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## ConstrainedTriangulationTraits_2

### Definition

The concept ConstrainedTriangulationTraits_2 defines the requirements for the geometric traits class of a constrained triangulation ( 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 Exact_intersections_tag or Exact_predicates_tag). This concept refines the concept TriangulationTraits_2, adding requirements for function objects to compute the intersection points of two constraints. When Exact_predicates_tag is used, the traits class is also required to provide additionnal types to compute the squared distance between a point and a line

### Refines

TriangulationTraits_2

### Types

ConstrainedTriangulationTraits_2::Intersect_2
| A function object whose operator() computes the intersection of two segments : Object_2 operator()(Segment_2 s1, Segment_2 s2); Returns the intersection of s1 and s2.

When the constrained triangulation is instantiated with the intersection tag Exact_predicates_tag, the used agorithms needs to be able to compare some distances between points and lines and the following types are further required.

ConstrainedTriangulationTraits_2::RT
| A number type supporting the comparison operator <.
ConstrainedTriangulationTraits_2::Line_2
| The line 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).
ConstrainedTriangulationTraits_2::Compute_squared_distance_2
| A function object with an operator() designed to compute the squared distance between a line and a point : RT operator()(Point_2 p1, Line_2); Return the squared distance betwen p and l.

### Access to constructor object

Intersect_2 | traits.intersect_2_object ()
Construct_line_2 | traits.construct_line_2_object ()
|  | required when the intersection tag is Exact_predicates_tag.
Compute_squared_distance_2
| traits.compute_squared_distance_2_object ()
|  | required when the intersection tag is Exact_predicates_tag.

### Has Models

The kernels of CGAL are models for this traits class.

### See Also

TriangulationTraits_2
ConstrainedDelaunayTriangulationTraits_2
CGAL:Constrained_Triangulation_2<Traits,Tds,Itag>

Next: Constrained_Delaunay_triangulation_2<Traits,Tds,Itag>

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The CGAL Project . Tue, December 21, 2004 .