boost :: geometry :: Polygon和“direct”Polyline的交集

Question

I need to find all intersection points of polyline and polygon such that polyline intersects polygon from outside. I marked such points with bold dots on an attached picture.

The problem is that a boost::geometry::intersection returns all intersection points and I need to check the intersection type somehow.

Here is some small example of using boost::geometry::intersection :

BOOST_GEOMETRY_REGISTER_POINT_2D(Eigen::Vector2d, double, cs::cartesian, x(), y())
BOOST_GEOMETRY_REGISTER_POINT_3D(Eigen::Vector3d, double, cs::cartesian, x(), y(), z())
BOOST_GEOMETRY_REGISTER_LINESTRING(std::vector<Eigen::Vector2d>)
BOOST_GEOMETRY_REGISTER_MULTI_LINESTRING(std::vector<std::vector<Eigen::Vector2d>>)

using Point = Eigen::Vector2d;
using Polyline = std::vector<Point>;
using Polygon = boost::geometry::model::polygon<Point>;

Polyline polyline{{0, -10}, {0, 10}};

Polygon polygon;
std::vector<Point> polygon_points{{-1., 1.}, {1., 1.}, {1, -1}, {-1, -1}, {-1, 1}};
boost::geometry::assign_points(polygon, polygon_points);

std::vector<Point> intersection_points;

boost::geometry::intersection(polygon, polyline, intersection_points);

for (const auto& p : intersection_points) {
  std::cout << p << std::endl << std::endl; //  here we have 2 points, but I need only one (0, -1)
}

Answer 1

This is how I'd do it:

Do for each segment of the polyline:

1. get the intersection 's of this segment only and the polygon; (If none then continue ).

2. use within to check if the start terminal is inside or outside the polygon;

3. if inside, then append every intersection with an odd-numbered index to the output;

4. if outside, then append every intersection with an even-numbered index (and zero) to the output.

Done.