NDLI: An optimal algorithm for constructing the Delaunay triangulation of a set of line segments

Content Provider	ACM Digital Library
Author	Wang, C. Schubert, L.
Abstract	In this paper, we first define a new Voronoi diagram for the endpoints of a set of line segments in the plane which do not intersect (except possibly at their endpoints), which is called a bounded Voronoi diagram. In this Voronoi diagram, the line segments themselves are regarded as obstacles. We present an optimal &THgr;(n log n) algorithm to construct it, where n is the number of input line segments.We then show that the straight-line dual of the bounded Voronoi diagram of a set of non-intersecting line segments is the Delaunay triangulation of that set. And the straight-line dual can be obtained in time proportional to the number of input line segments when the corresponding bounded Voronoi diagram is available. Consequently, we obtain an optimal &THgr;(n log n) algorithm to construct the Delaunay triangulation of a set of n non-intersecting line segments in the plane. Our algorithm improves the time bound &Ogr;(n2) of the previous best algorithm.
Starting Page	223
Ending Page	232
Page Count	10
File Format	PDF
ISBN	0897912314
DOI	10.1145/41958.41982
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1987-10-01
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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An optimal algorithm for constructing the Delaunay triangulation of a set of line segments