Bentley–Ottmann algorithm: Difference between revisions

Revision as of 01:05, 30 January 2023

Revision as of 12:26, 3 February 2023

Line 1:

{{short description|Sweep line algorithm}}

In [[computational geometry]], the '''Bentley–Ottmann algorithm''' is a [[sweep line algorithm]] for listing all [[line segment intersection|''crossings'' in a set of line segments]], i.e. it finds the ''intersection points'' (or, simply, ''intersections'') of line segments. It extends the [[Shamos–Hoey algorithm]],{{sfnp|Shamos|Hoey|1976}} a similar previous algorithm for testing whether or not a set of line segments has any crossings. For an input consisting of <math>n</math> line segments with <math>k</math> crossings (or intersections), the Bentley–Ottmann algorithm takes time <math>\mathcal{O}((n + k) \log n)</math>. In cases where <math>k = \mathcal{o}\left(\frac{n^2}{\log n} \right)</math>, this is an improvement on a naïve algorithm that tests every pair of segments, which takes <math>\Theta(n^2)</math>.