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boolean -> Boolean
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@ -75,7 +75,7 @@ static SegmentDelaunayGraphSite_2 construct_site_2(Point_2 p1, Point_2 p2,
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Point_2 q1, Point_2 q2);
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Point_2 q1, Point_2 q2);
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/*!
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/*!
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Constructs a site from four points and a boolean: the
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Constructs a site from four points and a Boolean: the
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site represents a segment. If `b` is `true` the endpoints
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site represents a segment. If `b` is `true` the endpoints
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are `p1` and \f$ p_\times\f$, otherwise \f$ p_\times\f$ and
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are `p1` and \f$ p_\times\f$, otherwise \f$ p_\times\f$ and
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`p2`. \f$ p_\times\f$ is the point of intersection of the segments
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`p2`. \f$ p_\times\f$ is the point of intersection of the segments
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@ -78,7 +78,7 @@ Point_handle hp2, Point_handle hq1, Point_handle hq2);
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/*!
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/*!
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Constructs
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Constructs
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a site from four point handles and a boolean. The storage site
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a site from four point handles and a Boolean. The storage site
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represents a segment. If `b` is `true`, the first endpoint
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represents a segment. If `b` is `true`, the first endpoint
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of the segment is the point associated with the handle `hp1` and
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of the segment is the point associated with the handle `hp1` and
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the second endpoint is the point of intersection of the segments the
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the second endpoint is the point of intersection of the segments the
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@ -233,12 +233,12 @@ the subsegments
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subsegments \f$ p_2s_1\f$ and \f$ s_1q_2\f$. How do we represent the five new
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subsegments \f$ p_2s_1\f$ and \f$ s_1q_2\f$. How do we represent the five new
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sites? \f$ s_1\f$ will be represented by its two defining segments \f$ t_1\f$
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sites? \f$ s_1\f$ will be represented by its two defining segments \f$ t_1\f$
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and \f$ t_2\f$. The segment \f$ p_1s_1\f$ will be represented by two segments, a
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and \f$ t_2\f$. The segment \f$ p_1s_1\f$ will be represented by two segments, a
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point, and a boolean. The first segment is \f$ t_1\f$, which is always the
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point, and a Boolean. The first segment is \f$ t_1\f$, which is always the
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segment with the same support as the newly created segment. The second
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segment with the same support as the newly created segment. The second
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segment is \f$ t_2\f$ and the point is \f$ p_1\f$. The boolean indicates whether
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segment is \f$ t_2\f$ and the point is \f$ p_1\f$. The Boolean indicates whether
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the first endpoint of \f$ p_1s_1\f$ is an input point; in this case the
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the first endpoint of \f$ p_1s_1\f$ is an input point; in this case the
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boolean is equal to `true`. The segment \f$ s_1q_1\f$ will also be
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Boolean is equal to `true`. The segment \f$ s_1q_1\f$ will also be
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represented by two segments, a point, and a boolean, namely, \f$ t_1\f$
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represented by two segments, a point, and a Boolean, namely, \f$ t_1\f$
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(the supporting segment of \f$ s_1q_1\f$), \f$ t_2\f$ and `false` (it is the
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(the supporting segment of \f$ s_1q_1\f$), \f$ t_2\f$ and `false` (it is the
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second endpoint of \f$ s_1q_1\f$ that is an input point). Subsegments
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second endpoint of \f$ s_1q_1\f$ that is an input point). Subsegments
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\f$ p_2s_1\f$ and \f$ s_1q_2\f$ are represented analogously.
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\f$ p_2s_1\f$ and \f$ s_1q_2\f$ are represented analogously.
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@ -246,7 +246,7 @@ Consider now what happens when we insert \f$ t_3\f$. The point
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\f$ s_2\f$ will again be represented by two segments, but not \f$ s_1q_1\f$ and
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\f$ s_2\f$ will again be represented by two segments, but not \f$ s_1q_1\f$ and
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\f$ t_3\f$. In fact, it will be represented by \f$ t_1\f$ (the supporting
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\f$ t_3\f$. In fact, it will be represented by \f$ t_1\f$ (the supporting
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segment of \f$ s_1q_1\f$) and \f$ t_3\f$. \f$ s_2q_1\f$ will be represented
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segment of \f$ s_1q_1\f$) and \f$ t_3\f$. \f$ s_2q_1\f$ will be represented
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by two segments, a point, and a boolean (\f$ t_1\f$, \f$ t_3\f$, \f$ q1\f$ and
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by two segments, a point, and a Boolean (\f$ t_1\f$, \f$ t_3\f$, \f$ q1\f$ and
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`false`), and similarly for \f$ p_3s_2\f$ and \f$ s_2q_3\f$. On the other
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`false`), and similarly for \f$ p_3s_2\f$ and \f$ s_2q_3\f$. On the other
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hand, both endpoints of \f$ s_1s_2\f$ are non-input points. In such a
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hand, both endpoints of \f$ s_1s_2\f$ are non-input points. In such a
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case we represent the segment by three input segments.
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case we represent the segment by three input segments.
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@ -258,7 +258,7 @@ supporting segment of \f$ s_1q_1\f$), \f$ t_2\f$ (it defines \f$ s_1\f$ along wi
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Site representation. The point \f$ s_1\f$ is represented by the four
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Site representation. The point \f$ s_1\f$ is represented by the four
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points \f$ p_1\f$, \f$ q_1\f$, \f$ p_2\f$ and \f$ q_2\f$. The segment
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points \f$ p_1\f$, \f$ q_1\f$, \f$ p_2\f$ and \f$ q_2\f$. The segment
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\f$ p_1s_1\f$ is represented by the points \f$ p_1\f$, \f$ q_1\f$, \f$
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\f$ p_1s_1\f$ is represented by the points \f$ p_1\f$, \f$ q_1\f$, \f$
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p_2\f$, \f$ q_2\f$ and a boolean which is set to <I>true</I> to
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p_2\f$, \f$ q_2\f$ and a Boolean which is set to `true` to
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indicate that the first endpoint in not a point of intersection. The
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indicate that the first endpoint in not a point of intersection. The
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segment \f$ s_1s_2\f$ is represented by the six points: \f$ p_1\f$,
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segment \f$ s_1s_2\f$ is represented by the six points: \f$ p_1\f$,
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\f$ q_1\f$, \f$ p_2\f$, \f$ q_2\f$, \f$ p_3\f$ and \f$ q_3\f$. The
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\f$ q_1\f$, \f$ p_2\f$, \f$ q_2\f$, \f$ p_3\f$ and \f$ q_3\f$. The
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@ -268,7 +268,7 @@ represented similarly.
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The five different presentations, two for points (coordinates; two
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The five different presentations, two for points (coordinates; two
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input segments) and three for segments (two input points; two input
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input segments) and three for segments (two input points; two input
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segments, an input point and a boolean; three input segments),
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segments, an input point and a Boolean; three input segments),
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form a closed set of representations and thus represent
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form a closed set of representations and thus represent
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any point of intersection or subsegment regardless of the number of
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any point of intersection or subsegment regardless of the number of
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input segments. Moreover, every point (input or intersection) has
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input segments. Moreover, every point (input or intersection) has
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@ -280,7 +280,7 @@ our predicates will always be \f$ O(b)\f$, independently of the
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size of the input.
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size of the input.
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The `SegmentDelaunayGraphSite_2` concept encapsulates the ideas
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The `SegmentDelaunayGraphSite_2` concept encapsulates the ideas
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presented above. A site is represented in this concept by up to four
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presented above. A site is represented in this concept by up to four
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points and a boolean, or up to six points, depending on its type. The
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points and a Boolean, or up to six points, depending on its type. The
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class `Segment_Delaunay_graph_site_2<K>` implements this
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class `Segment_Delaunay_graph_site_2<K>` implements this
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concept.
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concept.
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