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##### discrete_frechet_distance

Calculate the discrete Frechet distance between two geometries.

###### Description

The free function `discrete_frechet_distance` calculates the discrete Frechet distance between two geometries.

###### Synopsis

    template<typename Geometry1, typename Geometry2>
    auto discrete_frechet_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

###### Header

Either

`#include <boost/geometry.hpp>`

Or

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

###### Conformance

The function `discrete_frechet_distance` is not defined by OGC.

| Note
PostGIS contains an algorithm ST_FrechetDistance with similar functionality. See the PostGIS documentation.

###### Supported geometries

Geometries | Status
--- | ---
Linestring-Linestring |

| Note
The units of the distance depends on strategy. In order to change the default behavior a user has to create a strategy and pass it explicitly into the algorithm.

###### Example

Calculate Similarity between two geometries as the discrete frechet distance between them.

    #include <iostream>

    #include <boost/geometry.hpp>
    #include <boost/geometry/geometries/point_xy.hpp>
    #include <boost/geometry/geometries/linestring.hpp>

    int main()
    {
        using point_type = boost::geometry::model::d2::point_xy<double>;
        using linestring_type = boost::geometry::model::linestring<point_type>;

        linestring_type ls1, ls2;
        boost::geometry::read_wkt("LINESTRING(0 0,1 1,1 2,2 1,2 2)", ls1);
        boost::geometry::read_wkt("LINESTRING(1 0,0 1,1 1,2 1,3 1)", ls2);

        double res = boost::geometry::discrete_frechet_distance(ls1, ls2);

        std::cout << "Discrete Frechet Distance: " << res << std::endl;

        return 0;
    }

Output:

    Discrete Frechet Distance:  1.41421