boolean -> Boolean

This commit is contained in:
Andreas Fabri 2015-02-06 09:09:28 +01:00 committed by Panagiotis Cheilaris
parent 4a15ac8795
commit d6d5471161
3 changed files with 10 additions and 10 deletions

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@ -75,7 +75,7 @@ static SegmentDelaunayGraphSite_2 construct_site_2(Point_2 p1, Point_2 p2,
Point_2 q1, Point_2 q2);
/*!
Constructs a site from four points and a boolean: the
Constructs a site from four points and a Boolean: the
site represents a segment. If `b` is `true` the endpoints
are `p1` and \f$ p_\times\f$, otherwise \f$ p_\times\f$ and
`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);
/*!
Constructs
a site from four point handles and a boolean. The storage site
a site from four point handles and a Boolean. The storage site
represents a segment. If `b` is `true`, the first endpoint
of the segment is the point associated with the handle `hp1` and
the second endpoint is the point of intersection of the segments the

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