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
.