Geometric difference of regions with internal boundaries with boost geometry

Question

I'd like to take the geometric difference of two geometric objects with Boost Geometry. The first geometry is:

I always have line segments making up the geometry. I have the coordinates and the segments:

{{-1., -1.}, {1., -1.}, {1., 1.}, {-1., 1.}, {0.6, -1}, {0.6,1.}};
{Line[{{1, 5}, {5, 2}, {2, 3}, {3, 6}, {6, 4}, {4, 1}}], Line[{{5, 6}}]};

were each index in the lines refers to a coordinates. Either of the geometries can have internal boundaries (and holes).

The second geometry:

And I am expecting to obtain this:

I have started with polygon but I do not understand how I could include the interior boundary of the first geometric object. While one can have interior holes I am missing how to have a 'degenerated' polygon like a line. Also it's not clear to me which of the two polygons then would be the outer polygon. Then I thought about line, but there I can not add the internal segment. Can Boost Geometry be used find geometric Boolean operations for geometries with internal boundaries and it so, how would I do that?

The code for the polygon approach that misses the internal boundary; commented out is the line type approach; again with out the internal boundary in first geometric object.

#include <iostream>                                                             
#include <fstream>                                                              
#include <list>                                                                 

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

#include <boost/foreach.hpp>                                                    

int main()                                                                      
{                                                                               
    typedef boost::geometry::model::d2::point_xy<double> point_type;            
    typedef boost::geometry::model::polygon<point_type > polygon;               
    //typedef boost::geometry::model::linestring<point_type > line;             

    polygon p1, p2;                                                             
    //line l1, l2;                                                              

    boost::geometry::read_wkt(                                                  
        "POLYGON((-1 -1, 0.6 -1, 1 -1, 1 1, 0.6 1, -1 1))", p1);                

    boost::geometry::read_wkt(                                                  
        "POLYGON((-0.5 -0.5, 2 -0.5, 2 0.5, -0.5 0.5))", p2);                   

    /*                                                                          
    boost::geometry::read_wkt(                                                  
        "LINESTRING(-1 -1, 0.6 -1, 1 -1, 1 1, 0.6 1, -1 1)", l1);               

    boost::geometry::read_wkt(                                                  
        "LINESTRING(-0.5 -0.5, 2 -0.5, 2 0.5, -0.5 0.5)", l2);                  
    */                                                                          

    std::list<polygon> output;                                                  
    boost::geometry::difference(p2, p1, output);                                

    //std::list<line> loutput;                                                  
    //boost::geometry::difference(l2, l1, loutput);                             

    std::ofstream svg("my_map.svg");                                            
    boost::geometry::svg_mapper<point_type> mapper(svg, 400, 400);              

    int i = 0;                                                                  
    BOOST_FOREACH(polygon const& p, output)                                     
    {                                                                           
        mapper.add(p);                                                          
        mapper.map(p, "fill-opacity:0.3;fill:rgb(51,151,53);stroke:rgb(51,151,53);stroke-width:2");  
    }                                                                           

    /*                                                                          
    int i = 0;                                                                  
    BOOST_FOREACH(line const& l, loutput)                                       
    {                                                                           
        mapper.add(l);                                                          
        mapper.map(l, "opacity:0.4;fill:none;stroke:rgb(212,0,0);stroke-width:5");
    }                                                                           
    */                                                                          

    return 0;                                                                   
}

Answer 1

The inner line can be modeled as a spike from e.g. the bottom. This approximation works:

boost::geometry::read_wkt(
    "POLYGON((-1 -1, 0.6 -1, 0.6 1, 0.60000000000001 -1, 1 -1, 1 1, -1 1))", p1);

Two polygons are created: the small lower right almost-rectangle (0.60000000000001 -1, 1 -1, 1 -0.5, 0.6 -0.5) is not connected to the rest.

This exact list of points

boost::geometry::read_wkt(
    "POLYGON((-1 -1, 0.6 -1, 0.6 1, 0.6 -1, 1 -1, 1 1, -1 1))", p1);

raises an exception because of a self intersection. When jumping over the check for self intersection we get a result, but it is incomplete (only the bigger of the two above polygons is computed).

What would, of course, also work, is splitting the polygon p1 into two rectangles:

boost::geometry::read_wkt(
    "POLYGON((-1 -1, 0.6 -1, 0.6 1, -1 1))", p11);
boost::geometry::read_wkt(
    "POLYGON((0.6 -1, 1 -1, 1 1, 0.6 1))", p12);

Then computing each difference with p2 and joining the results gives the exact expected answer (as three separate rectangles).