RegularTriangulationTraits concept documentation

Triangulation/doc/Triangulation/Concepts/RegularTriangulationTraits.h

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+
+/*!
+\ingroup PkgTriangulationsConcepts
+\cgalConcept
+
+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>`.
+
+\cgalRefines ::TriangulationTraits.
+
+\cgalHasModel `CGAL::Epick_d<Dim>`
+
+\sa `TriangulationTraits`
+*/
+class RegularTriangulationTraits {
+public:
+
+/// \name Types
+/// @{
+
+/*!
+An arithmetic field type.
+*/
+typedef unspecified_type FT;
+
+/*!
+The weighted point type.
+*/
+typedef unspecified_type Weighted_point;
+
+/*!
+The un-weighted point type.
+*/
+typedef unspecified_type Bare_point;
+
+/*!
+A predicate object that must provide the templated operator
+`template Bare_point operator()(const Weighted_point & wp)`, returning
+`wp` without its weight.
+*/
+typedef unspecified_type Point_drop_weight_d;
+
+/*!
+A predicate object that must provide the templated operator
+`template FT operator()(const Weighted_point & wp)`, returning
+the weight of `wp`.
+*/
+typedef unspecified_type Point_weight_d;
+
+/*!
+A predicate object that must provide the templated operator
+`template<typename ForwardIterator> Oriented_side operator()(ForwardIterator start, ForwardIterator end, const Point_d & p)`.
+Let \f$ S \f$ be the power sphere of the weighted points in range `[start,end)`.
+The operator returns:
+- `ON_ORIENTED_BOUNDARY` if `p` is orthogonal to 
+  \f$ S \f$, 
+
+- `ON_NEGATIVE_SIDE` if `p` lies outside the oriented sphere of 
+  the same center as \f$ S \f$ and radius \f$ \sqrt{ w_S^2 + w_p^2 }\f$, 
+
+- `ON_POSITIVE_SIDE` if `p` lies inside this oriented sphere. 
+
+\pre If `Dimension`=`CGAL::``Dimension_tag<D>`, 
+then `std::distance(start,end)=D+1`.
+The points in range
+`[start,end)` must be affinely independent, i.e., the simplex must
+not be flat.
+*/
+typedef unspecified_type Power_test_d;
+
+/*!
+A predicate object that must provide the templated operator
+`template<typename ForwardIterator> Oriented_side operator()(Flat_orientation_d orient, ForwardIterator start, ForwardIterator end, const Point_d & p)`.
+
+The points in range `[start,end)` and `p` are supposed to belong to the lower dimensional flat
+whose orientation is given by `orient`.
+
+Let \f$ S \f$ 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
+\f$ S \f$,
+
+- `ON_NEGATIVE_SIDE` if `p` lies outside the oriented sphere of
+the same center as \f$ S \f$ and radius \f$ \sqrt{ w_S^2 + w_p^2 }\f$,
+
+- `ON_POSITIVE_SIDE` if `p` lies inside this oriented sphere.
+
+\pre `std::distance(start,end)=k+1` where \f$ k\f$ 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.
+*/
+typedef unspecified_type In_flat_power_test_d;
+
+/// @}
+
+/// \name Creation
+/// @{
+
+/*!
+The default constructor.
+*/
+RegularTriangulationTraits();
+
+/// @}
+
+/// \name Operations
+/// The following methods permit access to the traits class's predicates:
+/// @{
+
+/*!
+
+*/
+Point_drop_weight_d point_drop_weight_d_object() const;
+
+/*!
+
+*/
+Point_weight_d point_weight_d_object() const;
+
+/*!
+
+*/
+Power_test_d power_test_d_object() const;
+
+/*!
+
+*/
+In_flat_power_test_d in_flat_power_test_d_object() const;
+
+/// @}
+
+}; /* end RegularTriangulationTraits */