ConstrainedTriangulationTraits_2 Concept Reference

Definition

The concept ConstrainedTriangulationTraits_2 defines the requirements for the geometric traits class of a constrained triangulation ( CGAL::Constrained_triangulation_2<Traits,Tds,Itag>) that supports intersections of input constraints (i. e. when the template parameter Itag is instantiated by one of the tag classes CGAL::Exact_intersections_tag or CGAL::Exact_predicates_tag). This concept refines the concept TriangulationTraits_2, adding requirements for function objects to compute the intersection points of two constraints. When CGAL::Exact_predicates_tag is used, the traits class is also required to provide additional types to compute the squared distance between a point and a line.

Refines

TriangulationTraits_2

Has models

All models of the CGAL concept Kernel

CGAL::Projection_traits_3<K>

CGAL::Projection_traits_xy_3<K>

CGAL::Projection_traits_yz_3<K>

CGAL::Projection_traits_xz_3<K>

See also

TriangulationTraits_2

ConstrainedDelaunayTriangulationTraits_2

CGAL::Constrained_triangulation_2<Traits,Tds,Itag>

Types
typedef unspecified_type	Intersect_2
	A function object whose operator() computes the intersection of two segments.

Types required with Exact_predicates_tag
When the constrained triangulation is instantiated with the intersection tag CGAL::Exact_predicates_tag, the used algorithm needs to be able to compare some distances between points and lines and the following types are further required.
typedef unspecified_type	RT
	A number type supporting the comparison operator <.
typedef unspecified_type	Line_2
	The line type.
typedef unspecified_type	Construct_line_2
	A function object whose operator() constructs a line from two points.
typedef unspecified_type	Compute_squared_distance_2
	A function object whose operator() computes the squared distance between a line and a point.
typedef unspecified_type	Compute_bounding_box_2
	A function object whose operator() computes the bounding box of a point.

Access to Constructor Objects
Intersect_2	intersect_2_object ()
Construct_line_2	construct_line_2_object ()
	required when the intersection tag is CGAL::Exact_predicates_tag.
Compute_squared_distance_2	compute_squared_distance_2_object ()
	required when the intersection tag is CGAL::Exact_predicates_tag.

Member Typedef Documentation

Compute_bounding_box_2

typedef unspecified_type ConstrainedTriangulationTraits_2::Compute_bounding_box_2

A function object whose operator() computes the bounding box of a point.

CGAL::Bbox_2 operator()(Point_2 p); Returns the bounding box of p. The result type is CGAL::Bbox_2 (even for projection traits classes).

Compute_squared_distance_2

typedef unspecified_type ConstrainedTriangulationTraits_2::Compute_squared_distance_2

A function object whose operator() computes the squared distance between a line and a point.

RT operator()(Line_2 l, Point_2 p); Returns the squared distance between p and l.

Construct_line_2

typedef unspecified_type ConstrainedTriangulationTraits_2::Construct_line_2

A function object whose operator() constructs a line from two points.

Line_2 operator()(Point_2 p1, Point_2 p2).

Intersect_2

typedef unspecified_type ConstrainedTriangulationTraits_2::Intersect_2

A function object whose operator() computes the intersection of two segments.

std::optional<std::variant<Point_2,Segment_2> > operator()(Segment_2 s1, Segment_2 s2); Returns the intersection of s1 and s2.