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fix typos

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Sébastien Loriot 2021-04-28 15:36:15 +02:00
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commit 187e68f9cd
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12
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt
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@ -402,7 +402,7 @@ the `Arrangement_2` class template; their description follows.
our traits-class model in order to construct arrangements of line
segments. In succeeding sections we also use `Arr_segment_traits_2`
as our traits-class model. These two traits trade computation time
and storage space. The latter tores the underlying line of every
and storage space. The latter stores the underlying line of every
segment of the arrangement to expedite certain operations on the
arrangement segments. In Section \ref aos_sec-unbounded we use
`Arr_linear_traits_2` to construct arrangements of linear curves
@ -2000,7 +2000,7 @@ especially for polyline, as two polylines may overlap in more then one
connected component.) The generic implementation serves as the
foundation of a family of concrete operations described in the rest of
this section, such as aggregately constructing an arrangement induced
by a set of curves that lie in a two-dimensional surface and ouputing
by a set of curves that lie in a two-dimensional surface and outputting
the overlay of two arrangements.
<!----------------------------------------------------------------------------->
@ -3234,7 +3234,7 @@ graph, where a node of the graph represents a concept and an arc
represents a refinement relation. An arc directed from concept <span
class="textsc">A</span> to concept <span class="textsc">B</span>
indicates that concept <span class="textsc">B</span> refines concept
<span class="textsc">A</span>. A rather large direccted acyclic graph
<span class="textsc">A</span>. A rather large directed acyclic graph
is required to capture the entire hierarchy of the geometry
traits-class concepts. In the following sections we review individual
clusters of the graph and describe the relations between them.
@ -3676,7 +3676,7 @@ collected in two additional abstract layers called
\cgalFigureBegin{aos_fig-identified_clusters,identified_clusters.png}
Top portion of the refinement hierarchy of the geometry-traits
concepts for curves that reach the identified vertical sides of the
parameter space and for curves that reach the identified horizntal
parameter space and for curves that reach the identified horizontal
sides of the parameter space.
\cgalFigureEnd
<!----------------------------------------------------------------------------->
@ -3684,7 +3684,7 @@ sides of the parameter space.
Individual concepts for curves that reach the identified left side of
the parameter space and for curves that reach the identified right
side of the parameter space do not exist, because if one side is
identified the opposide side must be identified as well. Similarly,
identified the opposite side must be identified as well. Similarly,
individual concepts for curves that reach the identified bottom side
of the parameter space and for curves that reach the identified top
side of the parameter space do not exist either. Instead, the shared
@ -4056,7 +4056,7 @@ types are thus convertible to one another.
Computing the intersection between two segments is preceded by an
application of an efficient predicate that tests whether an
intersection exists at all. This optimization has negligble overhead;
intersection exists at all. This optimization has negligible overhead;
Thus, using an instance of the `Arr_segment_traits_2<Kernel>` class
template is still very efficient when constructing arrangements
induced by line segments with a large number of intersections.