# Item

ITEM ACTIONSEXPORT

Released

Report

#### Implementation of a sweep line algorithm for the Straight \& Line Segment Intersection Problem

##### External Resource

No external resources are shared

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

MPI-I-94-160.pdf

(Any fulltext), 19MB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Mehlhorn, K., & Näher, S.(1994). *Implementation of a sweep
line algorithm for the Straight \& Line Segment Intersection Problem* (MPI-I-94-160). Saarbrücken: Max-Planck-Institut
für Informatik.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-B7A7-5

##### Abstract

We describe a robust and efficient implementation of the Bentley-Ottmann
sweep line algorithm based on the LEDA library
of efficient data types and algorithms. The program
computes the planar graph $G$ induced by a set $S$ of straight line segments
in the plane. The nodes of $G$ are all endpoints and all proper
intersection
points of segments in $S$. The edges of $G$ are the maximal
relatively open
subsegments of segments in $S$ that contain no node of $G$. All edges
are
directed from left to right or upwards.
The algorithm runs in time $O((n+s) log n)$ where $n$ is the number of
segments and $s$ is the number of vertices of the graph $G$. The implementation
uses exact arithmetic for the reliable realization of the geometric
primitives and it uses floating point filters to reduce the overhead of
exact arithmetic.