Polygon Detection from a Set of Lines

TL;DR

This paper introduces an efficient polynomial-time algorithm for detecting polygons in a set of line segments, balancing computational complexity and implementation simplicity.

Contribution

It presents a novel combination of algorithms that efficiently detects polygons from arbitrary line segments in a plane.

Findings

Algorithm runs in polynomial time with complexity O((N + M)^4)

Detects polygons accurately from arbitrary line segments

Balances efficiency and ease of implementation

Abstract

Detecting polygons defined by a set of line segments in a plane is an important step in analyzing vector drawings. This paper presents an approach combining several algorithms to detect basic polygons from arbitrary line segments. The resulting algorithm runs in polynomial time and space, with complexities of $O\bigl((N + M)^4\bigr)$ and $O\bigl((N + M)^2\bigr)$, where $N$ is the number of line segments and $M$ is the number of intersections between line segments. Our choice of algorithms was made to strike a good compromise between efficiency and ease of implementation. The result is a simple and efficient solution to detect polygons from lines.