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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 interprated 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.
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Another name for the point type.
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The weighted point type, it has to be
a model of the concept WeightedPoint.
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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. Precondition: the bare points corresponding to p, q, r are not collinear. - Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r) which is the degenerated power test for collinear points p, q, r. Precondition: the bare points corresponding to p, q, r are collinear and p != q. - Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q) which is the degenerated power test for weighted points p and q whose corresponding bare-points are identical. Precondition: the bare points corresponding to p and q are identical.
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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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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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default constructor.
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copy constructor.
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