Computational geometry: an introduction
Computational geometry: an introduction
A sweepline algorithm for Voronoi diagrams
SCG '86 Proceedings of the second annual symposium on Computational geometry
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
ACM SIGACT News
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Manhattonian proximity in a simple polygon
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On the Complexity of Two Circle Strongly Connecting Problems
IEEE Transactions on Computers
A linear-time randomized algorithm for the bounded Voronoi diagram of a simple polygon
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Fast greedy triangulation algorithms
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Geodesic Voronoi diagrams in the presence of rectilinear barriers
Nordic Journal of Computing
A Parallel Algorithm for Finding the Constrained Voronoi Diagram of Line Segments in the Plane
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
A time efficient Delaunay refinement algorithm
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Geometry: Theory and Applications
An Improved Method for Real-Time 3D Construction of DTM
Proceedings of the FIRA RoboWorld Congress 2009 on Advances in Robotics
Surveillance with wireless sensor networks in obstruction: Breach paths as watershed contours
Computer Networks: The International Journal of Computer and Telecommunications Networking
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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.