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CGAL 6.0 - 2D Triangulations
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The concept RegularTriangulationTraits_2 describes the requirements for the traits class of regular triangulations. It refines the concept TriangulationTraits_2 requiring the type CGAL::Weighted_point_2 and the power test predicate on those weighted points. A weighted point is basically a point augmented with a scalar weight. It can be seen as a circle when the weight is interpreted as a square radius. The power test on weighted points is the fundamental test to build regular triangulations as the side_of_oriented_circle test is the fundamental test of Delaunay triangulations.
TriangulationTraits_2 Kernel CGAL::Regular_triangulation_2 Types | |
| typedef unspecified_type | Weighted_point_2 |
| The weighted point type. | |
| typedef unspecified_type | Power_side_of_oriented_power_circle_2 |
A predicate object, model of PowerSideOfOrientedPowerCircle_2, that must provide operators for the power test applied to two, three, and four points. | |
| typedef unspecified_type | Construct_point_2 |
A constructor type, model of Kernel::ConstructPoint_2. | |
Optional Types | |
The following type/predicate is required for a call to | |
| typedef unspecified_type | Compare_power_distance_2 |
A function object, model of Kernel::ComparePowerDistance_2 for comparing two power distances. | |
The following types/predicates are required to compute duals: | |
| typedef unspecified_type | Construct_weighted_circumcenter_2 |
A function object, model of Kernel::ConstructWeightedCircumcenter_2, that constructs the weighted circumcenter of three weighted points. | |
| typedef unspecified_type | Construct_radical_axis_2 |
A function object, model of Kernel::ConstructRadicalAxis_2, that constructs the radical axis of two weighted points. | |
Creation | |
| RegularTriangulationTraits_2 () | |
| Default constructor. | |
| RegularTriangulationTraits_2 (const RegularTriangulationTraits_2 &) | |
| Copy constructor. | |
| RegularTriangulationTraits_2 & | operator= (const RegularTriangulationTraits_2 &) |
| Assignment operator. | |
Access to Predicate and Constructors Objects | |
| Power_side_of_oriented_power_circle_2 | power_side_of_oriented_power_circle_2_object () |
| Compare_power_distance_2 | compare_power_distance_2_object () |
| Construct_point_2 | construct_point_2_object () |
| Construct_weighted_circumcenter_2 | construct_weighted_circumcenter_2_object () |
| Construct_radical_axis_2 | construct_radical_axis_2_object () |
A function object, model of Kernel::ComparePowerDistance_2 for comparing two power distances.
Must provide the operator:
Comparison_result operator()(Point_2 p, Weighted_point_2 q, Weighted_point_2 r), which compares the power distance between p and q to the power distance between p and r.
A constructor type, model of Kernel::ConstructPoint_2.
The operator() extracts the bare point from a weighted point.
Point_2 operator() ( Weighted_point_2 p);
A function object, model of Kernel::ConstructRadicalAxis_2, that constructs the radical axis of two weighted points.
Must provide the operator:
Line_2 operator() ( Weighted_point_2 p, Weighted_point_2 q);
A function object, model of Kernel::ConstructWeightedCircumcenter_2, that constructs the weighted circumcenter of three weighted points.
Must provide the operator:
Point_2 operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r);
A predicate object, model of PowerSideOfOrientedPowerCircle_2, that must provide operators for the power test applied to two, three, and four points.
Must provide the operators:
Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r, Weighted_point_2 s) which is the power test for points p, q, r and s. p, q, r are not collinear.Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r) which is the degenerate power test for collinear points p, q, r. p, q, r are collinear and p != q.Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q) which is the degenerate power test for weighted points p and q whose corresponding bare-points are identical. p and q are identical. The weighted point type.
It has to be a model of the concept Kernel::WeightedPoint_2.
Point_2 is requested by the concept TriangulationTraits_2, which this concept refines.