A Simple Algorithm for Computing BOCP

TL;DR

This paper presents a straightforward, efficient algorithm for computing the Boolean operation on circular-arc polygons, combining simplicity with competitive performance, especially when the number of intersections and edges is small.

Contribution

The authors introduce a concise, easy-to-implement algorithm for BOCP that maintains efficiency and is validated through empirical testing.

Findings

Runs in O(m+n+(l+k)log l) time

Uses O(m+n+k) space

Effective when intersections and edges are few

Abstract

In this article, we devise a concise algorithm for computing BOCP. Our method is simple, easy-to-implement but without loss of efficiency. Given two circular-arc polygons with $m$ and $n$ edges respectively, our method runs in $O(m+n+(l+k)\log l)$ time, using $O(m+n+k)$ space, where $k$ is the number of intersections, and $l$ is the number of {edge}s. Our algorithm has the power to approximate to linear complexity when $k$ and $l$ are small. The superiority of the proposed algorithm is also validated through empirical study.