|
CGAL 5.5 - 2D Triangulations
|
|
CGAL 5.5 - 2D Triangulations
|
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_3<K> (not for dual Voronoi functions)
CGAL::Projection_traits_xy_3<K> (not for dual Voronoi functions)
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.
1.8.13 #include <Concepts/DelaunayTriangulationTraits_2.h>
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_3<K> (not for dual Voronoi functions)
CGAL::Projection_traits_xy_3<K> (not for dual Voronoi functions)
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.
1.8.13