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#### difference

###### Description

Calculate the difference of two geometries

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

###### Synopsis

    template<typename Geometry1, typename Geometry2, typename Collection>
    void difference(Geometry1 const & geometry1, Geometry2 const & geometry2, Collection & output_collection)

###### 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
Collection & | output collection, either a multi-geometry, or a std::vector<Geometry> / std::deque<Geometry> etc | output_collection | the output collection

###### Header

Either

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

Or

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

###### Conformance

The function difference implements function Difference from the OGC Simple Feature Specification.

###### Behavior

Case | Behavior
--- | ---
areal (e.g. polygon) | All combinations of: box, ring, polygon, multi_polygon
linear (e.g. linestring) / areal (e.g. polygon) | A combinations of a (multi) linestring with a (multi) polygon results in a collection of linestrings
Other geometries | Not yet supported in this version
Spherical | Not yet supported in this version
Three dimensional | Not yet supported in this version

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

###### Example

Shows how to subtract one polygon from another polygon

    #include <iostream>
    #include <list>

    #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::list<polygon> output;
        boost::geometry::difference(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;
        }

        output.clear();
        boost::geometry::difference(blue, green, output);

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

        return 0;
    }

Output:

    green - blue:
    0: 0.02375
    1: 0.542951
    2: 0.0149697
    3: 0.226855
    4: 0.839424

    blue - green:
    0: 0.525154
    1: 0.015
    2: 0.181136
    3: 0.128798
    4: 0.340083
    5: 0.307778

###### See also

- sym_difference (symmetric difference)
- intersection
- union