...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
Checks if the first geometry is completely inside the second geometry.
The free function within checks if the first geometry is completely inside the second geometry.
template<typename Geometry1, typename Geometry2> bool within(Geometry1 const & geometry1, Geometry2 const & geometry2)
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 
true if geometry1 is completely contained within geometry2, else false
Either
#include <boost/geometry/geometry.hpp>
Or
#include <boost/geometry/algorithms/within.hpp>
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 
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. 
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.
Linear
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