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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 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.
| TriangulationTraits_2::Point_2 | |
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The point type.
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| TriangulationTraits_2::Segment_2 | |
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The segment type.
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| TriangulationTraits_2::Triangle_2 | |
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The triangle type.
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| TriangulationTraits_2::Construct_segment_2 | |
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A constructor object for
Segment_2. Provides : Segment_2 operator()(Point_2 p,Point_2 q), which constructs a segment from two points.
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| TriangulationTraits_2::Construct_triangle_2 | |
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A constructor object for
Triangle_2. Provides : Triangle_2 operator()(Point_2 p,Point_2 q,Point_2 r ), which constructs a triangle from three points.
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| TriangulationTraits_2::Less_x_2 | |
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Predicate object. Provides
the operator : bool operator()(Point p, Point q) which returns true if p is before q according to the x-ordering of points.
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| TriangulationTraits_2::Less_y_2 | |
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Predicate object. Provides
the operator : bool operator()(Point p, Point q) which returns true if p is before q according to the y-ordering of points.
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| TriangulationTraits_2::Compare_x_2 | |
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Predicate object. 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.
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| TriangulationTraits_2::Compare_y_2 | |
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Predicate object. 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.
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| TriangulationTraits_2::Orientation_2 | |
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Predicate object. 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.
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| TriangulationTraits_2::Side_of_oriented_circle_2 | |
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Predicate object. Must
provide 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.
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| TriangulationTraits_2::Construct_circumcenter_2 | |
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Constructor object. 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.
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| TriangulationTraits_2 traits; | |
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default constructor.
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| TriangulationTraits_2 traits ( gtr); | |
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Copy constructor
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| TriangulationTraits_2 | traits = gtr | Assignment operator. |
| Construct_segment_2 | traits.construct_segment_2_object () | |
| Construct_triangle_2 | traits.construct_triangle_2_object () | |
| Comparison_x_2 | traits.compare_x_2_object () | |
| Comparison_y_2 | traits.compare_y_2_object () | |
| Orientation_2 | traits.orientation_2_object () | |
| Side_of_oriented_circle_2 | traits.side_of_oriented_circle_2_object () | |
| Required only if side_of_oriented_circle is called called. | ||
| Construct_circumcenter_2 | traits.construct_circumcenter_2_object () | |
| Required only if circumcenter is called. | ||