\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.8.1 - 2D Triangulation
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
TriangulationTraits_2 Concept Reference
Concepts

Definition

The concept TriangulationTraits_2 describes the set of requirements to be fulfilled by any class used to instantiate the first template parameter of the class CGAL::Triangulation_2<Traits,Tds>. This concept provides the types of the geometric primitives used in the triangulation and some function object types for the required predicates on those primitives.

Has Models:

All the CGAL Kernels

CGAL::Triangulation_euclidean_traits_2<K>

CGAL::Projection_traits_xy_3<K>

CGAL::Projection_traits_yz_3<K>

CGAL::Projection_traits_xz_3<K>

See Also
CGAL::Triangulation_2<Traits,Tds>

Types

typedef unspecified_type Point_2
 The point type.
 
typedef unspecified_type Segment_2
 The segment type.
 
typedef unspecified_type Triangle_2
 The triangle type.
 
typedef unspecified_type Construct_segment_2
 A function object to construct a Segment_2. More...
 
typedef unspecified_type Construct_triangle_2
 A function object to construct a Triangle_2. More...
 
typedef unspecified_type Less_x_2
 A function object to compare the x-coordinate of two points. More...
 
typedef unspecified_type Less_y_2
 A function object to compare the y-coordinate of two points. More...
 
typedef unspecified_type Compare_x_2
 A function object to compare the x-coordinate of two points. More...
 
typedef unspecified_type Compare_y_2
 A function object to compare the y-coordinate of two points. More...
 
typedef unspecified_type Orientation_2
 A function object to compute the orientation of three points. More...
 
typedef unspecified_type Side_of_oriented_circle_2
 A function object to perform the incircle test for four points. More...
 
typedef unspecified_type Construct_circumcenter_2
 A function object to compute the circumcentr of three points. More...
 

Creation

Only a default constructor, copy constructor and an assignment operator are required.

Note that further constructors can be provided.

 TriangulationTraits_2 ()
 default constructor.
 
 TriangulationTraits_2 (TriangulationTraits_2 gtr)
 Copy constructor.
 
TriangulationTraits_2 operator= (TriangulationTraits_2 gtr)
 Assignment operator.
 

Predicate Functions

The following functions give access to the predicate and constructor objects.

Construct_segment_2 construct_segment_2_object ()
 
Construct_triangle_2 construct_triangle_2_object ()
 
Compare_x_2 compare_x_2_object ()
 
Compare_y_2 compare_y_2_object ()
 
Orientation_2 orientation_2_object ()
 
Side_of_oriented_circle_2 side_of_oriented_circle_2_object ()
 Required only if side_of_oriented_circle is called called.
 
Construct_circumcenter_2 construct_circumcenter_2_object ()
 Required only if circumcenter is called.
 

Member Typedef Documentation

typedef unspecified_type TriangulationTraits_2::Compare_x_2

A function object to compare the x-coordinate of two points.

Provides the operator:

Comparison_result operator()(Point p, Point q)

which returns SMALLER, EQUAL or LARGER according to the \( x\)-ordering of points p and q.

typedef unspecified_type TriangulationTraits_2::Compare_y_2

A function object to compare the y-coordinate of two points.

Provides the operator:

Comparison_result operator()(Point p, Point q)

which returns (SMALLER, EQUAL or LARGER) according to the \( y\)-ordering of points p and q.

typedef unspecified_type TriangulationTraits_2::Construct_circumcenter_2

A function object to compute the circumcentr of three points.

Provides the operator:

Point operator()(Point p, Point q, Point r)

which returns the circumcenter of the three points p, q and r. This type is required only if the function Point circumcenter(Face_handle f)is called.

typedef unspecified_type TriangulationTraits_2::Construct_segment_2

A function object to construct a Segment_2.

Provides:

Segment_2 operator()(Point_2 p,Point_2 q),

which constructs a segment from two points.

typedef unspecified_type TriangulationTraits_2::Construct_triangle_2

A function object to construct a Triangle_2.

Provides:

Triangle_2 operator()(Point_2 p,Point_2 q,Point_2 r ),

which constructs a triangle from three points.

typedef unspecified_type TriangulationTraits_2::Less_x_2

A function object to compare the x-coordinate of two points.

Provides the operator:

bool operator()(Point p, Point q)

which returns true if p is before q according to the \( x\)-ordering of points.

typedef unspecified_type TriangulationTraits_2::Less_y_2

A function object to compare the y-coordinate of two points.

Provides the operator:

bool operator()(Point p, Point q)

which returns true if p is before q according to the \( y\)-ordering of points.

typedef unspecified_type TriangulationTraits_2::Orientation_2

A function object to compute the orientation of three points.

Provides the operator:

Orientation operator()(Point p, Point q, Point r)

which returns LEFT_TURN, RIGHT_TURN or COLLINEAR depending on \( r\) being, with respect to the oriented line pq, on the left side , on the right side or on the line.

typedef unspecified_type TriangulationTraits_2::Side_of_oriented_circle_2

A function object to perform the incircle test for four points.

Provides the operator:

Oriented_side operator()(Point p, Point q, Point r, Point s) which takes four points \( p, q, r, s\) as arguments and returns ON_POSITIVE_SIDE, ON_NEGATIVE_SIDE or, ON_ORIENTED_BOUNDARY according to the position of points s with respect to the oriented circle through through \( p,q\) and \( r\). This type is required only if the function side_of_oriented_circle(Face_handle f, Point p) is called.