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##### distance

Calculate the distance between two geometries.

###### Description

The free function distance calculates the distance between two geometries. It uses the default strategy, based on the coordinate system of the geometry.

###### Synopsis

    template<typename Geometry1, typename Geometry2>
    auto distance(Geometry1 const & geometry1, Geometry2 const & geometry2)

###### Parameters

Type | Concept | Name | Description
--- | --- | --- | ---
Geometry1 const & | Any type fulfilling a Geometry Concept | geometry1 | A model of the specified concept
Geometry2 const & | Any type fulfilling a Geometry Concept | geometry2 | A model of the specified concept

###### Returns

The calculated distance

###### Header

Either

`#include <boost/geometry.hpp>`

Or

`#include <boost/geometry/algorithms/distance.hpp>`

###### Conformance

The function distance implements function Distance from the OGC Simple Feature Specification.

###### Supported geometries

| Point | Segment | Box | Linestring | Ring | Polygon | MultiPoint | MultiLinestring | MultiPolygon | Variant
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Point |  |  |  |  |  |  |  |  |  |
Segment |  |  |  |  |  |  |  |  |  |
Box |  |  |  |  |  |  |  |  |  |
Linestring |  |  |  |  |  |  |  |  |  |
Ring |  |  |  |  |  |  |  |  |  |
Polygon |  |  |  |  |  |  |  |  |  |
MultiPoint |  |  |  |  |  |  |  |  |  |
MultiLinestring |  |  |  |  |  |  |  |  |  |
MultiPolygon |  |  |  |  |  |  |  |  |  |
Variant |  |  |  |  |  |  |  |  |  |

###### Complexity

For point to geometry: linear

For multi-point to ring/polygon/multi-polygon: currently quadratic

For all other geometry combinations: linearithmic

###### Example

Shows calculation of distance of point to some other geometries

    #include <iostream>
    #include <list>

    #include <boost/geometry.hpp>
    #include <boost/geometry/geometries/linestring.hpp>
    #include <boost/geometry/geometries/point_xy.hpp>
    #include <boost/geometry/geometries/polygon.hpp>
    #include <boost/geometry/geometries/multi_point.hpp>
    #include <boost/geometry/geometries/multi_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_type;
        typedef boost::geometry::model::linestring<point_type> linestring_type;
        typedef boost::geometry::model::multi_point<point_type> multi_point_type;

        point_type p(1,2);
        polygon_type poly;
        linestring_type line;
        multi_point_type mp;

        boost::geometry::read_wkt(
            "POLYGON((2 1.3,2.4 1.7,2.8 1.8,3.4 1.2,3.7 1.6,3.4 2,4.1 3,5.3 2.6,5.4 1.2,4.9 0.8,2.9 0.7,2 1.3)"
                "(4.0 2.0, 4.2 1.4, 4.8 1.9, 4.4 2.2, 4.0 2.0))", poly);
        line.push_back(point_type(0,0));
        line.push_back(point_type(0,3));
        mp.push_back(point_type(0,0));
        mp.push_back(point_type(3,3));

        std::cout
            << "Point-Poly: " << boost::geometry::distance(p, poly) << std::endl
            << "Point-Line: " << boost::geometry::distance(p, line) << std::endl
            << "Point-MultiPoint: " << boost::geometry::distance(p, mp) << std::endl;

        return 0;
    }

Output:

    Point-Poly: 1.22066
    Point-Line: 1
    Point-MultiPoint: 2.23607