mirror of https://github.com/CGAL/cgal
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Andreas Fabri
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@ -3,7 +3,7 @@
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\ingroup PkgPolygon2Concepts
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\cgalconcept
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The `Polygon_2` class and the functions that implement the
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The `CGAL::Polygon_2` class and the functions that implement the
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functionality found in that class each are parameterized by a traits
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class that defines the primitives used in the algorithms. The concept
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`PolygonTraits_2` defines this common set of requirements.
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@ -94,7 +94,7 @@ typedef Hidden_type Compute_area_2;
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/// @}
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/// \name Operations
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CONVERROR Check if this needs to be spread\n/// The following functions that create instances of the above predicate object types must exist.
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/// The following functions that create instances of the above predicate object types must exist.
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/// @{
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/*!
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@ -25,14 +25,14 @@ The following algorithms are available:
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All those operations take two forward iterators as parameters in order to
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describe the polygon. These parameters have a point type as value type.
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The type Polygon_2 can be used to represent polygons.
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The type `Polygon_2` can be used to represent polygons.
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Polygons are dynamic. Vertices can be modified, inserted and erased.
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They provide the algorithms described above as member functions.
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Moreover, they provide ways of iterating over the vertices and edges.
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Currently, the Polygon_2 class is a nice wrapper around a container of
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Currently, the `Polygon_2` class is a nice wrapper around a container of
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points, but little more. Especially, computed values are not cached.
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That is, when the Polygon_2::is_simple() member function is called
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That is, when the `Polygon_2::is_simple()` member function is called
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twice or more, the result is computed each time anew.
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\section Examples
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@ -62,8 +62,8 @@ are organized in parallel slices, generated by segmentation
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of image data from a scanner.
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In order to avoid an explixit projection on the \c xy plane, one can
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use the traits class Projection_traits_xy_3 which is part of the 2D
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and 3D Linear Geometric Kernel.
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use the traits class `Projection_traits_xy_3` which is part of the 2D
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and 3D Linear Geometric %Kernel.
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\include projected_polygon.cpp
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@ -53,8 +53,7 @@ namespace CGAL {
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/// can be any class that fulfills the requirements for an STL
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/// container. It defaults to the std::vector class.
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///
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/// Implementation
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/// --------------
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/// ### Implementation ###
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///
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/// The methods `is_simple()`, `is_convex()`, `orientation()`,
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/// `oriented_side()`, `bounded_side()`, `bbox()`, `area()`, `left_vertex()`,
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@ -63,11 +62,7 @@ namespace CGAL {
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/// the corresponding global functions for information about which
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/// algorithms were used and what complexity they have.
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///
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/// Example
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/// -------
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/// The following code fragment creates a polygon and checks if it is convex.
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///
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/// \cgalexample{Polygon.cpp}
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template <class Traits_P, class Container_P
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= std::vector<typename Traits_P::Point_2> >
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class Polygon_2 {
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@ -50,7 +50,7 @@ namespace CGAL {
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/// with the smallest `y`-coordinate is taken.
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///
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/// \requires `Traits` is a model of the concept `PolygonTraits_2`.
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/// In fact, only the members `Less_xy_2` and
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/// Only the members `Less_xy_2` and
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/// `less_xy_2_object()` are used.
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/// \requires The value type of `ForwardIterator` must be `Traits::Point_2`,
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///
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@ -68,7 +68,7 @@ ForwardIterator left_vertex_2(ForwardIterator first,
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/// with the largest `y`-coordinate is taken.
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///
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2`
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/// `PolygonTraits_2`.
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/// In fact, only the members `Less_xy_2` and
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/// `less_xy_2_object()` are used.
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/// \requires The value type of `ForwardIterator` must be `Traits::Point_2`,
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@ -88,8 +88,8 @@ ForwardIterator right_vertex_2(ForwardIterator first,
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/// with the largest `x`-coordinate is taken.
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///
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2`
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/// In fact, only the members `Less_yx_2` and
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/// `PolygonTraits_2`.
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/// Only the members `Less_yx_2` and
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/// `less_yx_2_object()` are used.
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/// \requires The value type of `ForwardIterator` must be `Traits::Point_2`,
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///
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@ -107,8 +107,8 @@ ForwardIterator top_vertex_2(ForwardIterator first,
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/// with the smallest `x`-coordinate is taken.
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///
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2`
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/// In fact, only the members `Less_yx_2` and
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/// `PolygonTraits_2`.
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/// Only the members `Less_yx_2` and
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/// `less_yx_2_object()` are used.
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/// \requires The value type of `ForwardIterator` must be `Traits::Point_2`,
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///
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@ -126,8 +126,8 @@ ForwardIterator bottom_vertex_2(ForwardIterator first,
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/// Returns the bounding box of the range `[first,last)`.
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///
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2`
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/// In fact, only the members `Construct_bbox_2` and
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/// `PolygonTraits_2`.
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/// Only the members `Construct_bbox_2` and
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/// `construct_bbox_2_object()` are used.
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/// \requires The value type of `InputIterator` must be `Traits::Point_2`.
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///
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@ -146,7 +146,7 @@ Bbox_2 bbox_2(InputIterator first,
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/// returns the area instead of taking it as a parameter.
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///
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2
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/// `PolygonTraits_2.
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/// Only the following members of this traits class are used:
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/// - `Compute_area_2` : Computes the signed area of the
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/// oriented triangle defined by 3 `Point_2` passed as arguments.
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@ -218,10 +218,10 @@ polygon_area_2( ForwardIterator first, ForwardIterator last,
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return result;
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}
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/// The function is_convex_2 computes if a polygon is convex.
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/// Checks if the polygon is convex.
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///
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2`
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Less_xy_2`
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/// - `Orientation_2`
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@ -236,14 +236,12 @@ bool is_convex_2(ForwardIterator first,
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ForwardIterator last,
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const Traits& traits);
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/// The function is_simple_2 computes if a polygon is simple, that is, if the edges
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/// Checks if the polygon defined by the
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/// iterator range `[first,last)` is simple, that is, if the edges
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/// do not intersect, except consecutive edges in their common vertex.
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///
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/// Checks if the polygon defined by the
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/// iterator range `[first,last)` is simple.
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///
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2`
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Point_2`
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/// - `Less_xy_2`
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@ -252,12 +250,11 @@ bool is_convex_2(ForwardIterator first,
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/// - `orientation_2_object()`
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/// \requires The value type of `ForwardIterator` must be `Traits::Point_2`,
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///
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/// Implementation
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/// --------------
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/// ### Implementation##
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///
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/// The simplicity test is implemented by means of a plane sweep algorithm.
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/// The algorithm is quite robust when used with inexact number types.
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/// The running time is O(n log n), where n is the number of vertices of the
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/// The running time is `O(n log n)`, where n is the number of vertices of the
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/// polygon.
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///
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/// \sa `PolygonTraits_2 `
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// In the following two functions we would like to use Traits::Point_2
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// instead of Point, but this is not allowed by g++ 2.7.2.
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///
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/// The function oriented_side_2 computes on which side of a polygon a point lies.
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/// Computes on which side of a polygon a point lies.
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2`
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Less_xy_2`
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/// - `Compare_x_2`
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@ -295,8 +292,7 @@ Oriented_side oriented_side_2(ForwardIterator first,
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const Point& point,
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const Traits& traits);
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/// The function bounded_side_2 computes if a point lies inside a polygon.
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/// The function bounded_side_2 computes if a point lies inside a polygon.
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/// Computes if a point lies inside a polygon.
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/// The polygon is defined by the sequence of points `[first,last)`.
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/// Being inside is defined by the odd-even rule. If we take a ray starting at the
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/// point and extending to infinity (in any direction), we count the number of
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@ -307,7 +303,7 @@ Oriented_side oriented_side_2(ForwardIterator first,
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///
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///
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2`
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Compare_x_2`
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/// - `Compare_y_2`
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@ -317,8 +313,7 @@ Oriented_side oriented_side_2(ForwardIterator first,
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/// - `orientation_2_object()`
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/// \requires The value type of `ForwardIterator` must be `Traits::Point_2`,
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///
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/// Implementation
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/// --------------
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/// ### Implementation ###
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///
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/// The running time is linear in the number of vertices of the polygon.
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/// A horizontal ray is taken to count the number of intersections.
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const Point& point,
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const Traits& traits);
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/// The function orientation_2 computes if a polygon is clockwise or counterclockwise
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/// oriented.
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/// Computes if a polygon is clockwise or counterclockwise oriented.
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/// \pre `is_simple_2(first, last, traits);`
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///
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/// \requires `Traits` is a model of the concept
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/// `PolygonTraits_2`
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Less_xy_2`
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/// - `less_xy_2_object()`
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