CGAL 5.1.2 - 2D Triangulation
|
In addition to the requirements of the concept TriangulationTraits_2
the concept DelaunayTriangulationTraits_2
requires a predicate to check the empty circle property. The corresponding predicate type is called type Side_of_oriented_circle_2
.
The additional types Line_2
, Ray_2
and the constructor objects Construct_ray_2
, Construct_circumcenter_2
, Construct_bisector_2
, Construct_midpoint
are used to build the dual Voronoi diagram and are required only if the dual functions are called. The additional predicate type Compare_distance_2
is required if the method nearest_vertex()
is used.
CGAL kernels
CGAL::Projection_traits_xy_3<K>
(not for dual Voronoi functions)
CGAL::Projection_traits_yz_3<K>
(not for dual Voronoi functions)
CGAL::Projection_traits_xz_3<K>
(not for dual Voronoi functions)
TriangulationTraits_2
Types | |
typedef unspecified_type | Line_2 |
The line type. More... | |
typedef unspecified_type | Ray_2 |
The type for ray. More... | |
typedef unspecified_type | Side_of_oriented_circle_2 |
A function object to perform an incircle test for a point and three other points. More... | |
typedef unspecified_type | Compare_distance_2 |
A function object to compare two distances for three points. More... | |
typedef unspecified_type | Construct_circumcenter_2 |
A function object to construct the circumcenter of three points. More... | |
typedef unspecified_type | Construct_bisector_2 |
A function object to construct the bisector of two points. More... | |
typedef unspecified_type | Construct_ray_2 |
A function object to build a ray from a point and a line. More... | |
Creation | |
DelaunayTriangulationTraits_2 () | |
default constructor. | |
DelaunayTriangulationTraits_2 (DelaunayTriangulationTraits_2 dtt) | |
copy constructor | |
DelaunayTriangulationTraits_2 | operator= (traits2) |
Assignment operator. | |
Access to Predicate and Constructor Objects | |
Side_of_oriented_circle_2 | side_of_oriented_circle_2_object () |
The following functions are required only if member functions of the Delaunay triangulation relative to the dual Voronoi diagram are called. | |
Compare_distance_2 | compare_distance_2_object () |
Construct_circumcenter_2 | construct_circumcenter_2_object () |
Construct_bisector_2 | construct_bisector_2_object () |
Construct_ray_2 | construct_ray_2_object () |
A function object to compare two distances for three points.
Provides the operator:
Comparison_result operator()(Point_2 p, Point_2 q, Point_2 r)
which returns SMALLER
, EQUAL
or LARGER
according to the distance between p
and q
being smaller, equal or larger than the distance between p
and r
. This type is only require if nearest_vertex
queries are issued.
A function object to construct the bisector of two points.
Provides the operator:
Line_2 operator()(Point_2 p, Point_2 q)
which constructs the bisector line of points p
and q
. This type is required only if functions relative to the dual Voronoi diagram are called.
A function object to construct the circumcenter of three points.
Provides the operator:
Point_2 operator()(Point_2 p, Point_2 q, Point_2 r)
which returns the circumcenter of the three points p, q
and r
. This type is required only if functions relative to the dual Voronoi diagram are called.
A function object to build a ray from a point and a line.
Provides the operator:
Ray_2 operator() ( Point_2 p, Line_2 l);
The line type.
This type is required only if some dual functions are called.
The type for ray.
This type is required only if some dual functions are called.
A function object to perform an incircle test for a point and three other 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 p, q
and r
.