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CGAL 6.0 - dD Triangulations
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This concept describes the geometric types and predicates required to build a Delaunay triangulation. It corresponds to the first template parameter of the class CGAL::Delaunay_triangulation<DelaunayTriangulationTraits_, TriangulationDataStructure_>.
TriangulationTraits CGAL::Epick_d<Dim> CGAL::Epeck_d<Dim> TriangulationTraits Types | |
| typedef unspecified_type | Side_of_oriented_sphere_d |
A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(ForwardIterator start, ForwardIterator end, const Point_d & p). | |
| typedef unspecified_type | In_flat_side_of_oriented_sphere_d |
A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(Flat_orientation_d orient, ForwardIterator start, ForwardIterator end, const Point_d & p). | |
Creation | |
| DelaunayTriangulationTraits () | |
| The default constructor (optional). | |
Operations | |
The following methods permit access to the traits class's predicates and functors: | |
| Side_of_oriented_sphere_d | side_of_oriented_sphere_d_object () const |
| In_flat_side_of_oriented_sphere_d | in_flat_side_of_oriented_sphere_d_object () const |
A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(Flat_orientation_d orient, ForwardIterator start, ForwardIterator end, const Point_d & p).
The operator returns ON_POSITIVE_SIDE, ON_NEGATIVE_SIDE or ON_ORIENTED_BOUNDARY depending of the side of the query point p with respect to the sphere circumscribing the simplex defined by the points in range [start,end). If the simplex is positively oriented according to orient, then the positive side of sphere corresponds geometrically to its bounded side. The points in range [start,end) and p are supposed to belong to the lower dimensional flat whose orientation is given by orient.
std::distance(start,end)=k+1 where \( k\) is the number of points used to construct orient. The points in range [start,end) must be affinely independent, i.e., the simplex must not be flat. p must be in the flat generated by this simplex. A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(ForwardIterator start, ForwardIterator end, const Point_d & p).
The operator returns ON_POSITIVE_SIDE, ON_NEGATIVE_SIDE or ON_ORIENTED_BOUNDARY depending of the side of the query point p with respect to the sphere circumscribing the simplex defined by the points in range [start,end). If the simplex is positively oriented, then the positive side of sphere corresponds geometrically to its bounded side.
Dimension=CGAL::Dimension_tag<D>, then std::distance(start,end)=D+1. The points in range [start,end) must be affinely independent, i.e., the simplex must not be flat. | DelaunayTriangulationTraits::DelaunayTriangulationTraits | ( | ) |
The default constructor (optional).
This is not required when an instance of the traits is provided to the constructor of CGAL::Delaunay_triangulation.