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The Polygon Concept describes the requirements for a polygon type. All algorithms in Boost.Geometry will check any geometry arguments against the concept requirements.
A polygon is A polygon is a planar surface defined by one exterior boundary and zero or more interior boundaries (OGC Simple Feature Specification).
So the definition of a Boost.Geometry polygon differs a bit from e.g. Wiki, where a polygon does not have holes. A polygon of Boost.Geometry is a polygon with or without holes. (A polygon without holes is a helper geometry within Boost.Geometry, and referred to as a ring.)
The Polygon Concept is defined as following:
traits::tag
              defining polygon_tag
              as type
            traits::ring_type
              defining the type of its exterior ring and interior rings as type
            ring_type
              must fulfill the Ring
              Concept
            traits::interior_type
              defining the type of the collection of its interior rings as type;
              this collection itself must fulfill a Boost.Range Random Access Range
              Concept
            traits::exterior_ring
              with two functions named get,
              returning the exterior ring, one being const, the other being non const
            traits::interior_rings
              with two functions named get,
              returning the interior rings, one being const, the other being non
              const
            Besides the Concepts, which are checks on compile-time, there are some other rules that valid polygons must fulfill. This follows the opengeospatial rules (see link above).
ring_type
              is defined as clockwise, the exterior ring must have the clockwise
              orientation, and any interior ring must be reversed w.r.t. the defined
              orientation (so: counter clockwise for clockwise exterior rings). If
              the ring_type is defined
              counter clockwise, it is vice versa.
            ring_type
              is defined as closed, all rings must be closed: the first point must
              be spatially equal to the last point.
            The algorithms such as intersection, area, centroid, union, etc. do not check validity. There will be an algorithm is_valid which checks for validity against these rules, at runtime, and which can be called (by the library user) before.
If the input is invalid, the output might be invalid too. For example: if a polygon which should be closed is not closed, the area will be incorrect.
#include
              boost/geometry/geometries/adapted/boost_polygon/polygon.hpp>)