ck_plane.hpp

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#pragma once
 
#include <array>
 
#include "pg_plane.hpp"
 
#if __cpp_concepts >= 201907L
#    include "ck_concepts.hpp"
#endif
 
namespace fun {
    template <class Line, class Point = typename Line::Dual>
#if __cpp_concepts >= 201907L
        requires CayleyKleinPlanePrimitiveDual<Line, Point>
#endif
    constexpr auto is_perpendicular(const Line& l_1, const Line& l_2) -> bool {
        return l_1.perp().incident(l_2);
    }
 
    template <class Point, class Line>
#if __cpp_concepts >= 201907L
        requires CayleyKleinPlanePrimitiveDual<Point, Line>
#endif
    constexpr auto altitude(const Point& pt_p, const Line& ln_m) -> Line {
        return ln_m.perp().meet(pt_p);
    }
 
    template <class Point, class Line = typename Point::Dual>
#if __cpp_concepts >= 201907L
        requires CayleyKleinPlanePrimitiveDual<Point, Line>
#endif
    constexpr auto orthocenter(const std::array<Point, 3>& triangle) -> Point {
        const auto& [a_1, a_2, a_3] = triangle;
        assert(!coincident(a_1, a_2, a_3));
        const auto t1 = altitude(a_1, a_2.meet(a_3));
        const auto t2 = altitude(a_2, a_3.meet(a_1));
        return t1.meet(t2);
    }
 
    template <class Point, class Line>
#if __cpp_concepts >= 201907L
        requires CayleyKleinPlanePrimitiveDual<Point, Line>
#endif
    constexpr auto tri_altitude(const std::array<Point, 3>& triangle) -> std::array<Line, 3> {
        const auto [l1, l2, l3] = tri_dual(triangle);
        const auto& [a_1, a_2, a_3] = triangle;
        assert(!coincident(a_1, a_2, a_3));
        auto&& t1 = altitude(a_1, l1);
        auto&& t2 = altitude(a_2, l2);
        auto&& t3 = altitude(a_3, l3);
        return {t1, t2, t3};
    }
 
    template <typename Value, class Point, class Line = typename Point::Dual>
#if __cpp_concepts >= 201907L
        requires CayleyKleinPlaneDual<Value, Point, Line>
#endif
    constexpr auto reflect(const Line& mirror, const Point& pt_p) -> Point {
        return involution(mirror.perp(), mirror, pt_p);
    }
 
}  // namespace fun