#include <iostream>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>

using point_t = boost::geometry::model::d2::point_xy<double>;
using segment_t = boost::geometry::model::segment<point_t>;

int main() {
    segment_t e1{point_t{100, 350}, point_t{-100, 400}};
    segment_t e2{point_t{0, 0}, point_t{90, 600}};
    std::vector<point_t> iv;
    boost::geometry::intersection(e1, e2, iv);
    assert(iv.size() == 1);
    const auto& v = iv[0];
    bool is_within = boost::geometry::within(v, e1);
    std::cout << "is within? " << is_within << std::endl;
    is_within = boost::geometry::within(v, e2);
    std::cout << "is within? " << is_within << std::endl;

    return 0;
}