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
On the geodesic Voronoi diagram of point sites in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
An optimal algorithm for constructing the Delaunay triangulation of a set of line segments
SCG '87 Proceedings of the third annual symposium on Computational geometry
Voronoi diagrams with barriers and the shortest diagonal problem
Information Processing Letters
An O(n log n) Algorithm for Rectilinear Minimal Spanning Trees
Journal of the ACM (JACM)
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
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The problem of constructing the geodesic Voronoi diagram for a set of sites S with a set of parallel line segments O as obstacles is addressed and an O ((m + n) log (m + n)) time and O (m + n) space algorithm is presented for constructing the diagram, where |S| = n and |O| = m. The algorithm is a plane-sweep algorithm which does not use geometric transformation. It uses two plane sweeps, advancing from two opposite directions, to produce two data structures, called the shortest path maps. The two maps are then tailored to produce the desired geodesic Voronoi diagram. When m = 0, the algorithm produces the original Voronoi diagram for the sites S in O(n log n) time and O (n) space, and when the sites in S are assigned weights, a minor modification of the algorithm can construct the weighted Voronoi diagram for S in O (n log n) time and O (n) space.