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#### equals

Checks if a geometry are spatially equal.

###### Description

The free function equals checks if the first geometry is spatially equal the second geometry. Spatially equal means that the same point set is included. A box can therefore be spatially equal to a ring or a polygon, or a linestring can be spatially equal to a multi-linestring or a segment. This only works theoretically, not all combinations are implemented yet.

###### Synopsis

    template<typename Geometry1, typename Geometry2>
    bool equals(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

###### Returns

Returns true if two geometries are spatially equal

###### Header

Either

`#include <boost/geometry.hpp>`

Or

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

###### Conformance

The function equals implements function Equals from the OGC Simple Feature Specification.

###### Supported geometries

| Point | Segment | Box | Linestring | Ring | Polygon | MultiPoint | MultiLinestring | MultiPolygon | Variant
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Point |  |  |  |  |  |  |  |  |  |
Segment |  |  |  |  |  |  |  |  |  |
Box |  |  |  |  |  |  |  |  |  |
Linestring |  |  |  |  |  |  |  |  |  |
Ring |  |  |  |  |  |  |  |  |  |
Polygon |  |  |  |  |  |  |  |  |  |
MultiPoint |  |  |  |  |  |  |  |  |  |
MultiLinestring |  |  |  |  |  |  |  |  |  |
MultiPolygon |  |  |  |  |  |  |  |  |  |
Variant |  |  |  |  |  |  |  |  |  |

###### Complexity

Linear

###### Example

Shows the predicate equals, which returns true if two geometries are spatially equal

    #include <iostream>

    #include <boost/geometry.hpp>
    #include <boost/geometry/geometries/polygon.hpp>
    #include <boost/geometry/geometries/adapted/boost_tuple.hpp>

    BOOST_GEOMETRY_REGISTER_BOOST_TUPLE_CS(cs::cartesian)

    #include <boost/assign.hpp>

    int main()
    {
        using boost::assign::tuple_list_of;

        typedef boost::tuple<int, int> point;

        boost::geometry::model::polygon<point> poly1, poly2;
        boost::geometry::exterior_ring(poly1) = tuple_list_of(0, 0)(0, 5)(5, 5)(5, 0)(0, 0);
        boost::geometry::exterior_ring(poly2) = tuple_list_of(5, 0)(0, 0)(0, 5)(5, 5)(5, 0);

        std::cout
            << "polygons are spatially "
            << (boost::geometry::equals(poly1, poly2) ? "equal" : "not equal")
            << std::endl;

        boost::geometry::model::box<point> box;
        boost::geometry::assign_values(box, 0, 0, 5, 5);

        std::cout
            << "polygon and box are spatially "
            << (boost::geometry::equals(box, poly2) ? "equal" : "not equal")
            << std::endl;

        return 0;
    }

Output:

    polygons are spatially equal
    polygon and box are spatially equal