papers/9909007
type: paper
arxiv_id: '9909007'
arxiv_url: https://arxiv.org/abs/9909007
published: '1999-09-03'
categories:
- cs.CG
---

# Circular Separability of Polygons

## 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.