mirror of https://github.com/CGAL/cgal
178 lines
4.2 KiB
C++
178 lines
4.2 KiB
C++
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/*!
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\ingroup PkgTriangulation2Concepts
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\cgalConcept
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The concept `RegularTriangulationTraits_2` describes the requirements
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for the traits class of regular triangulations. It refines the
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concept `TriangulationTraits_2` requiring the type
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`CGAL::Weighted_point_2` and the *power test* predicate on those
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weighted points.
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A weighted point is basically
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a point augmented with a scalar weight. It can be seen as a circle
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when the weight is interpreted as a square radius.
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The power test on weighted points
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is the fundamental test to build regular triangulations
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as the `side_of_oriented_circle` test is the fundamental test
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of Delaunay triangulations.
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\cgalRefines `TriangulationTraits_2`
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\cgalHasModel All CGAL Kernels
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\cgalHasModel `CGAL::Regular_triangulation_euclidean_traits_2`
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\sa `TriangulationTraits_2`
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*/
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class RegularTriangulationTraits_2 {
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public:
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/// \name Types
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/// @{
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/*!
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The (unweighted) point type.
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It has to be a model of the concept `Kernel::Point_2`.
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*/
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typedef unspecified_type Point_2;
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/*!
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The weighted point type. It has to be a model of the concept `Kernel::WeightedPoint_2`.
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*/
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typedef unspecified_type Weighted_point_2;
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/*!
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A predicate object,
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model of `PowerSideOfOrientedPowerCircle_2`,
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that must provide operators for the power test applied to two, three, and four points.
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Must provide the operators:
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- `Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r, Weighted_point_2 s) `
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which is the power test for points `p`, `q`, `r` and
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`s`. \pre the bare points corresponding to `p`, `q`, `r` are not collinear.
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- `Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r) `
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which is the degenerate power test for collinear points
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`p`, `q`, `r`.
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\pre the bare points corresponding to `p`, `q`, `r` are collinear and `p != q`.
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- `Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q) `
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which is the degenerate power test for weighted points
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`p` and `q` whose corresponding bare-points are identical.
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\pre the bare points corresponding to `p` and `q` are identical.
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*/
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typedef unspecified_type Power_side_of_oriented_power_circle_2;
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/*!
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A constructor type,
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model of `Kernel::ConstructPoint_2`.
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The `operator()` extracts the bare point from a weighted point.
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`Point_2 operator() ( Weighted_point_2 p);`
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*/
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typedef unspecified_type Construct_point_2;
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/// @}
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/// \name Optional Types
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/// The following type/predicate is required for a call to `nearest_power_vertex()`:
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/// @{
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/*!
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A function object,
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model of `Kernel::ComparePowerDistance_2`
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for comparing two power distances.
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Must provide the operator:
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`Comparison_result operator()(Point_2 p, Weighted_point_2 q, Weighted_point_2 r)`,
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which compares the power distance between `p` and `q` to the
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power distance between `p` and `r`.
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*/
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typedef unspecified_type Compare_power_distance_2;
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/*!
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A function object,
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model of `Kernel::ConstructWeightedCircumcenter_2`,
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that constructs the weighted circumcenter of three
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weighted points.
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Must provide the operator:
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`Point_2 operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r);`
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*/
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typedef unspecified_type Construct_weighted_circumcenter_2;
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/*!
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A function object,
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model of `Kernel::ConstructRadicalAxis_2`,
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that constructs
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the radical axis of two weighted points.
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Must provide the operator:
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`Line_2 operator() ( Weighted_point_2 p, Weighted_point_2 q);`
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*/
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typedef unspecified_type Construct_radical_axis_2;
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/// @}
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/// \name Creation
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/// @{
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/*!
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%Default constructor.
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*/
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RegularTriangulationTraits_2();
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/*!
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Copy constructor.
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*/
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RegularTriangulationTraits_2 (
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const RegularTriangulationTraits_2& );
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/*!
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Assignment operator.
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*/
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RegularTriangulationTraits_2& operator=
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(const RegularTriangulationTraits_2& );
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/// @}
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/// \name Access to Predicate and Constructors Objects
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/// @{
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/*!
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*/
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Power_side_of_oriented_power_circle_2 power_side_of_oriented_power_circle_2_object();
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/*!
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*/
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Compare_power_distance_2 compare_power_distance_2_object();
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/*!
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*/
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Construct_point_2 construct_point_2_object();
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/*!
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*/
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Construct_weighted_circumcenter_2
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construct_weighted_circumcenter_2_object();
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/*!
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*/
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Construct_radical_axis_2
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construct_radical_axis_2_object();
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/// @}
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}; /* end RegularTriangulationTraits_2 */
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