使用 Boost Geometry 的线相交

Question

How line can be represented using Boost Geometry?

I don't need finite segment, but I need infinite lines (maybe Segment or Linestring can be extended?)

As I understand I can use boost::geometry::intersects , but I don't know how to define infinite line.

Answer 1

If you want to test whether an infinite line A intersects a line segment B , this can be done using boost::geometry::strategy::side::side_by_triangle :

template <typename Point>
struct line
{
    boost::geometry::model::segment<Point> segment;
};

template <typename Point>
bool intersects(line<Point> const& A, boost::geometry::model::segment<Point> const& B)
{
    using side = boost::geometry::strategy::side::side_by_triangle<>;
    auto const firstSide  = side::apply(A.segment.first, A.segment.second, B.first);
    auto const secondSide = side::apply(A.segment.first, A.segment.second, B.second);
    return firstSide == 0 || secondSide == 0 || (firstSide < 0) != (secondSide < 0);
}

The line type simply represents a line using a segment that is part of that line, but as a separate type so it can be distinguished from a segment by the type system, for the purposes of overloading.

It first queries on which side of A the two endpoints ( first and second ) of B lie. Then, if either of firstSide or secondSide are zero, this means the corresponding endpoint is touching A , so intersects is true. Otherwise, intersects is true iff the endpoints are on opposite sides of A .

Answer 2

Maybe it will helps, function intersection_point calculates intersection point of two infinite lines. https://www.boost.org/doc/libs/1_72_0/boost/geometry/geometries/infinite_line.hpp https://www.boost.org/doc/libs/1_72_0/boost/geometry/arithmetic/infinite_line_functions.hpp