\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11 - 2D Polygon Partitioning
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
PartitionTraits_2 Concept Reference
Concepts

Definition

The polygon partitioning functions are each parameterized by a traits class that defines the primitives used in the algorithms. Many requirements are common to all traits classes. The concept PartitionTraits_2 defines this common set of requirements.

Has Models:
CGAL::Partition_traits_2<R>
See Also
CGAL::approx_convex_partition_2()
CGAL::greene_approx_convex_partition_2()
CGAL::optimal_convex_partition_2()
CGAL::y_monotone_partition_2()

Types

typedef unspecified_type Point_2
 The point type on which the partitioning algorithm operates.
 
typedef unspecified_type Polygon_2
 The polygon type to be created by the partitioning algorithm. More...
 
typedef unspecified_type Less_xy_2
 Predicate object type that compares Point_2s lexicographically. More...
 
typedef unspecified_type Less_yx_2
 Same as Less_xy_2 with the roles of \( x\) and \( y\) interchanged.
 
typedef unspecified_type Left_turn_2
 Predicate object type that provides bool operator()(Point_2 p,Point_2 q,Point_2 r), which returns true iff r lies to the left of the oriented line through p and q.
 
typedef unspecified_type Orientation_2
 Predicate object type that provides CGAL::Orientation 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 \( q\), returns CGAL::RIGHT_TURN if \( r\) lies to the right of \( l\), and returns CGAL::COLLINEAR if \( r\) lies on \( l\).
 
typedef unspecified_type Compare_y_2
 Predicate object type that provides CGAL::Comparision_result operator()(Point_2 p, Point_2 q) to compare the \( y\) values of two points. More...
 
typedef unspecified_type Compare_x_2
 The same as Compare_y_2, except that \( x\) coordinates are compared instead of \( y\).
 

Creation

A copy constructor and default constructor are required.

 PartitionTraits_2 ()
 
 PartitionTraits_2 (PartitionTraits_2 tr)
 

Operations

The following functions that create instances of the above predicate object types must exist.

Less_yx_2 less_yx_2_object () const
 
Less_xy_2 less_xy_2_object () const
 
Left_turn_2 left_turn_2_object () const
 
Orientation_2 orientation_2_object () const
 
Compare_y_2 compare_y_2_object () const
 
Compare_x_2 compare_x_2_object () const
 

Member Typedef Documentation

typedef unspecified_type PartitionTraits_2::Compare_y_2

Predicate object type that provides CGAL::Comparision_result operator()(Point_2 p, Point_2 q) to compare the \( y\) values of two points.

The operator must return CGAL::SMALLER if \( p_y < q_y\), CGAL::LARGER if \( p_y > q_y\) and CGAL::EQUAL if \( p_y = q_y\).

typedef unspecified_type PartitionTraits_2::Less_xy_2

Predicate object type that compares Point_2s lexicographically.

Must provide bool operator()(Point_2 p, Point_2 q) where true is returned iff \( p <_{xy} q\). We have \( p<_{xy}q\), iff \( p_x < q_x\) or \( p_x = q_x\) and \( p_y < q_y\), where \( p_x\) and \( p_y\) denote the \( x\) and \( y\) coordinates of point \( p\), respectively.

typedef unspecified_type PartitionTraits_2::Polygon_2

The polygon type to be created by the partitioning algorithm.

For testing the validity postcondition of the partition, this type should provide a nested type Vertex_const_iterator that is the type of the iterator over the polygon vertices and member functions Vertex_const_iterator vertices_begin() and Vertex_const_iterator vertices_end().