id	summary	reporter	owner	description	type	status	milestone	component	version	severity	resolution	keywords	cc
10772	boost::geometry::within() does not recognize empty boxes	bromeon@…	awulkiew	"If boost::geometry::within() is used to check whether an empty box (i.e. a point) is within another box, false is always returned. This is not the correct behavior because:
1. OGC defines: a.Within(b) ⇔ (a∩b=a) ∧ (I(a)∩E(b)=∅) which holds true. The intersection of an empty box ''a'' and a surrounding box ''b'' yields ''a''. Since ''a'' has no interior, I(a)=∅, thus the second condition is also true.
2. Empty boxes should be treated as points. When using a point model instead of an empty box, the check returns the correct result as expected.

See also the following complete minimal code (it includes also other geometry algorithms that are computed consistently for points and empty boxes):

{{{
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/box.hpp>
#include <boost/geometry/algorithms/convert.hpp>
#include <boost/geometry/algorithms/within.hpp>
#include <boost/geometry/algorithms/covered_by.hpp>
#include <boost/geometry/algorithms/intersects.hpp>
#include <boost/geometry/algorithms/disjoint.hpp>
#include <boost/geometry/algorithms/distance.hpp> // needed for within() -- is this intended?
#include <iostream>

namespace bg = boost::geometry;
typedef bg::model::d2::point_xy<float> Point;
typedef bg::model::box<Point> Box;

int main()
{
    Point point(3, 4);
    Box pointAsBox;
    bg::convert(point, pointAsBox);

    Box surrounding;
    surrounding.min_corner() = Point(2, 2);
    surrounding.max_corner() = Point(5, 5);

    std::cout << ""            Point Box"" << std::endl;
    std::cout << ""within:        "" << bg::within(point,      surrounding)
                         << ""    "" << bg::within(pointAsBox, surrounding)     << ""\n""; // 1 0 <-
    std::cout << ""within (self): "" << bg::within(point,      point)           
                         << ""    "" << bg::within(pointAsBox, pointAsBox)      << ""\n""; // 1 0 <-
    std::cout << ""covered_by:    "" << bg::covered_by(point,      surrounding) 
                         << ""    "" << bg::covered_by(pointAsBox, surrounding) << ""\n""; // 1 1
    std::cout << ""intersects:    "" << bg::intersects(point,      surrounding) 
                         << ""    "" << bg::intersects(pointAsBox, surrounding) << ""\n""; // 1 1
    std::cout << ""disjoint:      "" << bg::disjoint(point,      surrounding)   
                         << ""    "" << bg::disjoint(pointAsBox, surrounding)   << ""\n""; // 0 0
    std::cout << std::endl;
}
}}}

The implementation looks as follows (boost/geometry/strategies/cartesian/box_in_box.hpp, line 32):

{{{
struct box_within_range
{
    template <typename BoxContainedValue, typename BoxContainingValue>
    static inline bool apply(BoxContainedValue const& bed_min
                , BoxContainedValue const& bed_max
                , BoxContainingValue const& bing_min
                , BoxContainingValue const& bing_max)
    {
        return bing_min <= bed_min && bed_max <= bing_max // contained in containing
            && bed_min < bed_max;                         // interiors overlap
    }
};
}}}


The problem is the second line, which uses < and thus returns false if the coordinates are equal. I'm not sure what the intention is (despite the comment), and whether it is needed at all.

The documentation about box model and concept doesn't state whether max_corner's coordinates must be component-wise greater or equal than min_corner's. If so, it seems like valid boxes are a precondition to within() and this line could be removed."	Bugs	assigned	To Be Determined	geometry	Boost 1.57.0	Problem