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Algebraic_foundations/doc/Algebraic_foundations/Algebraic_foundations.txt

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@@ -267,7 +267,7 @@ compute the <i>least</i> common multiple of the denominators.
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The package is part of \cgal since release 3.3. Of course the package is based
269269
on the former Number type support of CGAL. This goes back to Stefan Schirra and Andreas Fabri. But on the other hand the package is to a large extend influenced
270-
by the experience with the number type support in <span class="textsc">Exacus</span> \cgalCite{beh-eeeafcs-05},
270+
by the experience with the number type support in \exacus \cgalCite{beh-eeeafcs-05},
271271
which in the main goes back to
272272
Lutz Kettner, Susan Hert, Arno Eigenwillig and Michael Hemmer.
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However, the package abstracts from the pure support for

Algebraic_kernel_d/doc/Algebraic_kernel_d/Algebraic_kernel_d.txt

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@@ -310,7 +310,7 @@ that does not follow the generic programming paradigm, by avoiding
310310
interfaces between layers. Specifically, working with
311311
only one number type allows to optimize some polynomial operations
312312
as well as memory handling. The implementation of these kernels
313-
make heavy use of the <span class="textsc">Mpfr</span> \cgalCite{cgal:mt-mpfr} and <span class="textsc">Mpfi</span> \cgalCite{cgal:r-mpfi}
313+
make heavy use of the \mpfr \cgalCite{cgal:mt-mpfr} and \mpfi \cgalCite{cgal:r-mpfi}
314314
libraries, and of their \cgal interfaces, `Gmpfr` and `Gmpfi`.
315315
The algebraic numbers (roots of the polynomials) are represented
316316
in the two RS kernels by a `Gmpfi` interval and a pointer to
@@ -368,12 +368,12 @@ ideas that was brought to them throughout the last years. In particular,
368368
they want to thank Menelaos Karavelas and Elias Tsigaridas for their
369369
initial contributions.
370370

371-
The two generic models where initially developed as part of the <span class="textsc">Exacus</span> \cgalCite{beh-eeeafcs-05} project.
371+
The two generic models where initially developed as part of the \exacus \cgalCite{beh-eeeafcs-05} project.
372372
However, the models are now fully integrated into the \cgal library,
373-
since also the relevant layers of <span class="textsc">Exacus</span> are now part of \cgal.
373+
since also the relevant layers of \exacus are now part of \cgal.
374374
The main authors for `Algebraic_kernel_d_1<Coeff>` and `Algebraic_kernel_d_2<Coeff>` are
375375
Michael Hemmer and Michael Kerber, respectively. Notwithstanding, the authors also want to emphasize the
376-
contribution of all authors of the <span class="textsc">Exacus</span> project,
376+
contribution of all authors of the \exacus project,
377377
particularly the contribution of Arno Eigenwillig, Sebastian Limbach and Pavel Emeliyanenko.
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379379
The two univariate kernels that interface the library RS \cgalCite{cgal:r-rs} were

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt

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@@ -662,9 +662,9 @@ functions can be used. The program works in three
662662
steps, as demonstrated in \cgalFigureRef{arr_figex_3}. Note that
663663
here we still stick to integer coordinates, but as we work on a
664664
larger scale we use an unbounded integer number-type (in this
665-
case, the `Gmpz` type taken from the <span class="textsc">Gmp</span> library)
665+
case, the `Gmpz` type taken from the \gmp library)
666666
instead of the built-in `int` type.\cgalFootnote{As a rule of thumb, one can use a bounded integer type for representing line segments whose coordinates are bounded by \f$ \lfloor\sqrt[3]{M}\rfloor\f$, where \f$ M\f$ is the maximal representable integer value. This guarantees that no overflows occur in the computations carried out by the traits class, hence all traits-class predicates always return correct results.}
667-
In case the <span class="textsc">Gmp</span> library is not installed (as indicated by
667+
In case the \gmp library is not installed (as indicated by
668668
the `CGAL_USE_GMP` flag defined in `CGAL/basic.h`), we
669669
use `MP_Float`, a number-type included in \cgal's support
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library that is capable of storing floating-point numbers with
@@ -2064,8 +2064,7 @@ rational numbers, and this ensures the robustness and correctness of
20642064
any computation.\cgalFootnote{Many of the example programs in the rest
20652065
of the chapter include a header file named `arr_rational_nt.h`, which
20662066
defines a type named `Number_type` as either `Gmpq` or
2067-
`Quotient<MP_Float>`, depending on whether <span
2068-
class="textsc">Gmp</span> is installed or not.}
2067+
`Quotient<MP_Float>`, depending on whether \gmp is installed or not.}
20692068

20702069
An instance of the `Arr_segment_traits_2<Kernel>` class
20712070
template can be very efficient for constructing arrangements induced
@@ -2480,7 +2479,7 @@ and extracting the real roots of a polynomial with integer
24802479
coefficients. It is highly recommended to use the
24812480
`CORE_algebraic_number_traits` class, which is included in the
24822481
arrangement package. It relies on the exact number types
2483-
implemented in the <span class="textsc">Core</span> library and performs exact
2482+
implemented in the \core library and performs exact
24842483
computations on the number types it defines.
24852484
</UL>
24862485

@@ -3588,15 +3587,15 @@ and defines a simple textual input/output format.
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35893588
\section arr_secbgl Adapting to Boost Graphs
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3591-
<span class="textsc">Boost</span>\cgalFootnote{See also <span class="textsc">Boost</span>'s homepage at: <TT>www.boost.org</TT>.}
3592-
is a collection of portable \cpp libraries that extend the Standard Template Library (<span class="textsc">Stl</span>). The <span class="textsc">Boost</span> Graph Library (<span class="textsc">bgl</span>), which one of the libraries in the collection, offers an
3590+
\boost\cgalFootnote{See also \boost's homepage at: <TT>www.boost.org</TT>.}
3591+
is a collection of portable \cpp libraries that extend the Standard Template Library (\stl). The \boost Graph Library (\bgl), which one of the libraries in the collection, offers an
35933592
extensive set of generic graph algorithms parameterized through templates.
35943593
As our arrangements are embedded as planar graphs, it is only
35953594
natural to extend the underlying data structure with the interface that the
3596-
<span class="textsc">bgl</span> expects, and gain the ability to perform the operations that the <span class="textsc">bgl</span> supports, such as shortest-path computation. This section describes how apply
3597-
the graph algorithms implemented in the <span class="textsc">bgl</span> to `Arrangement_2` instances.
3595+
\bgl expects, and gain the ability to perform the operations that the \bgl supports, such as shortest-path computation. This section describes how apply
3596+
the graph algorithms implemented in the \bgl to `Arrangement_2` instances.
35983597

3599-
An instance of `Arrangement_2` is adapted to a <span class="textsc">Boost</span> graph through the
3598+
An instance of `Arrangement_2` is adapted to a \boost graph through the
36003599
provision of a set of free functions that operate on the arrangement features
36013600
and conform with the relevant BGL concepts. Besides the straightforward
36023601
adaptation, which associates a vertex with each \dcel vertex and an edge
@@ -3607,7 +3606,7 @@ faces.
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36083607
\subsection arr_ssecbgl_primal The Primal Arrangement Representation
36093608

3610-
Arrangement instances are adapted to <span class="textsc">Boost</span> graphs by specializing the
3609+
Arrangement instances are adapted to \boost graphs by specializing the
36113610
\link BGLArgtGT `boost:graph_traits` \endlink template for `Arrangement_2` instances. The
36123611
graph-traits states the graph concepts that the arrangement class models
36133612
(see below) and defines the types required by these concepts.
@@ -3620,11 +3619,11 @@ graph-edge type. As halfedges are directed, we consider the graph to be
36203619
directed as well. Moreover, as several interior-disjoint \f$ x\f$-monotone curves
36213620
(say circular arcs) may share two common endpoints, inducing an arrangement
36223621
with two vertices that are connected with several edges, we allow parallel
3623-
edges in our <span class="textsc">Boost</span> graph.
3622+
edges in our \boost graph.
36243623

36253624
Given an `Arrangement_2` instance, we can efficiently traverse its
36263625
vertices and halfedges. Thus, the arrangement graph is a model of the concepts
3627-
`VertexListGraph` and `EdgeListGraph` introduced by the <span class="textsc">bgl</span>.
3626+
`VertexListGraph` and `EdgeListGraph` introduced by the \bgl.
36283627
At the same time, we use an iterator adapter of the circulator over the
36293628
halfedges incident to a vertex (`Halfedge_around_vertex_circulator` - see
36303629
Section \ref arr_sssectr_vertex), so it is possible to go over the ingoing
@@ -3634,17 +3633,17 @@ is a model of the concept `BidirectionalGraph` (this concept refines
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36353634
It is important to notice that the vertex descriptors we use are
36363635
`Vertex_handle` objects and <I>not</I> vertex indices. However, in order
3637-
to gain more efficiency in most <span class="textsc">bgl</span> algorithm, it is better to have them
3636+
to gain more efficiency in most \bgl algorithm, it is better to have them
36383637
indexed \f$ 0, 1, \ldots, (n-1)\f$, where \f$ n\f$ is the number of vertices. We
36393638
therefore introduce the `Arr_vertex_index_map<Arrangement>` class-template,
36403639
which maintains a mapping of vertex handles to indices, as required by the
3641-
<span class="textsc">bgl</span>. An instance of this class must be attached to a valid arrangement
3640+
\bgl. An instance of this class must be attached to a valid arrangement
36423641
vertex when it is created. It uses the notification mechanism (see
36433642
Section \ref arr_secnotif) to automatically maintain the mapping of vertices
36443643
to indices, even when new vertices are inserted into the arrangement or
36453644
existing vertices are removed.
36463645

3647-
In most algorithm provided by the <span class="textsc">bgl</span>, the output is given by
3646+
In most algorithm provided by the \bgl, the output is given by
36483647
<I>property maps</I>, such that each map entry corresponds to a vertex.
36493648
For example, when we compute the shortest paths from a given source vertex
36503649
\f$ s\f$ to all other vertices we can obtain a map of distances and a map of
@@ -3659,7 +3658,7 @@ allows for an efficient mapping of `Vertex_handle` objects to
36593658
properties of type `Type`. Note however that unlike the
36603659
`Arr_vertex_index_map` class, the vertex property-map class is not
36613660
kept synchronized with the number of vertices in the arrangement, so it
3662-
should not be reused in calls to <span class="textsc">bgl</span> functions in case the arrangement
3661+
should not be reused in calls to \bgl functions in case the arrangement
36633662
is modified in between these calls.
36643663

36653664
\cgalFigureBegin{arr_figex_bgl,ex_bgl.png}
@@ -3668,7 +3667,7 @@ An arrangement of 7 line segments, as constructed by `bgl_primal_adapter.cpp` an
36683667

36693668
In the following example we construct an arrangement of 7 line segments,
36703669
as shown in \cgalFigureRef{arr_figex_bgl},
3671-
then use Dijkstra's shortest-paths algorithm from the <span class="textsc">bgl</span> to compute
3670+
then use Dijkstra's shortest-paths algorithm from the \bgl to compute
36723671
the graph distance of all vertices from the leftmost vertex in the
36733672
arrangement \f$ v_0\f$. Note the usage of the `boost::vector_property_map<Type, IndexMap>` and
36743673
the `Arr_vertex_property_map` classes. The latter one, instantiated by
@@ -3692,7 +3691,7 @@ graph-edge type. We treat the graph edges as directed, such that a halfedge
36923691
`e` is directed from \f$ f_1\f$, which is its incident face, to \f$ f_2\f$, which
36933692
is the incident face of its twin halfedge. As two arrangement faces may
36943693
share more than a single edge on their boundary, we allow parallel
3695-
edges in our <span class="textsc">Boost</span> graph. As is the case in the primal graph, the dual
3694+
edges in our \boost graph. As is the case in the primal graph, the dual
36963695
arrangement graph is also a model of the concepts `VertexListGraph`,
36973696
`EdgeListGraph` and `BidirectionalGraph` (thus also of
36983697
`IncidenceGraph`).
@@ -3740,7 +3739,7 @@ exhibits slightly better performance than the default one
37403739
(`Arr_segment_traits_2`
37413740
even when the segments intersect each other, due to the small overhead
37423741
of the latter (optimized) traits class. (For example, when the so
3743-
called <span class="textsc">Leda</span> rational kernel is used).
3742+
called \leda rational kernel is used).
37443743

37453744
<LI>Prior knowledge of the combinatorial structure of the arrangement can
37463745
be used to accelerate operations that insert \f$ x\f$-monotone curves,

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_Bezier_curve_traits_2.h

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@@ -43,7 +43,7 @@ geometric kernels templated with the `NtTraits::Rational` and
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instantiate the `CORE_algebraic_number_traits` class as the `NtTraits`
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parameter, with `Cartesian<NtTraits::Rational>` and
4545
`Cartesian<NtTraits::Algebraic>` instantiating the two kernel types,
46-
respectively. The number types in this case are provided by the <span class="textsc">Core</span>
46+
respectively. The number types in this case are provided by the \core
4747
library, with its ability to exactly represent simple algebraic numbers.
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4949
While `Arr_Bezier_curve_traits_2` models the concept

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_conic_traits_2.h

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@@ -61,7 +61,7 @@ It is recommended to instantiate the `CORE_algebraic_number_traits`
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class as the `NtTraits` parameter, with
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`Cartesian<NtTraits::Rational>` and `Cartesian<NtTraits::Algebraic>`
6363
instantiating the two kernel types, respectively.
64-
The number types in this case are provided by the <span class="textsc">Core</span> library, with its
64+
The number types in this case are provided by the \core library, with its
6565
ability to exactly represent simple algebraic numbers.
6666
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The traits class inherits its point type from `AlgKernel::Point_2`,

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_dcel_base.h

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@@ -7,11 +7,11 @@ namespace CGAL {
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\anchor arr_refarr_dcel_base
88
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The `Arr_dcel_base` class is an important ingredient in the
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definition of <span class="textsc">Dcel</span> data structures. It serves as a basis class for
10+
definition of \dcel data structures. It serves as a basis class for
1111
any instance of the `Dcel` template parameter of the
1212
`Arrangement_2` template. In particular it is the basis class of
1313
the default `Dcel` template parameter, and the basis class of any
14-
extended <span class="textsc">Dcel</span>. The template parameters `V`, `H`, and `F`
14+
extended \dcel. The template parameters `V`, `H`, and `F`
1515
must be instantiated with models of the concepts
1616
`ArrangementDcelVertex`, `ArrangementDcelHalfedge`,
1717
and `ArrangementDcelFace` respectively.
@@ -26,7 +26,7 @@ class Arr_dcel_base {
2626

2727
/*!
2828
29-
The basic <span class="textsc">Dcel</span> face type. Serves as a basis class for an extended
29+
The basic \dcel face type. Serves as a basis class for an extended
3030
face record with auxiliary data fields.
3131
3232
\cgalModels `ArrangementDcelFace`
@@ -39,7 +39,7 @@ class Arr_face_base {
3939
/*!
4040
4141
42-
The basic <span class="textsc">Dcel</span> halfedge type. Serves as a basis class for an
42+
The basic \dcel halfedge type. Serves as a basis class for an
4343
extended halfedge record with auxiliary data fields. The `Curve`
4444
parameter is the type of \f$ x\f$-monotone curves associated with the vertices.
4545
@@ -54,7 +54,7 @@ class Arr_halfedge_base {
5454
/*!
5555
5656
57-
The basic <span class="textsc">Dcel</span> vertex type. Serves as a basis class for an extended
57+
The basic \dcel vertex type. Serves as a basis class for an extended
5858
vertex record with auxiliary data fields. The `Point` parameter is
5959
the type of points associated with the vertices.
6060

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_default_dcel.h

Lines changed: 2 additions & 2 deletions
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@@ -4,12 +4,12 @@ namespace CGAL {
44
/*!
55
\ingroup PkgArrangementOnSurface2DCEL
66
7-
The default <span class="textsc">Dcel</span> class used by the `Arrangement_2` class-template
7+
The default \dcel class used by the `Arrangement_2` class-template
88
is parameterized by a traits class, which is a model of the
99
`ArrangementBasicTraits_2` concept. It simply uses the nested
1010
`Traits::Point_2` and `Traits::X_monotone_curve_2` to instantiate
1111
the base vertex and halfedge types, respectively. Thus, the default
12-
<span class="textsc">Dcel</span> records store no other information, except for the topological
12+
\dcel records store no other information, except for the topological
1313
incidence relations and the geometric data attached to vertices and edges.
1414
1515
\cgalModels `ArrangementDcelWithRebind`

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_default_overlay_traits.h

Lines changed: 5 additions & 5 deletions
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@@ -6,8 +6,8 @@ namespace CGAL {
66
\ingroup PkgArrangementOnSurface2Overlay
77
88
An instance of `Arr_default_overlay_traits` should be used for overlaying two arrangements
9-
of type `Arrangement` that store no auxiliary data with their <span class="textsc">Dcel</span> records, where the resulting overlaid arrangement stores no auxiliary
10-
<span class="textsc">Dcel</span> data as well. This class simply gives empty implementation for all
9+
of type `Arrangement` that store no auxiliary data with their \dcel records, where the resulting overlaid arrangement stores no auxiliary
10+
\dcel data as well. This class simply gives empty implementation for all
1111
traits-class functions.
1212
1313
\cgalModels `OverlayTraits`
@@ -30,10 +30,10 @@ namespace CGAL {
3030
3131
An instance of `Arr_face_overlay_traits` should be used for overlaying two arrangements
3232
of types `Arr_A` and `Arr_B`, which are instantiated using the same
33-
geometric traits-class and with the <span class="textsc">Dcel</span> classes `Dcel_A` and
33+
geometric traits-class and with the \dcel classes `Dcel_A` and
3434
`Dcel_B` respectively, in order to store their overlay in an arrangement
35-
of type `Arr_R`, which is instantiated using a third <span class="textsc">Dcel</span> class
36-
`Dcel_R`. All three <span class="textsc">Dcel</span> classes are assumed to be instantiations of the
35+
of type `Arr_R`, which is instantiated using a third \dcel class
36+
`Dcel_R`. All three \dcel classes are assumed to be instantiations of the
3737
`Arr_face_extended_dcel` template with types `FaceData_A`,
3838
`FaceData_B` and `FaceData_R`, respectively.
3939

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_extended_dcel.h

Lines changed: 7 additions & 7 deletions
Original file line numberDiff line numberDiff line change
@@ -4,11 +4,11 @@ namespace CGAL {
44
/*!
55
\ingroup PkgArrangementOnSurface2DCEL
66
7-
The `Arr_extended_dcel` class-template extends the topological-features of the <span class="textsc">Dcel</span>
7+
The `Arr_extended_dcel` class-template extends the topological-features of the \dcel
88
namely the vertex, halfedge, and face types. While it is possible to maintain
99
extra (non-geometric) data with the curves or points of the arrangement by
1010
extending their types respectively, it is also possible to extend the vertex,
11-
halfedge, or face types of the <span class="textsc">Dcel</span> through inheritance. As the technique to
11+
halfedge, or face types of the \dcel through inheritance. As the technique to
1212
extend these types is somewhat cumbersome and difficult for inexperienced
1313
users, the `Arr_extended_dcel` class-template provides a convenient way to do that.
1414
Each one of the three features is extended with a corresponding data type
@@ -54,7 +54,7 @@ namespace CGAL {
5454
\ingroup PkgArrangementOnSurface2DCEL
5555
5656
The `Arr_extended_face` class-template extends the face topological-features of the
57-
<span class="textsc">Dcel</span>. It is parameterized by a face base-type `FaceBase` and a data type
57+
\dcel. It is parameterized by a face base-type `FaceBase` and a data type
5858
`FData` used to extend the face base-type.
5959
6060
\cgalModels `ArrangementDcelFace`
@@ -106,7 +106,7 @@ namespace CGAL {
106106
\ingroup PkgArrangementOnSurface2DCEL
107107
108108
The `Arr_extended_halfedge` class-template extends the halfedge topological-features of
109-
the <span class="textsc">Dcel</span>. It is parameterized by a halfedge base-type `HalfedgeBase`
109+
the \dcel. It is parameterized by a halfedge base-type `HalfedgeBase`
110110
and a data type `HData` used to extend the halfedge base-type.
111111
112112
\cgalModels `ArrangementDcelHalfedge`
@@ -158,7 +158,7 @@ namespace CGAL {
158158
\ingroup PkgArrangementOnSurface2DCEL
159159
160160
The `Arr_extended_vertex` class-template extends the vertex
161-
topological-features of the <span class="textsc">Dcel</span>. It is parameterized by a
161+
topological-features of the \dcel. It is parameterized by a
162162
vertex base-type `VertexBase` and a data type `VData` used to extend
163163
the vertex base-type.
164164
@@ -210,12 +210,12 @@ namespace CGAL {
210210
/*!
211211
\ingroup PkgArrangementOnSurface2DCEL
212212
213-
The `Arr_face_extended_dcel` class-template extends the <span class="textsc">Dcel</span> face-records, making it
213+
The `Arr_face_extended_dcel` class-template extends the \dcel face-records, making it
214214
possible to store extra (non-geometric) data with the arrangement faces.
215215
The class should be instantiated by an `FData` type which represents the
216216
extra data stored with each face.
217217
218-
Note that all types of <span class="textsc">Dcel</span> features (namely vertex, halfedge and face)
218+
Note that all types of \dcel features (namely vertex, halfedge and face)
219219
are provided as template parameters. However, by default they are defined
220220
as follows:
221221

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