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CGAL 6.0 - 2D Conforming Triangulations and Meshes
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The concept ConformingDelaunayTriangulationTraits_2 refines the concept ConstrainedDelaunayTriangulationTraits_2 by providing a numeric field type FT, a type Vector_2 and several constructors on Vector_2, Point_2, and a predicate on angles. The field type has to be a model of the concept FieldWithSqrt. This field type and the constructors are used by the conforming algorithm to compute Steiner points on constrained edges.
DelaunayTriangulationTraits_2 Kernel CGAL::Projection_traits_xy_3<K> Types | |
| typedef unspecified_type | FT |
| The field type. | |
| typedef unspecified_type | Vector_2 |
| The vector type. | |
| typedef unspecified_type | Construct_vector_2 |
| Constructor object. | |
| typedef unspecified_type | Construct_scaled_vector_2 |
| Constructor object. | |
| typedef unspecified_type | Construct_translated_point_2 |
| Constructor object. | |
| typedef unspecified_type | Construct_midpoint_2 |
| Constructor object. | |
| typedef unspecified_type | Compute_squared_distance_2 |
| Constructor object. | |
| typedef unspecified_type | Angle_2 |
| Predicate object. | |
| typedef unspecified_type | Oriented_side_2 |
| Predicate object. | |
Access to predicate and constructor objects | |
| Construct_vector_2 | construct_vector_2_object () |
| Construct_scaled_vector_2 | construct_scaled_vector_2_object () |
| Construct_translated_point_2 | construct_translated_point_2_object () |
| Construct_midpoint_2 | construct_midpoint_2_object () |
| Compute_squared_distance_2 | compute_squared_distance_2_object () |
| Angle_2 | angle_2_object () |
Predicate object.
Must provide the operator CGAL::Angle operator()(Point_2 p, Point_2 q, Point_2 r) that returns OBTUSE, RIGHT or ACUTE depending on the angle formed by the three points p, q, r (q being the vertex of the angle).
Constructor object.
Must provide the operator FT operator()(Point_2 a, Point_2 b) that computes the squared distance between a and b.
Constructor object.
Must provide the operator Point_2 operator()(Point_2 a, Point_2 b) that computes the midpoint of the segment \( ab\).
Constructor object.
Must provide the operator Vector_2 operator()(Vector_2 v, FT scale) that computes the vector scale \(\cdot\) v.
Constructor object.
Must provide the operator Point_2 operator()(Point_2 p, Vector_2 v) that computes the point p+v.
Constructor object.
Must provide the operator Vector_2 operator()(Point a, Point b) that computes the vector b-a.
The field type.
It must be a model of FieldWithSqrt, that is must be a number type supporting the operations \( +\), \( -\), \( *\), \( /\), and \( \sqrt{\cdot}\).
Predicate object.
Must provide the operator CGAL::Oriented_side operator()(Segment_2 s, Triangle_2 t) that returns CGAL::ON_ORIENTED_BOUNDARY, CGAL::ON_NEGATIVE_SIDE, or CGAL::ON_POSITIVE_SIDE, depending on the position of the circumcenter of t relative to the oriented supporting line of s. The orientation of the supporting line is the same as the orientation of s.