...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
Calculates the area of a geometry.
The free function area calculates the area of a geometry. It uses the default strategy, based on the coordinate system of the geometry.
The area algorithm calculates the surface area of all geometries having a surface, namely box, polygon, ring, multipolygon. The units are the square of the units used for the points defining the surface. If subject geometry is defined in meters, then area is calculated in square meters.
The area calculation can be done in all three common coordinate systems, Cartesian, Spherical and Geographic as well.
template<typename Geometry> default_area_result<Geometry>::type area(Geometry const & geometry)
Type 
Concept 
Name 
Description 

Geometry const & 
Any type fulfilling a Geometry Concept 
geometry 
A model of the specified concept 
The calculated area
Either
#include <boost/geometry/geometry.hpp>
Or
#include <boost/geometry/algorithms/area.hpp>
The function area implements function Area from the OGC Simple Feature Specification.
Case 
Behavior 

pointlike (e.g. point) 
Returns 0 
linear (e.g. linestring) 
Returns 0 
areal (e.g. polygon) 
Returns the area 
Cartesian 
Returns the area in the same units as the input coordinates 
Spherical 
Returns the area on a unit sphere (or another sphere, if specified as such in the constructor of the strategy) 
Reversed polygon (coordinates not according their orientiation) 
Returns the negative area 
Geometry 
Status 

Point 

Segment 

Box 

Linestring 

Ring 

Polygon 

MultiPoint 

MultiLinestring 

MultiPolygon 

Linear
Calculate the area of a polygon
#include <iostream> #include <boost/geometry.hpp> #include <boost/geometry/geometries/point_xy.hpp> #include <boost/geometry/geometries/polygon.hpp> #include <boost/geometry/io/wkt/wkt.hpp> namespace bg = boost::geometry; int main() { // Calculate the area of a cartesian polygon bg::model::polygon<bg::model::d2::point_xy<double> > poly; bg::read_wkt("POLYGON((0 0,0 7,4 2,2 0,0 0))", poly); double area = bg::area(poly); std::cout << "Area: " << area << std::endl; // Calculate the area of a spherical equatorial polygon bg::model::polygon<bg::model::point<float, 2, bg::cs::spherical_equatorial<bg::degree> > > sph_poly; bg::read_wkt("POLYGON((0 0,0 45,45 0,0 0))", sph_poly); area = bg::area(sph_poly); std::cout << "Area: " << area << std::endl; return 0; }
Output:
Area: 16 Area: 0.339837