CGAL 5.4  2D Polygons

The CGAL::Polygon_2
class and the functions that implement the functionality found in that class each are parameterized by a traits class that defines the primitives used in the algorithms. The concept PolygonTraits_2
defines this common set of requirements.
The requirements of PolygonTraits_2
are a subset of the kernel requirements. We only list the types and methods which are required and refer to the description of the kernel concept for details.
DefaultConstructible
and CopyConstructable
The kernels supplied by CGAL are models of PolygonTraits_2
.
CGAL::Projection_traits_xy_3<K>
CGAL::Polygon_2<PolygonTraits_2, Container>
Types  
typedef unspecified_type  FT 
number type  
typedef unspecified_type  Point_2 
The point type.  
typedef unspecified_type  Segment_2 
The segment type.  
typedef unspecified_type  Construct_segment_2 
functor providing Segment_2 operator()(Point_2, Point_2) to construct a segment from two points.  
typedef unspecified_type  Equal_2 
functor providing bool operator()(Point_2, Point_2) to test equality of two points.  
typedef unspecified_type  Less_xy_2 
functor providing bool operator()(Point_2, Point_2) to compare lexicographically of two points.  
typedef unspecified_type  Less_yx_2 
functor providing bool operator()(Point_2, Point_2) to compare inverselexicographically of two points.  
typedef unspecified_type  Compare_x_2 
functor providing bool operator()(Point_2, Point_2) to compare the xcoordinate of two points.  
typedef unspecified_type  Compare_y_2 
functor providing bool operator()(Point_2, Point_2) to compare the ycoordinate of two points.  
typedef unspecified_type  Orientation_2 
functor providing Oriention operator()(Point_2 p, Point_2 q, Point_2 r) that returns CGAL::LEFT_TURN, if r lies to the left of the oriented line l defined by p and q, CGAL::RIGHT_TURN if r lies to the right of l, and CGAL::COLLINEAR if r lies on l.  
typedef unspecified_type  Compute_area_2 
Computes the signed area of the oriented triangle defined by 3 Point_2 passed as arguments.  
Operations  
The following functions that create instances of the above predicate object types must exist.  
Equal_2  equal_2_object () 
returns the corresponding function object  
Less_xy_2  less_xy_2_object () 
returns the corresponding function object  
Less_yx_2  less_yx_2_object () 
returns the corresponding function object  
Compare_y_2  compare_y_2_object () 
returns the corresponding function object  
Compare_x_2  compare_x_2_object () 
returns the corresponding function object  
Orientation_2  orientation_2_object () 
returns the corresponding function object  
Compute_area_2  compute_area_2_object () 
returns the corresponding function object  
Construct_segment_2  construct_segment_2_object () 
returns the corresponding function object  