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##### centroid

Calculates the centroid of a geometry.

###### Description

The free function centroid calculates the geometric center (or: center of mass) of a geometry. It uses the default strategy, based on the coordinate system of the geometry.

###### Synopsis

    template<typename Geometry, typename Point>
    void centroid(Geometry const & geometry, Point & c)

###### Parameters

Type | Concept | Name | Description
--- | --- | --- | ---
Geometry const & | Any type fulfilling a Geometry Concept | geometry | A model of the specified concept
Point & | Any type fulfilling a Point Concept | c | The calculated centroid will be assigned to this point reference

###### Header

Either

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

Or

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

###### Conformance

The function centroid implements function Centroid from the OGC Simple Feature Specification.

###### Behavior

Case | Behavior
--- | ---
Point | Returns the point itself as the centroid
Multi Point | Calculates centroid (based on average)
linear (e.g. linestring) | Calculates centroid (based on weighted length)
areal (e.g. polygon) | Calculates centroid
Empty (e.g. polygon without points) | Throws a centroid_exception
Cartesian | Implemented
Spherical | Calculates the centroid as if based on Cartesian coordinates

###### Supported geometries

| 2D | 3D
--- | --- | ---
Point |  |
Segment |  |
Box |  |
Linestring |  |
Ring |  |
Polygon |  |
MultiPoint |  |
MultiLinestring |  |
MultiPolygon |  |

###### Complexity

Linear

###### Example

Shows calculation of a centroid of a 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>

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

        polygon_type poly;
        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);

        point_type p;
        boost::geometry::centroid(poly, p);

        std::cout << "centroid: " << boost::geometry::dsv(p) << std::endl;

        return 0;
    }

Output:

    centroid: (4.04663, 1.6349)

Note that the centroid might be located in a hole or outside a polygon, easily.