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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 regular triangulation. It corresponds to the first template parameter of the class CGAL::Regular_triangulation<RegularTriangulationTraits_, TriangulationDataStructure_>.
TriangulationTraits CGAL::Epick_d<Dim> CGAL::Epeck_d<Dim> TriangulationTraits Types | |
| typedef unspecified_type | FT |
A number type that is a model for FieldNumberType. | |
| typedef unspecified_type | Weighted_point_d |
| The weighted point type. | |
| typedef unspecified_type | Construct_point_d |
A function object that must provide the operator Point_d operator()(const Weighted_point_d & wp), returning wp without its weight. | |
| typedef unspecified_type | Compute_weight_d |
A function object that must provide the operator FT operator()(const Weighted_point_d & wp), returning the weight of wp. | |
| typedef unspecified_type | Power_side_of_power_sphere_d |
A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(ForwardIterator start, ForwardIterator end, const Weighted_point_d & p). | |
| typedef unspecified_type | In_flat_power_side_of_power_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 Weighted_point_d & p). | |
Creation | |
| RegularTriangulationTraits () | |
| The default constructor (optional). | |
Operations | |
The following methods permit access to the traits class's predicates and functors: | |
| Construct_point_d | construct_point_d_object () const |
| Compute_weight_d | compute_weight_d_object () const |
| Power_side_of_power_sphere_d | power_side_of_power_sphere_d_object () const |
| In_flat_power_side_of_power_sphere_d | in_flat_power_side_of_power_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 Weighted_point_d & p).
The points in range [start,end) and p are supposed to belong to the lower-dimensional flat whose orientation is given by orient.
Let \( S \) be the power sphere of the weighted points in range [start,end) in this lower dimensional flat. The operator returns:
ON_ORIENTED_BOUNDARY if p is orthogonal to \( S \),ON_NEGATIVE_SIDE if the power distance between p and \( S \) is positive.ON_POSITIVE_SIDE otherwise.std::distance(start,end)=k+1 where \( k\) is the number of points used to construct orient (dimension of the flat). The points in range [start,end) must be affinely independent. p must be in the flat generated by these points. A predicate object that must provide the templated operator template<typename ForwardIterator> Oriented_side operator()(ForwardIterator start, ForwardIterator end, const Weighted_point_d & p).
Let \( S \) be the power sphere of the weighted points in range [start,end). The operator returns:
ON_ORIENTED_BOUNDARY if p is orthogonal to \( S \),ON_NEGATIVE_SIDE if the power distance between p and \( S \) is positive.ON_POSITIVE_SIDE otherwise.Dimension is CGAL::Dimension_tag<D>, then std::distance(start,end)=D+1. The weighted points in range [start,end) must be affinely independent, i.e., the simplex must not be flat. | RegularTriangulationTraits::RegularTriangulationTraits | ( | ) |
The default constructor (optional).
This is not required when an instance of the traits is provided to the constructor of CGAL::Regular_triangulation.