Boost geometry intersection does not output correctly

Question

From the following code I calculate the intersection of two polygons. I hope the output can be NULL if it is not polygon. However the output is (((240, 52.9999), (240, 53), (240, 53), (240, 52.9999))). This is not a polygon. Is there any way to check whether the output is really a polygon??

#include <iostream>
#include <deque>
#include <vector>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/polygon.hpp>
#include <boost/geometry/io/wkt/wkt.hpp>
#include <boost/geometry/algorithms/append.hpp>

#include <algorithm> // for reverse, unique
#include <iostream>
#include <string>


int main()
{
   typedef boost::geometry::model::d2::point_xy<double,    boost::geometry::cs::cartesian> point_2d;
   typedef boost::geometry::model::polygon<point_2d> polygon_2d;

    polygon_2d green;
    boost::geometry::append(green, point_2d(286.188, 90.9575));
    boost::geometry::append(green, point_2d(274.902, 56.2215));
    boost::geometry::append(green, point_2d(274.238, 55.7393));
    boost::geometry::append(green, point_2d(246.908, 51.9765));
    boost::geometry::append(green, point_2d(194.477, 59.7441));
    boost::geometry::append(green, point_2d(159.213, 101.141));
    boost::geometry::append(green, point_2d(203.576, 149.537));
    boost::geometry::append(green, point_2d(286.188, 90.9575));

    polygon_2d blue;
    boost::geometry::append(blue, point_2d(240, 53));
    boost::geometry::append(blue, point_2d(240, -53));
    boost::geometry::append(blue, point_2d(-60, -53));
    boost::geometry::append(blue, point_2d(-60, 53));
    boost::geometry::append(blue, point_2d(240, 53));

    boost::geometry::correct(green);
    boost::geometry::correct(blue);

    std::vector<polygon_2d> output;
    boost::geometry::intersection(green, blue, output);

    std::cout << "green && blue:" << std::endl;
    if(output.size())
    {
       std::cout<<boost::geometry::dsv(output[0])<<std::endl;
       std::cout<<boost::geometry::area(output[0])<<std::endl;
    }

    return 0;
}

Answer 1

You can weed out the invalid geometries:

output.erase(
        std::remove_copy_if(output.begin(), output.end(), output.begin(), [](polygon_2d const&g) { return boost::geometry::is_valid(g); }),
        output.end());

Now, the result will be empty as expected.

See it Live On Coliru

---

It's interesting to me how "invalid" geometries would result in the first place. As you were probably aware that your polygons are very well chosen:

Let's zoom in a little:

Now, you're likely looking at some floating point accuracy issues, as the same experiment with long long points or boost multiprecision, eg:

typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<1024*128>> oopmh; // that's a lotta oomph
typedef boost::geometry::model::d2::point_xy<oopmh, boost::geometry::cs::cartesian> point_2d;

You will see that we get

green && blue:
(((2.4e+06, 530000), (-600000, 530000), (-600000, -530000), (2.4e+06, -530000), (2.4e+06, 530000)))
nan

So it looks very much like we just get a singular point of area. If you don't want this, then maybe you should just define an "epsilon" value of sorts, a threshold at which you stop considering an overlap an overlap.