The power of geometric duality
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...These results do not improve the algorithm of [ 6 ] for haifplane queries; that algorithm requires O(n) storage, O(n log n) preprocessing, and O(A+log n) query time....
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Cites methods from "The power of geometric duality"
...It should be noted that better bounds are possible for reporting in two dimensions (specifically O(log n + t) time, where t is the number of points reported [3]), but these techniques only work for half-planes....
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"The power of geometric duality" refers methods in this paper
...Possible choices are Kirkpatrick's method [ 13 ] based on a hierarchy of coarser and coarser subdivisions, or Lipton and Tarjan's remarkable, yet impractical algorithm [14]....
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788 citations
"The power of geometric duality" refers methods in this paper
...To handle singularities such as the collinearity of several points in the primal plane and still retain the capability of efficient face traversal, we convert the traditional adjacency-list representation into the doubly-connected-edge-list representation or the quad-edge structure [ 11 ]....
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"The power of geometric duality" refers methods in this paper
...Let u be the total number of layers; from now on, any use of duality will refer to the transform T, with the origin placed anywhere in the interior of Su. Overmars and van Leeuwen have shown how to compute the layers of n points in O(nlog 2 n) time using a general technique for computing convex hulls in a dynamic environment [ 16 ]....
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