pg_concepts.hpp

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#pragma once
 
#include <array>
#include <cassert>
 
#include "common_concepts.h"
 
namespace fun {
    template <class Point, class Line>
    concept ProjectivePlanePrimitive =   //
        std::equality_comparable<Point>  //
        && requires(const Point& pt_p, const Point& pt_q, const Line& ln_l) {
               { pt_p.incident(ln_l) } -> std::convertible_to<bool>;  // incidence
               { pt_p.meet(pt_q) } -> std::convertible_to<Line>;      // join or meet
           };
 
    template <class Point, class Line>
    concept ProjPlanePrimDual
        = ProjectivePlanePrimitive<Point, Line> && ProjectivePlanePrimitive<Line, Point>;
 
    template <typename Value, class Point, class Line>
    concept ProjectivePlane
        = std::equality_comparable<Point> && ProjectivePlanePrimitive<Point, Line>  //
          && requires(const Point& pt_p, const Point& pt_q, const Line& ln_l, const Value& a) {
                 { pt_p.aux() } -> std::convertible_to<Line>;       // line not incident with pt_p
                 { pt_p.dot(ln_l) } -> std::convertible_to<Value>;  // for basic measurement
                 { Point::parametrize(a, pt_p, a, pt_q) } -> std::convertible_to<Point>;
             };
 
    template <typename Value, class Point, class Line>
    concept ProjectivePlaneDual
        = ProjectivePlane<Value, Point, Line> && ProjectivePlane<Value, Line, Point>;
 
}  // namespace fun