Inscribe rectangle

[petrasvestartas]

Does the cgal has an algorithm to compute an inscribed rectangle for a convex/concave polygons similar to image below?

If yes, could you show an example, because there is no example for the "Largest Empty Rectangle".
The second example only works with points, is there any implementation with lines or polygons?
Does it mean that I must divide the polygon edges with points, if this is true, I do not know the division distance.

Update:
I did some tests below, after multiple trial an error process.
Key problems remains as a question for you:

1. only works with points input, but polygons or lines would be preferred.
2. searching for a workaround for convex polygons

https://doc.cgal.org/latest/Inscribed_areas/index.html

Assuming this image in the cgal documentation:

Test case - Question - What is wrong with the output?

this is the data-set:

0 0 0
36.441 -10.2252 0
59.4002 26.3647 0
25.3483 3.405 0
4.06267 20.9257 0
14.0884 62.5452 0
-32.8599 41.4315 0

Snippet:

        /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
        // Compute the inscribed area
        /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
        IK::Iso_rectangle_2 bbox_rectangle(bbox); 
        CGAL::Largest_empty_iso_rectangle_2<IK> empty_rect(bbox_rectangle); // if the bbox is not given, the result is wrong

        for (auto &polyline : polylines_copy)
            for (int i = 0; i < polyline.size() - 1; i++)
            {
                //interpolate point of a polyline
                CGAL_Polyline division_points;
                int divisions = (int)std::min(100.0, std::sqrt(CGAL::squared_distance(polyline[i], polyline[i + 1])) / 1);
                cgal_vector_util::interpolate_points(polyline[i], polyline[i + 1], divisions, division_points, 2);
                
                //add points to  Largest_empty_iso_rectangle_2
                for (auto &point : division_points)
                    empty_rect.push_back(IK::Point_2(point.hx(), point.hy()));
            }

        //result
        IK::Iso_rectangle_2 rectangle = empty_rect.get_largest_empty_iso_rectangle();
        CGAL_Polyline rect = {
            IK::Point_3(rectangle.min().hx(), rectangle.min().hy(), 0),
            IK::Point_3(rectangle.min().hx(), rectangle.max().hy(), 0),
            IK::Point_3(rectangle.max().hx(), rectangle.max().hy(), 0),
            IK::Point_3(rectangle.max().hx(), rectangle.min().hy(), 0),
            IK::Point_3(rectangle.min().hx(), rectangle.min().hy(), 0),
        };

Result for concave polygon:

Result for convex polygon: