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##### discrete_hausdorff_distance (with strategy)

Calculate the discrete Hausdorff distance between two geometries using the specified strategy.

###### Description

The free function `discrete_hausdorff_distance` calculates the discrete Hausdorff distance between two geometries.

###### Synopsis

    template<typename Geometry1, typename Geometry2, typename Strategy>
    auto discrete_hausdorff_distance(Geometry1 const & geometry1, Geometry2 const & geometry2, Strategy const & strategy)

###### 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
Strategy const & | Any type fulfilling a Distance Strategy Concept | strategy | The strategy which will be used for point to point distance calculations

###### Header

Either

`#include <boost/geometry.hpp>`

Or

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

###### Conformance

The function `discrete_hausdorff_distance` is not defined by OGC.

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

###### Supported geometries

Geometries | Status
--- | ---
Linestring-Linestring |
MultiPoint-MultiPoint |
Point-MultiPoint |
MultiLineString-MultiLinestring |

| 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.

###### Available Strategies

- Pythagoras (cartesian)
- Haversine (spherical)
- One of the geographic point to point strategies

###### Example

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

    #include <iostream>

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

    int main()
    {
        namespace bg = boost::geometry;
        using point_type = bg::model::point<double, 2, bg::cs::geographic<bg::degree>>;
        using linestring_type = bg::model::linestring<point_type>;

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

        bg::srs::spheroid<double> spheroid(6378137.0, 6356752.3142451793);
        bg::strategy::distance::geographic<> strategy(spheroid);

        double res = bg::discrete_hausdorff_distance(ls1, ls2, strategy);

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

        return 0;
    }

Output:

    Discrete Hausdorff Distance: 110574