Haversine distance does not always multiply by radius

[daedric]

Hello, I might have found an issue in the point to polygon distance calculation.

Given this code:

#include <iostream>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/multi_polygon.hpp>
#include <boost/geometry/geometries/polygon.hpp>
#include <boost/geometry/strategies/spherical/distance_haversine.hpp>

using coordinate_system = boost::geometry::cs::spherical_equatorial<boost::geometry::degree>;
using lonlat = boost::geometry::model::point<double, 2, coordinate_system>;
using polygon = boost::geometry::model::polygon<lonlat, false>;
using multi_polygon = boost::geometry::model::multi_polygon<polygon>;
static const constexpr double mean_radius = 6371.0 * 1000;
static const auto Haversine = [] {
    return boost::geometry::strategy::distance::haversine<double>(
        mean_radius);
};

int main()
{
    std::string c = "POINT(2.37314 48.854)";
    std::string p = "MULTIPOLYGON(((2.37198 48.8539, 2.37214 48.8539, 2.3721 48.854, 2.37198 48.854, 2.37198 48.8539)))";
    
    lonlat center;
    multi_polygon poly;
    boost::geometry::read_wkt(c, center);
    boost::geometry::read_wkt(p, poly);
    
    {
        int i = 0;
        for (auto p : poly[0].outer())
        {
            auto distance = boost::geometry::distance(center, p, Haversine());
            std::cout << "Haversine distance center<>polygons[0][" << i++ << "]: " << distance << std::endl;
        }
    }
    
    {
        auto distance = boost::geometry::distance(center, poly, Haversine());
        std::cout << "Haversine distance center<>polygons: " << distance << std::endl;
        std::cout << "Haversine distance center<>polygons * radius: " << distance*mean_radius << std::endl;
    }
}

The output with boost 1.67 is:

Haversine distance center<>polygons[0][0]: 85.5957
Haversine distance center<>polygons[0][1]: 74.0043
Haversine distance center<>polygons[0][2]: 76.0906
Haversine distance center<>polygons[0][3]: 84.8703
Haversine distance center<>polygons[0][4]: 85.5957
Haversine distance center<>polygons: 1.16158e-05
Haversine distance center<>polygons * radius: 74.0043

As one can see, the distance returned does not seem to be multiplied by the given radius.

~This leads to another question, it is not clear in the documentation that the distance between a point and a polygon is the distance between the point and the closest point of the polygon.~

Cheers :)

[daedric]

The bug seems to be caused by some fallback on the strategy::distance::cross_track to which the Haversine strategy is not given so it is instantiated with the default radius of 1.

[vissarion]

First of all, when computing the distance between point and polygon the correct strategy to use is strategy::distance::cross_track and not strategy::distance::haversine. Then you will get the desired result.

On the other hand the fallback call that you mention is indeed buggy since it neglects the radius of the passed haversine strategy.