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CGAL 5.5.5 - 2D Triangulations
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CGAL 5.5.5 - 2D Triangulations
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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.
All models of Kernel.
CGAL::Projection_traits_xy_3<K>
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. | |
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.
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.
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.
A function object to construct a Point_2.
Provides:
Point_2 operator()(Point_2 p),
which simply returns p.
p to avoid useless copies.CGAL::Triangulation_2 internally manipulates points with a Point type that is not always Point_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.
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.
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.
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.
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.
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.
1.8.13