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##### within

Checks if the first geometry is completely inside the second geometry.

###### Description

The free function within checks if the first geometry is completely inside the second geometry.

###### Synopsis

    template<typename Geometry1, typename Geometry2>
    bool within(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 which might be within the second geometry
Geometry2 const & | Any type fulfilling a Geometry Concept | geometry2 | A model of the specified concept which might contain the first geometry

###### Returns

true if geometry1 is completely contained within geometry2, else false

###### Header

Either

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

Or

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

###### Conformance

The function within implements function Within from the OGC Simple Feature Specification.

| Note
OGC defines within as completely within and not on the border. See the notes for within / on the border

###### Supported geometries

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

| Note
In this status matrix above: columns are types of first parameter and rows are types of second parameter. So a point can be checked to be within a polygon, but not vice versa.

###### Notes

If a point is located exactly on the border of a geometry, the result depends on the strategy. The default strategy (Winding (coordinate system agnostic)) returns false in that case.

If a polygon has a reverse oriented (e.g. counterclockwise for a clockwise typed polygon), the result also depends on the strategy. The default strategy returns still true if a point is completely within the reversed polygon. There is a specific strategy which returns false in this case.

###### Complexity

Linear

###### See also

- covered_by

###### Example

Shows how to detect if a point is inside a polygon, or not

    #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(4, 1);

        std::cout << "within: " << (boost::geometry::within(p, poly) ? "yes" : "no") << std::endl;

        return 0;
    }

Output:

    within: yes