songsenand
/
cgal
mirror of https://github.com/CGAL/cgal
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

substituted with => substituted by

This commit is contained in:
Efi Fogel 2024-01-24 22:16:57 +02:00
parent 42e6052008
commit 6c17b256d5
9 changed files with 45 additions and 45 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

62
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt
View File

@ -69,10 +69,10 @@ class Arrangement_2 { ... };
An instance of this template represents an arrangement embedded in the An instance of this template represents an arrangement embedded in the
plane. When the template is instantiated, the `GeometryTraits` plane. When the template is instantiated, the `GeometryTraits`
parameter must be substituted with a type that defines a set of parameter must be substituted by a type that defines a set of
geometric-object types, such as point and curve, and a set of geometric-object types, such as point and curve, and a set of
operations on objects of these types (see Section \ref operations on objects of these types (see Section \ref
aos_sec-geom_traits); the `Dcel` parameter must be substituted with a aos_sec-geom_traits); the `Dcel` parameter must be substituted by a
type that represents a doubly-connected edge list (\dcel) data type that represents a doubly-connected edge list (\dcel) data
structure. It defines types of topological objects, such as vertices, structure. It defines types of topological objects, such as vertices,
edges, and faces, and the operations required to maintain the edges, and faces, and the operations required to maintain the
@ -91,7 +91,7 @@ An instance of this template represents a two-dimensional arrangement
embedded in a surface in three dimensional space. When the template is embedded in a surface in three dimensional space. When the template is
instantiated, the `GeometryTraits` parameter must be substituted as instantiated, the `GeometryTraits` parameter must be substituted as
described above; the `TopologyTraits` parameter must be substituted described above; the `TopologyTraits` parameter must be substituted
with a type that deals with the topology of the surface (see Section by a type that deals with the topology of the surface (see Section
\ref aos_sec-topol_traits). In particular, it maintains a \ref aos_sec-topol_traits). In particular, it maintains a
representation of the arrangement graph embedded in the surface using representation of the arrangement graph embedded in the surface using
a doubly-connected edge list (\dcel) data-structure suitable for a doubly-connected edge list (\dcel) data-structure suitable for
@ -390,7 +390,7 @@ the `Arrangement_2` class template; their description follows.
<UL> <UL>
<LI>The `Traits` template-parameter should be substituted with a <LI>The `Traits` template-parameter should be substituted by a
model of the `ArrangementBasicTraits_2` concept and optionally model of the `ArrangementBasicTraits_2` concept and optionally
additional geometry traits concepts. A model of the additional geometry traits concepts. A model of the
`ArrangementBasicTraits_2` concept defines the types of `ArrangementBasicTraits_2` concept defines the types of
@ -415,10 +415,10 @@ the `Arrangement_2` class template; their description follows.
rational functions. We exemplify the usage of these traits classes rational functions. We exemplify the usage of these traits classes
in Section \ref aos_sec-geom_traits. in Section \ref aos_sec-geom_traits.
<LI>The `Dcel` template-parameter should be substituted with a class <LI>The `Dcel` template-parameter should be substituted by a class
that models the `ArrangementDcel` concept, which is used to represent that models the `ArrangementDcel` concept, which is used to represent
the topological layout of the arrangement. This parameter is the topological layout of the arrangement. This parameter is
substituted with `Arr_default_dcel<Traits>` by default, and substituted by `Arr_default_dcel<Traits>` by default, and
we use this default value in this and in the following three we use this default value in this and in the following three
sections. However, in many applications it is necessary to extend the sections. However, in many applications it is necessary to extend the
\dcel features. This is done by substituting the `Dcel` parameter with \dcel features. This is done by substituting the `Dcel` parameter with
@ -1002,7 +1002,7 @@ segments common to all examples that do not construct new geometric
objects. They are kept in the header file objects. They are kept in the header file
`arr_inexact_construction_segments.h`. In these examples the `Traits` `arr_inexact_construction_segments.h`. In these examples the `Traits`
parameter of the `Arrangement_2<Traits, Dcel>` class template is parameter of the `Arrangement_2<Traits, Dcel>` class template is
substituted with an instance of the substituted by an instance of the
`Arr_non_caching_segment_traits_2<Kernel>` class template. The `Arr_non_caching_segment_traits_2<Kernel>` class template. The
`Arr_non_caching_segment_traits_2` class template is instantiated with `Arr_non_caching_segment_traits_2` class template is instantiated with
the predefined kernel that evaluates predicates in an exact manner, the predefined kernel that evaluates predicates in an exact manner,
@ -1439,7 +1439,7 @@ vary according to the user choice.} for answering queries:
The landmark strategy requires that the type of the attached The landmark strategy requires that the type of the attached
arrangement be an instance of the `Arrangement_2<Traits,Dcel>` class arrangement be an instance of the `Arrangement_2<Traits,Dcel>` class
template, where the `Traits` parameter is substituted with a template, where the `Traits` parameter is substituted by a
geometry-traits class that models the `ArrangementLandmarkTraits_2` geometry-traits class that models the `ArrangementLandmarkTraits_2`
concept, which refines the basic `ArrangementBasicTraits_2` concept; concept, which refines the basic `ArrangementBasicTraits_2` concept;
see Section \ref aos_sssec-tr_landmarks_concept for details. Most see Section \ref aos_sssec-tr_landmarks_concept for details. Most
@ -1743,7 +1743,7 @@ query results, and insert \f$c\f$ at its proper
location.\cgalFootnote{The \cgalFootnoteCode{CGAL::insert_non_intersecting_curve<>()} location.\cgalFootnote{The \cgalFootnoteCode{CGAL::insert_non_intersecting_curve<>()}
function template, as all other functions reviewed in this section, is function template, as all other functions reviewed in this section, is
parameterized by an arrangement type and a point-location type (The parameterized by an arrangement type and a point-location type (The
latter must be substituted with a model of the latter must be substituted by a model of the
`ArrangementPointLocation_2` concept).} The insertion operation thus `ArrangementPointLocation_2` concept).} The insertion operation thus
hardly requires any geometric operations on top of the ones needed to hardly requires any geometric operations on top of the ones needed to
answer the point-location queries. Moreover, it is sufficient that the answer the point-location queries. Moreover, it is sufficient that the
@ -1847,7 +1847,7 @@ condition. Consider the call \link CGAL::insert<>() `insert(arr, c,
pl)`\endlink, where \f$c\f$ is not necessarily \f$x\f$-monotone. In pl)`\endlink, where \f$c\f$ is not necessarily \f$x\f$-monotone. In
this case the type of `arr` must be an instance of the this case the type of `arr` must be an instance of the
`Arrangement_2<Traits, Dcel>` class template, where the `Traits` `Arrangement_2<Traits, Dcel>` class template, where the `Traits`
template parameter is substituted with a traits class that models the template parameter is substituted by a traits class that models the
concept `ArrangementTraits_2`, which refines the concept `ArrangementTraits_2`, which refines the
`ArrangementXMonotoneTraits_2` concept. It has to define an additional `ArrangementXMonotoneTraits_2` concept. It has to define an additional
\link ArrangementTraits_2::Curve_2 `Curve_2`\endlink type, which may \link ArrangementTraits_2::Curve_2 `Curve_2`\endlink type, which may
@ -2268,7 +2268,7 @@ accepts the name of an input file that contains the plain-text
description of the geometric objects and an output iterator for description of the geometric objects and an output iterator for
storing the newly constructed objects. When the function is storing the newly constructed objects. When the function is
instantiated, the first template parameter, namely `Type`, must be instantiated, the first template parameter, namely `Type`, must be
substituted with the type of objects to read. It is assumed that an substituted by the type of objects to read. It is assumed that an
extractor operator (`>>`) that extracts objects of the given type from extractor operator (`>>`) that extracts objects of the given type from
the input stream is available. The listing of the function template, the input stream is available. The listing of the function template,
which is defined in the file `read_objects.h`, is omitted here which is defined in the file `read_objects.h`, is omitted here
@ -2705,7 +2705,7 @@ All the free functions that operate on arrangements of bounded curves
of unbounded curves. For example, consider a container of linear of unbounded curves. For example, consider a container of linear
curves that has to be inserted into an arrangement object, the type of curves that has to be inserted into an arrangement object, the type of
which is an instance of the `Arrangement_2<Traits,Dcel>` class which is an instance of the `Arrangement_2<Traits,Dcel>` class
template, where the `Traits` parameter is substituted with the traits template, where the `Traits` parameter is substituted by the traits
class that handles linear curves; see Section \ref class that handles linear curves; see Section \ref
arr_sssectr_linear. You can do it incrementally; namely, insert the arr_sssectr_linear. You can do it incrementally; namely, insert the
curves one by one as follows: curves one by one as follows:
@ -3486,7 +3486,7 @@ point-location strategy.
The type of an arrangement associated with the landmark point-location The type of an arrangement associated with the landmark point-location
strategy (see Section \ref arr_ssecpl) must be an instance of the strategy (see Section \ref arr_ssecpl) must be an instance of the
`Arrangement_on_surface_2<GeomTraits, TopolTraits>` class template, `Arrangement_on_surface_2<GeomTraits, TopolTraits>` class template,
where the `GeomTraits` parameter is substituted with a model of the where the `GeomTraits` parameter is substituted by a model of the
concept `ArrangementLandmarkTraits_2`. (Naturally, it can also model concept `ArrangementLandmarkTraits_2`. (Naturally, it can also model
either the `ArrangementXMonotoneTraits_2` concept or the either the `ArrangementXMonotoneTraits_2` concept or the
`ArrangementTraits_2` concept.) The `ArrangementLandmarkTraits_2` `ArrangementTraits_2` concept.) The `ArrangementLandmarkTraits_2`
@ -4542,7 +4542,7 @@ PkgBooleanSetOperations2Ref. Note that it is not a model of the
computations with square root numbers, which makes it attractive for computations with square root numbers, which makes it attractive for
arrangements induced by line segments, circular arcs, and whole arrangements induced by line segments, circular arcs, and whole
circles. When the traits class-template is instantiated, the `Kernel` circles. When the traits class-template is instantiated, the `Kernel`
template parameter must be substituted with a geometric kernel that template parameter must be substituted by a geometric kernel that
models the `Kernel` concept. Always plug in a kernel that uses a models the `Kernel` concept. Always plug in a kernel that uses a
rational number type, such as rational number type, such as
`Exact_predicates_exact_constructions_kernel`. Observe that the nested `Exact_predicates_exact_constructions_kernel`. Observe that the nested
@ -4723,20 +4723,20 @@ follows:
<UL> <UL>
<LI>The `RatKernel` template parameter must be substituted with a <LI>The `RatKernel` template parameter must be substituted by a
geometric kernel whose field type is an exact rational type. It is geometric kernel whose field type is an exact rational type. It is
used to define basic geometric entities (e.g., a line segment or a used to define basic geometric entities (e.g., a line segment or a
circle) with rational coefficients. Typically we use one of the circle) with rational coefficients. Typically we use one of the
standard \cgal kernels, instantiated with the number type standard \cgal kernels, instantiated with the number type
`NtTraits::Rational` (see below). `NtTraits::Rational` (see below).
<LI>The `AlgKernel` template parameter must be substituted with a <LI>The `AlgKernel` template parameter must be substituted by a
geometric kernel whose field type is an exact algebraic type. It is geometric kernel whose field type is an exact algebraic type. It is
used to define points with algebraic coordinates. Typically, we use used to define points with algebraic coordinates. Typically, we use
one of the standard \cgal kernels, instantiated with the number type one of the standard \cgal kernels, instantiated with the number type
`NtTraits::Algebraic` (see below). `NtTraits::Algebraic` (see below).
<LI>The `NtTraits` template parameter must be substituted with a type <LI>The `NtTraits` template parameter must be substituted by a type
that encapsulates all the numeric operations needed for performing that encapsulates all the numeric operations needed for performing
geometric computation carried out by the geometric traits class. It geometric computation carried out by the geometric traits class. It
defines the `Integer`, `Rational`, and `Algebraic` number-types, and defines the `Integer`, `Rational`, and `Algebraic` number-types, and
@ -4917,7 +4917,7 @@ provided by the traits in form of functors.
When the `Arr_rational_function_traits_2<AlgebraicKernel_d_1>` class When the `Arr_rational_function_traits_2<AlgebraicKernel_d_1>` class
template is instantiated, the template parameter must be substituted template is instantiated, the template parameter must be substituted
with a model of the `AlgebraicKernel_d_1` concept. Models of this by a model of the `AlgebraicKernel_d_1` concept. Models of this
concept, such as the `Algebraic_kernel_d_1<Coefficient>` class concept, such as the `Algebraic_kernel_d_1<Coefficient>` class
template provided by the package \ref PkgAlgebraicFoundations are template provided by the package \ref PkgAlgebraicFoundations are
meant to support algebraic functionalities on univariate polynomials meant to support algebraic functionalities on univariate polynomials
@ -5177,11 +5177,11 @@ polynomial. Currently supported integral number types are `Gmpz`,
statements included in the header file `integer_type.h`, the listings statements included in the header file `integer_type.h`, the listings
of which are omitted here. This header file is used by the two example of which are omitted here. This header file is used by the two example
programs listed in this section. The template parameter `Coefficient` programs listed in this section. The template parameter `Coefficient`
can be substituted in addition with an instance of the can be substituted in addition by an instance of the
`Sqrt_extension<A,B>` class template, where the template parameters `Sqrt_extension<A,B>` class template, where the template parameters
`NT` and `Root` are substituted in turn with one of the integral `NT` and `Root` are substituted in turn by one of the integral
number types above. Finally, the template parameter `Coefficient` can number types above. Finally, the template parameter `Coefficient` can
be substituted also with a rational number type, where the type of the be substituted also by a rational number type, where the type of the
numerator and denominator is one of the types above. numerator and denominator is one of the types above.
The type \link Arr_algebraic_segment_traits_2::Curve_2 The type \link Arr_algebraic_segment_traits_2::Curve_2
@ -5488,7 +5488,7 @@ decorator used to attach a data field to curves and to
\f$x\f$-monotone curves. It is a class template named \f$x\f$-monotone curves. It is a class template named
`Arr_curve_data_traits_2<BaseTraits, XMonotoneCurveData, Merge, `Arr_curve_data_traits_2<BaseTraits, XMonotoneCurveData, Merge,
CurveData, Convert>` parameterized by a base-traits class, which must CurveData, Convert>` parameterized by a base-traits class, which must
be substituted with one of the geometric traits models described in be substituted by one of the geometric traits models described in
the previous subsections or with a user-defined traits model, when the the previous subsections or with a user-defined traits model, when the
decorator is instantiated. The curve-data decorator derives from the decorator is instantiated. The curve-data decorator derives from the
base-traits class, and in particular inherits its \link base-traits class, and in particular inherits its \link
@ -6108,7 +6108,7 @@ ovl_traits)`\endlink constructs the arrangement `arr_o`, which is the
overlay of two input arrangement `arr_r` and `arr_b`. All three overlay of two input arrangement `arr_r` and `arr_b`. All three
arrangements must use the same geometric primitives. In other words, arrangements must use the same geometric primitives. In other words,
their types are instances of the `Arrangement_2<Traits,Dcel>` class their types are instances of the `Arrangement_2<Traits,Dcel>` class
template, where the `Traits` parameter is substituted with three template, where the `Traits` parameter is substituted by three
geometry-traits classes, respectively. The geometry-traits classes of geometry-traits classes, respectively. The geometry-traits classes of
the input arrangements must be convertible to the geometry-traits the input arrangements must be convertible to the geometry-traits
class of the resulting arrangement.\cgalFootnote{It is sufficient that class of the resulting arrangement.\cgalFootnote{It is sufficient that
@ -6169,7 +6169,7 @@ arrangement that results from overlaying two face-extended
arrangements typically also stores additional data-fields with its arrangements typically also stores additional data-fields with its
faces. The types of such arrangements, for example, could be instances faces. The types of such arrangements, for example, could be instances
of the `Arrangement_2<Traits,Dcel>` class template, where the `Dcel` of the `Arrangement_2<Traits,Dcel>` class template, where the `Dcel`
parameters are substituted with instances of the parameters are substituted by instances of the
`Arr_face_extended_dcel` class template (see Section \ref `Arr_face_extended_dcel` class template (see Section \ref
arr_sssecex_dcel_face). The data field that is attached to an overlay arr_sssecex_dcel_face). The data field that is attached to an overlay
face can be computed from the data fields of the two faces (in `arr_r` face can be computed from the data fields of the two faces (in `arr_r`
@ -6179,7 +6179,7 @@ data fields with all their \dcel records typically also stores
additional data-fields with all its \dcel records. The types of additional data-fields with all its \dcel records. The types of
such arrangements, for example, could be instances of the such arrangements, for example, could be instances of the
`Arrangement_2<Traits,Dcel>` class template, where the `Dcel` `Arrangement_2<Traits,Dcel>` class template, where the `Dcel`
parameters are substituted with instances of the `Arr_extended_dcel` parameters are substituted by instances of the `Arr_extended_dcel`
class template (see Section \ref arr_sssecex_dcel_all). The data field class template (see Section \ref arr_sssecex_dcel_all). The data field
attached to an overlay feature can be computed from the data fields of attached to an overlay feature can be computed from the data fields of
the two features (in `arr_r` and `arr_b`) that induce the overlay the two features (in `arr_r` and `arr_b`) that induce the overlay
@ -6194,7 +6194,7 @@ of the overlay traits can be an instance of the class template
`Arr_face_overlay_traits<ArrangementR,ArrangementB,ArrangementO,OverlayFaceData>`, `Arr_face_overlay_traits<ArrangementR,ArrangementB,ArrangementO,OverlayFaceData>`,
which models the concept `OverlayTraits`. An object of this type which models the concept `OverlayTraits`. An object of this type
operates on face-extended arrangements. When instantiated, the operates on face-extended arrangements. When instantiated, the
`OverlayFaceData` parameter must be substituted with a functor that is `OverlayFaceData` parameter must be substituted by a functor that is
capable of combining two face-data fields of types capable of combining two face-data fields of types
`ArrangementR::Dcel::Face_data` and `ArrangementB::Dcel::Face_data` `ArrangementR::Dcel::Face_data` and `ArrangementB::Dcel::Face_data`
and computing the output `ArrangementO::Dcel::Face_data` object. The and computing the output `ArrangementO::Dcel::Face_data` object. The
@ -6209,7 +6209,7 @@ flag. A polygon is represented as a <em>marked</em> arrangement face
(whose flag is set). The example uses an instance of the (whose flag is set). The example uses an instance of the
`Arr_face_overlay_traits<ArrR,ArrB,ArrO,OverlayFaceData>` class `Arr_face_overlay_traits<ArrR,ArrB,ArrO,OverlayFaceData>` class
template as the face-overlay traits class where the `OverlayFaceData` template as the face-overlay traits class where the `OverlayFaceData`
template parameter is substituted with a functor that simply performs template parameter is substituted by a functor that simply performs
a logical <em>and</em> operation on Boolean flags. As a result, a face a logical <em>and</em> operation on Boolean flags. As a result, a face
in the overlay arrangement is marked only when it corresponds to an in the overlay arrangement is marked only when it corresponds to an
overlapping region of two marked faces in the input overlapping region of two marked faces in the input
@ -6407,12 +6407,12 @@ between these curves and the arrangement edges they induce. Similarly,
the `Arrangement_with_history_2<GeometryTraits,Dcel>` class-template the `Arrangement_with_history_2<GeometryTraits,Dcel>` class-template
extends the `Arrangement_2<GeometryTraits,Dcel>` class template. The extends the `Arrangement_2<GeometryTraits,Dcel>` class template. The
`GeometryTraits` template parameter, of either class templates, must `GeometryTraits` template parameter, of either class templates, must
be substituted with a model of the `ArrangementTraits_2` concept; see be substituted by a model of the `ArrangementTraits_2` concept; see
Section \ref aos_ssec-insert_gen. It should define the \link Section \ref aos_ssec-insert_gen. It should define the \link
ArrangementTraits_2::Curve_2 `Curve_2`\endlink type and support its ArrangementTraits_2::Curve_2 `Curve_2`\endlink type and support its
subdivision into \link ArrangementBasicTraits_2::X_monotone_curve_2 subdivision into \link ArrangementBasicTraits_2::X_monotone_curve_2
`X_monotone_curve_2`\endlink objects, among the others. The `Dcel` `X_monotone_curve_2`\endlink objects, among the others. The `Dcel`
parameter must be substituted with a model of the `ArrangementDcel` parameter must be substituted by a model of the `ArrangementDcel`
concept. You can use either the default \dcel class or an extended concept. You can use either the default \dcel class or an extended
\dcel class (see Section \ref arr_ssecex_dcel) based on your needs. An \dcel class (see Section \ref arr_ssecex_dcel) based on your needs. An
arrangement that support the cross-mapping mentioned above is referred arrangement that support the cross-mapping mentioned above is referred
@ -6489,7 +6489,7 @@ iterators is \link Arrangement_with_history_2::Curve_2
Overlaying two arrangement-with-history objects is possible only if Overlaying two arrangement-with-history objects is possible only if
their types are instances of the their types are instances of the
`Arrangement_with_history_2<Traits,Dcel>` class template, where the `Arrangement_with_history_2<Traits,Dcel>` class template, where the
respective `Traits` parameters are substituted with two traits classes respective `Traits` parameters are substituted by two traits classes
that are convertible to one another. In this case, the resulting that are convertible to one another. In this case, the resulting
arrangement stores a consolidated container of input curves, and arrangement stores a consolidated container of input curves, and
automatically preserves the cross-mapping between the arrangement automatically preserves the cross-mapping between the arrangement
@ -6974,7 +6974,7 @@ algorithm on a dual arrangement. It uses the functor template
information stored inside the faces. The functor implements a property information stored inside the faces. The functor implements a property
map that utilizes the `data()` and `set_data()` member functions of the map that utilizes the `data()` and `set_data()` member functions of the
extended face to update or obtain the property. When the property map extended face to update or obtain the property. When the property map
is instantiated, the `Type` parameter must be substituted with the is instantiated, the `Type` parameter must be substituted by the
same type that is used to extend the arrangement face; see Section same type that is used to extend the arrangement face; see Section
\ref arr_sssecex_dcel_face. The functor template is defined in the \ref arr_sssecex_dcel_face. The functor template is defined in the
header file `Extended_face_property_map.h` listed below. header file `Extended_face_property_map.h` listed below.

4
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_bounded_planar_topology_traits_2.h
View File

@ -9,13 +9,13 @@ namespace CGAL {
* *
* The `Arr_bounded_planar_topology_traits_2` template has two parameters: * The `Arr_bounded_planar_topology_traits_2` template has two parameters:
* <UL> * <UL>
* <LI>The `GeometryTraits_2` template-parameter should be substituted with * <LI>The `GeometryTraits_2` template-parameter should be substituted by
* a model of the `ArrangementBasicTraits_2` concept. The traits * a model of the `ArrangementBasicTraits_2` concept. The traits
* class defines the types of \f$x\f$-monotone curves and two-dimensional * class defines the types of \f$x\f$-monotone curves and two-dimensional
* points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
* `ArrangementBasicTraits_2::Point_2`, * `ArrangementBasicTraits_2::Point_2`,
* respectively, and supports basic geometric predicates on them. * respectively, and supports basic geometric predicates on them.
* <LI>The `Dcel` template-parameter should be substituted with * <LI>The `Dcel` template-parameter should be substituted by
* a class that is a model of the `ArrangementDcel` concept. The * a class that is a model of the `ArrangementDcel` concept. The
* value of this parameter is by default * value of this parameter is by default
* `Arr_default_dcel<Traits>`. * `Arr_default_dcel<Traits>`.

2
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_conic_traits_2.h
View File

@ -58,7 +58,7 @@ namespace CGAL {
* <I>integer</I> coefficient of degree \f$d\f$ such that \f$p(\alpha) = 0\f$). * <I>integer</I> coefficient of degree \f$d\f$ such that \f$p(\alpha) = 0\f$).
* We therefore require separate representations of the curve * We therefore require separate representations of the curve
* coefficients and the point coordinates. The `NtTraits` should be substituted * coefficients and the point coordinates. The `NtTraits` should be substituted
* with a class that defines nested `Integer`, `Rational`, and `Algebraic` number * by a class that defines nested `Integer`, `Rational`, and `Algebraic` number
* types and supports various operations on them, yielding certified computation * types and supports various operations on them, yielding certified computation
* results (for example, it can convert rational numbers to algebraic numbers * results (for example, it can convert rational numbers to algebraic numbers
* and can compute roots of polynomials with integer coefficients). The other * and can compute roots of polynomials with integer coefficients). The other

4
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_spherical_topology_traits_2.h
View File

@ -9,13 +9,13 @@ namespace CGAL {
* *
* The `Arr_spherical_topology_traits_2` template has two parameters: * The `Arr_spherical_topology_traits_2` template has two parameters:
* <UL> * <UL>
* <LI>The `GeometryTraits_2` template-parameter should be substituted with * <LI>The `GeometryTraits_2` template-parameter should be substituted by
* a model of the `ArrangementBasicTraits_2` concept. The traits * a model of the `ArrangementBasicTraits_2` concept. The traits
* class defines the types of \f$x\f$-monotone curves and two-dimensional * class defines the types of \f$x\f$-monotone curves and two-dimensional
* points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
* `ArrangementBasicTraits_2::Point_2`, * `ArrangementBasicTraits_2::Point_2`,
* respectively, and supports basic geometric predicates on them. * respectively, and supports basic geometric predicates on them.
* <LI>The `Dcel` template-parameter should be substituted with * <LI>The `Dcel` template-parameter should be substituted by
* a class that is a model of the `ArrangementDcel` concept. The * a class that is a model of the `ArrangementDcel` concept. The
* value of this parameter is by default * value of this parameter is by default
* `Arr_default_dcel<Traits>`. * `Arr_default_dcel<Traits>`.

4
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_unb_planar_topology_traits_2.h
View File

@ -9,13 +9,13 @@ namespace CGAL {
* *
* The `Arr_unb_planar_topology_traits_2` template has two parameters: * The `Arr_unb_planar_topology_traits_2` template has two parameters:
* <UL> * <UL>
* <LI>The `GeometryTraits_2` template-parameter should be substituted with * <LI>The `GeometryTraits_2` template-parameter should be substituted by
* a model of the `ArrangementBasicTraits_2` concept. The traits * a model of the `ArrangementBasicTraits_2` concept. The traits
* class defines the types of \f$x\f$-monotone curves and two-dimensional * class defines the types of \f$x\f$-monotone curves and two-dimensional
* points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
* `ArrangementBasicTraits_2::Point_2`, * `ArrangementBasicTraits_2::Point_2`,
* respectively, and supports basic geometric predicates on them. * respectively, and supports basic geometric predicates on them.
* <LI>The `Dcel` template-parameter should be substituted with * <LI>The `Dcel` template-parameter should be substituted by
* a class that is a model of the `ArrangementDcel` concept. The * a class that is a model of the `ArrangementDcel` concept. The
* value of this parameter is by default * value of this parameter is by default
* `Arr_default_dcel<Traits>`. * `Arr_default_dcel<Traits>`.

4
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_2.h
View File

@ -16,14 +16,14 @@ namespace CGAL {
* The `Arrangement_on_surface_2` template has two parameters: * The `Arrangement_on_surface_2` template has two parameters:
* <UL> * <UL>
* <LI>The `GeometryTraits` template-parameter should be substituted with * <LI>The `GeometryTraits` template-parameter should be substituted by
* a model of a geometry traits. The minimal requirements are defined by the * a model of a geometry traits. The minimal requirements are defined by the
* `ArrangementBasicTraits_2` concept. A model of this concept defines * `ArrangementBasicTraits_2` concept. A model of this concept defines
* the types of \f$ x\f$-monotone curves and two-dimensional points, namely * the types of \f$ x\f$-monotone curves and two-dimensional points, namely
* `ArrangementBasicTraits_2::X_monotone_curve_2` and * `ArrangementBasicTraits_2::X_monotone_curve_2` and
* `ArrangementBasicTraits_2::Point_2`, respectively, and supports basic * `ArrangementBasicTraits_2::Point_2`, respectively, and supports basic
* geometric predicates on them. * geometric predicates on them.
* <LI>The `TopologyTraits` template-parameter should be substituted with a * <LI>The `TopologyTraits` template-parameter should be substituted by a
* class that is a model of the `ArrangementTopologyTraits` concept. * class that is a model of the `ArrangementTopologyTraits` concept.
* </UL> * </UL>
* *

4
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_with_history_2.h
View File

@ -25,14 +25,14 @@ namespace CGAL {
* The `Arrangement_on_surface_with_history_2` template has two parameters: * The `Arrangement_on_surface_with_history_2` template has two parameters:
* *
* <UL> * <UL>
* <LI>The `GeometryTraits` template-parameter should be substituted with a * <LI>The `GeometryTraits` template-parameter should be substituted by a
* model of the `ArrangementTraits_2` concept. The traits class defines the * model of the `ArrangementTraits_2` concept. The traits class defines the
* `Curve_2` type, which represents an input curve. It also defines the types * `Curve_2` type, which represents an input curve. It also defines the types
* of \f$ x\f$-monotone curves and two-dimensional points, namely * of \f$ x\f$-monotone curves and two-dimensional points, namely
* `ArrangementTraits_2::X_monotone_curve_2` and * `ArrangementTraits_2::X_monotone_curve_2` and
* `ArrangementTraits_2::Point_2`, respectively, and supports basic * `ArrangementTraits_2::Point_2`, respectively, and supports basic
* geometric predicates on them. * geometric predicates on them.
* <LI>The `TopologyTraits` template-parameter should be substituted with a * <LI>The `TopologyTraits` template-parameter should be substituted by a
* class that is a model of the `ArrangementTopologyTraits` concept. * class that is a model of the `ArrangementTopologyTraits` concept.
* </UL> * </UL>
* *

4
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_with_history_2.h
View File

@ -23,13 +23,13 @@ namespace CGAL {
* *
* The `Arrangement_with_history_2` template has two parameters: * The `Arrangement_with_history_2` template has two parameters:
* <UL> * <UL>
* <LI>The `Traits` template-parameter should be substituted with a model of * <LI>The `Traits` template-parameter should be substituted by a model of
* the `ArrangementTraits_2` concept. The traits class defines the `Curve_2` * the `ArrangementTraits_2` concept. The traits class defines the `Curve_2`
* type, which represents an input curve. It also defines the types of \f$ * type, which represents an input curve. It also defines the types of \f$
* x\f$-monotone curves and two-dimensional points, namely * x\f$-monotone curves and two-dimensional points, namely
* `ArrangementTraits_2::X_monotone_curve_2` and `ArrangementTraits_2::Point_2`, * `ArrangementTraits_2::X_monotone_curve_2` and `ArrangementTraits_2::Point_2`,
* respectively, and supports basic geometric predicates on them. * respectively, and supports basic geometric predicates on them.
* <LI>The `Dcel` template-parameter should be substituted with a class that is * <LI>The `Dcel` template-parameter should be substituted by a class that is
* a model of the `ArrangementDcelWithRebind` concept. The value of this * a model of the `ArrangementDcelWithRebind` concept. The value of this
* parameter is by default `Arr_default_dcel<Traits>`. * parameter is by default `Arr_default_dcel<Traits>`.
* </UL> * </UL>

2
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementLandmarkTraits_2.h
View File

@ -7,7 +7,7 @@
* associated with the landmark point-location strategy (see * associated with the landmark point-location strategy (see
* `CGAL::Arr_landmarks_point_location`) must be an instance of the * `CGAL::Arr_landmarks_point_location`) must be an instance of the
* `CGAL::Arrangement_2<Traits,Dcel>` class template, where the Traits parameter * `CGAL::Arrangement_2<Traits,Dcel>` class template, where the Traits parameter
* is substituted with a model of this concept. * is substituted by a model of this concept.
* *
* \cgalRefines{ArrangementApproximateTraits_2,ArrangementConstructXMonotoneCurveTraits_2} * \cgalRefines{ArrangementApproximateTraits_2,ArrangementConstructXMonotoneCurveTraits_2}
* *