what should I have to use in boost geometry function

Now i'm analyzing polygon example in boost geometry

http://geometrylibrary.geodan.nl/03_polygon_example_8cpp-example.html

After draw a few lines, if I want to get cross point between polygon border line and normal lines, what function should I use??

Click to See a sample image what i want

I want to know those red circle point coordinate. I don't know that a way of combination of line points i inserted and the polygon

Would the function documented here (get_intersection_points) help? You could intersect your line segment with the shapes you want to check.