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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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Hide details for BibTeXBibTeX
@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},
}