mirror of https://github.com/CGAL/cgal
Incorporated the changes proposed by Marc:
- Changed to code to show the menus - Added a sentence to mention the distribution of the points
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@ -135,7 +135,7 @@ data structure, is `locally valid`
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<B>(c)</B> Any cell has its vertices ordered according to positive
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orientation. See Figure \cgalFigureRef{P2Triangulation2figorient}.
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# Delaunay Triangulation #
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\section P2T2_Delaunay Delaunay Triangulation
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The class `Periodic_2_Delaunay_triangulation_2` implements Delaunay
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triangulations of point sets in \f$ \mathbb T_c^2\f$.
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@ -150,7 +150,7 @@ four points are co-circular. Note however that the \cgal implementation computes
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This implementation is fully dynamic: it supports both insertions of
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points and vertex removal.
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# Triangulation Hierarchy #
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\section P2T2_Hierarchy Triangulation Hierarchy
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The class `Periodic_2_triangulation_hierarchy_2` is the adaptation
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of the hierarchical structure described in
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@ -372,7 +372,7 @@ requires <I>exact constructions</I>.
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\cgalExample{Periodic_2_triangulation_2/p2t2_geometric_access.cpp}
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# Design and Implementation History #
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\section P2T2_Design Design and Implementation History
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The periodic 2D-triangulation is based on the 2D triangulation package
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developed by Mariette Yvinec and the periodic 3D-triangulation package
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@ -383,11 +383,12 @@ developed by Manuel Caroli and Monique Teillaud. The periodic
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In 2009, Nico Kruithof started implementation of the
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`Periodic_2_triangulation_2` package.
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# Performance #
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\section P2T2_Performance Performance
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The performance of the 2D periodic Delaunay triangulation is compared
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to the Euclidean 2D Delaunay triangulation. The plot shows the running
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time in seconds for different numbers of batch inserted points. The
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points are uniformly randomly distributed in the unit rectangle. The
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tests were done on an Intel i7 @ 2.67GHz.
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\image html p2dt2_performance.png
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