proj_plane_measure.hpp

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#pragma once
 
#include "fractions.hpp"
#include "proj_plane.hpp"
 
namespace fun {
 
    template <Ring K> constexpr auto ratio_ratio(const K& a, const K& b, const K& c, const K& d) {
        if constexpr (Integral<K>) {
            return Fraction(a, b) / Fraction(c, d);
        } else {
            return (a * d) / (b * c);
        }
    }
 
    template <typename Point, typename Line>
        requires ProjectivePlane<Point, Line>
    constexpr auto x_ratio(const Point& A, const Point& B, const Line& line_l, const Line& line_m) {
        return ratio_ratio(A.dot(line_l), A.dot(line_m), B.dot(line_l), B.dot(line_m));
    }
 
    template <ProjectivePlaneCoord2 Point>
    constexpr auto R(const Point& A, const Point& B, const Point& C, const Point& D)
 
    {
        using K = Value_type<Point>;
        if (cross0(A, B) != K(0)) {  // Project points to yz-plane
            return R0(A, B, C, D);
        }
        // Project points to xz-plane
        return R1(A, B, C, D);
    }
 
    template <ProjectivePlane2 Point>
    constexpr auto R(const Point& A, const Point& B, const Point& C, const Point& D) {
        const auto O = (C * D).aux();
        return x_ratio(A, B, O * C, O * D);
    }
 
    template <ProjectivePlaneCoord2 Point>
    constexpr auto R0(const Point& A, const Point& B, const Point& C, const Point& D) {
        return ratio_ratio(cross0(A, C), cross0(A, D), cross0(B, C), cross0(B, D));
    }
 
    template <ProjectivePlaneCoord2 Point>
    constexpr auto R1(const Point& A, const Point& B, const Point& C, const Point& D) {
        return ratio_ratio(cross1(A, C), cross1(A, D), cross1(B, C), cross1(B, D));
    }
 
}  // namespace fun