...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 using the specified strategy.
The free function within checks if the first geometry is completely inside the second geometry, using the specified strategy. Reasons to specify a strategy include: use another coordinate system for calculations; construct the strategy beforehand (e.g. with the radius of the Earth); select a strategy when there are more than one available for a calculation.
template<typename Geometry1, typename Geometry2, typename Strategy> bool within(Geometry1 const & geometry1, Geometry2 const & geometry2, Strategy const & strategy)
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 
Strategy const & 
strategy 
strategy to be used 
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
[within_strategy] [within_strategy_output]