# MPI-I-94-160

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

### Mehlhorn, Kurt and Näher, Stefan

**MPI-I-94-160**. October** **1994, 41 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

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.

Acknowledgement:** **

References to related material:

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1994-160

**BibTeX**
`@TECHREPORT{``MehlhornNaeher94``,`

` AUTHOR = {Mehlhorn, Kurt and N{\"a}her, Stefan},`

` TITLE = {Implementation of a sweep line algorithm for the Straight \& Line Segment Intersection Problem},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-94-160},`

` MONTH = {October},`

` YEAR = {1994},`

` ISSN = {0946-011X},`

`}`