Definition

Refines:: SpatialSortingTraits_2

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 models of Kernel.

CGAL::Projection_traits_xy_3<K>

CGAL::Projection_traits_yz_3<K>

CGAL::Projection_traits_xz_3<K>

See Also: CGAL::Triangulation_2

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_point_2
	A function object to construct a `Point_2`. More...

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_point_2	construct_point_2_object ()

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_point_2

A function object to construct a Point_2.

Provides:

Point_2 operator()(Point_2 p),

which simply returns p.

Note: It is advised to return a const reference to p to avoid useless copies.; This peculiar requirement is necessary because CGAL::Triangulation_2 internally manipulates points with a Point type that is not always Point_2.

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.

Definition

Types

Creation

Predicate Functions

Member Typedef Documentation