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The concept RegularTriangulationTraits_2 describe the requirements for the traits class of regular triangulations. It refines the concept TriangulationTraits_2 providing the type 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.
RegularTriangulationTraits_2::Bare_point | |||||||
Another name for the point type.
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RegularTriangulationTraits_2::Weighted_point_2 | |||||||
The weighted point type, it has to be
a model of the concept WeightedPoint.
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RegularTriangulationTraits_2::Power_test_2 | |||||||
A predicate object type. 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.
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The following type/predicate is required if a call to nearest_power_vertex is issued:
RegularTriangulationTraits_2::Compare_power_distance_2 | |
A predicate object type. Must
provide the operator: Comparison_result operator()(Bare_point 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.
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RegularTriangulationTraits_2::Construct_weighted_circumcenter_2 | |
A constructor
object which constructs the weighted circumcenter of three
weighted points. Provides the operator Bare_point operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r);
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RegularTriangulationTraits_2::Construct_radical_axis_2 | |
A constructor type which
constructs
the radical axis of two weighted points. Provides the operator : Line_2 operator() ( Weighted_point_2 p, Weighted_point_2 q);
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RegularTriangulationTraits_2 traits; | |
default constructor.
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RegularTriangulationTraits_2 traits ( RegularTriangulatioTraits_2); | |
copy constructor.
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RegularTriangulationTraits_2& | traits = RegularTriangulationTraits_2 | |
assignment operator |