Wrong area calculation for box in a spherical_equatorial CS

[daedric]

Given the code (http://cpp.sh/43sl):

#include <iostream>
#include <boost/geometry.hpp>

using coordinate_system = boost::geometry::cs::spherical_equatorial<boost::geometry::degree>;
using lonlat = boost::geometry::model::point<double, 2, coordinate_system>;
using box = boost::geometry::model::box<lonlat>;
using polygon = boost::geometry::model::polygon<lonlat>;

int main()
{
    box b{
        lonlat{0, 0},
        lonlat{1, 1},
    };

    polygon p;
    p.outer().push_back(lonlat{0, 0});
    p.outer().push_back(lonlat{0, 1});
    p.outer().push_back(lonlat{1, 1});
    p.outer().push_back(lonlat{1, 0});
    p.outer().push_back(lonlat{0, 0});

    std::cout << wkt(b) << std::endl;
    std::cout << wkt(p) << std::endl;
    std::cout << area(b) << std::endl;
    std::cout << area(p) << std::endl;
}

It gives the following output:

POLYGON((0 0,0 1,1 1,1 0,0 0))
POLYGON((0 0,0 1,1 1,1 0,0 0))
1
0.00030461

The problem is that boost::geometry calls the following code to calculate the are of the box:

{
    template <typename Box, typename Strategy>
    static inline typename coordinate_type<Box>::type
    apply(Box const& box, Strategy const&)
    {
        // Currently only works for 2D Cartesian boxes
        assert_dimension<Box, 2>();

        return (get<max_corner, 0>(box) - get<min_corner, 0>(box))
             * (get<max_corner, 1>(box) - get<min_corner, 1>(box));
    }
};

Which as stated can't work in a spherical referential.
Even giving the strategy explicitely does not workaround the bug :)

Cheers,

[awulkiew]

Thanks for report!

Indeed the result is wrong however it should not be the same as the result for Polygon. In Boost.Geometry the Box in non-cartesian cordinate systems is not Polygon, i.e. its edges aren't defined by great circles or geodesics. Instead, the edges of a Box are defined by meridians and parallels. E.g. in spherical equatorial the result should be area of a part of spherical frustum/segment (don't confuse with a Boost.Geometry Segment on the surface of a sphere defined by great circle).