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@ -117,7 +117,7 @@ diagram are one-dimensional and that all Voronoi cells are simply
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connected. Moreover, we further distinguish between two cases,
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according to the type of intersecting pair that our input data set
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contains. A pair of sites is called \emph{weakly intersecting} if they
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a single common point and this common point does not lie in the
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have a single common point and this common point does not lie in the
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interior of any of the two sites. A pair of sites is called
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\emph{strongly intersecting} if they intersect and they either have
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more than one common point or their common point lies in the interior
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@ -284,12 +284,12 @@ boolean is equal to \ccc{true}. The segment $s_1q_1$ will also be
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represented by two segments, a point, and a boolean, namely, $t_1$
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(the supporting segment of $s_1q_1$), $t_2$ and \ccc{false} (it is the
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second endpoint of $s_1q_1$ that is an input point). Subsegments
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$p_2s_2$ and $s_2q_2$ are represented analogously.
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$p_2s_1$ and $s_1q_2$ are represented analogously.
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Consider now what happens when we insert $t_3$. The point
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$s_2$ will again be represented by two segments, but not $s_1q_1$ and
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$t_3$. In fact, it will be represented by $t_1$ (the supporting
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segment of $s_1q_1$) and $t_3$. $s_2q_1$ will be represented
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by two segments, a point, and a boolean ($t_1$, $t_3$ and
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by two segments, a point, and a boolean ($t_1$, $t_3$, $q1$ and
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\ccc{false}), and similarly for $p_3s_2$ and $s_2q_3$. On the other
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hand, both endpoints of $s_1s_2$ are non-input points. In such a
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case we represent the segment by three input segments.
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@ -21,7 +21,7 @@
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\subsection{First Example}
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The following example shows to use the segment Delaunay graph traits
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The following example shows how to use the segment Delaunay graph traits
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in conjunction with the \ccc{Filtered_exact<CT,ET>} mechanism. In
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addition it shows how to use a few of the iterators provided by the
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\ccc{Segment_Delaunay_graph_2} class in order to count a few
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