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reference biblio
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@ -151908,3 +151908,13 @@ pages = {179--189}
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year={2010}
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}
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@TechReport{Devillers2014Generator
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, author = "Olivier Devillers and Philippe Duchon and R{\'e}my Thomasse"
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, title = "A generator of random convex polygon in a disc"
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, institution = "INRIA"
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, type = "Research Report"
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, number = "RR-8467"
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, month = "Feb"
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, year = "2014"
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, url = "http://hal.inria.fr/hal-00943409"
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}
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@ -27,7 +27,7 @@ The generated polygon will have an average number of vertices \f$ n^\frac{1}{3}(
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\cgalHeading{Implementation}
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The implementation is based on an incremental construction of a convex hull. At each step, we choose a number of points to pick uniformly at random in the disc. Then, a subset of these points, that won't change the convex hull, is evaluated using a Binomial law.
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As these points won't be generated, the time and size complexities are reduced.
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As these points won't be generated, the time and size complexities are reduced \cgalCite{Devillers2014Generator}.
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A tradeoff between time and memory is provided with the option `fast`, true by default. Using the `fast` option, both time and size expected complexities are \f$O\left(n^\frac{1}{3}\log^\frac{2}{3}n \right)\f$.
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If this option is disabled, the expected size complexity becomes \f$O\left(n^\frac{1}{3}\right)\f$ but the expected time complexity becomes \f$O\left(n^\frac{1}{3}\log^2 n \right)\f$.
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