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キーワード:
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要旨:
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.
