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#### intersection

Calculate the intersection of two geometries.

###### Description

The free function intersection calculates the spatial set theoretic intersection of two geometries.

###### Synopsis

    template<typename Geometry1, typename Geometry2, typename GeometryOut>
    bool intersection(Geometry1 const & geometry1, Geometry2 const & geometry2, GeometryOut & geometry_out)

###### 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
GeometryOut & | Collection of geometries (e.g. std::vector, std::deque, boost::geometry::multi*) of which the value_type fulfills a Point, LineString or Polygon concept, or it is the output geometry (e.g. for a box) | geometry_out | The output geometry, either a multi_point, multi_polygon, multi_linestring, or a box (for intersection of two boxes)

###### Header

Either

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

Or

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

###### Conformance

The function intersection implements function Intersection from the OGC Simple Feature Specification.

###### Behavior

Case | Behavior
--- | ---
GeometryOut is a Point | Calculates intersection points of input geometries
GeometryOut is a Linestring | Calculates intersection linestrings of input geometries (NYI)
GeometryOut is a Polygon | Calculates intersection polygons of input (multi)polygons and/or boxes

| Note
Check the Polygon Concept for the rules that polygon input for this algorithm should fulfill

###### Example

Shows the intersection of two polygons

    #include <iostream>
    #include <deque>

    #include <boost/geometry.hpp>
    #include <boost/geometry/geometries/point_xy.hpp>
    #include <boost/geometry/geometries/polygon.hpp>
    #include <boost/geometry/io/wkt/wkt.hpp>

    #include <boost/foreach.hpp>

    int main()
    {
        typedef boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > polygon;

        polygon green, blue;

        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))", green);

        boost::geometry::read_wkt(
            "POLYGON((4.0 -0.5 , 3.5 1.0 , 2.0 1.5 , 3.5 2.0 , 4.0 3.5 , 4.5 2.0 , 6.0 1.5 , 4.5 1.0 , 4.0 -0.5))", blue);

        std::deque<polygon> output;
        boost::geometry::intersection(green, blue, output);

        int i = 0;
        std::cout << "green && blue:" << std::endl;
        BOOST_FOREACH(polygon const& p, output)
        {
            std::cout << i++ << ": " << boost::geometry::area(p) << std::endl;
        }

        return 0;
    }

Output:

    green && blue:
    0: 2.50205

###### See also

- union
- difference
- sym_difference (symmetric difference)