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::ring_typedefining the type of its exterior ring and interior rings as type
ring_typemust fulfill the Ring Concept
traits::interior_typedefining 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_ringwith two functions named
get, returning the exterior ring, one being const, the other being non const
traits::interior_ringswith 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_typeis defined as clockwise, the exterior ring must have the clockwise orientation, and any interior ring must be counter clockwise. If the
ring_typeis defined counter clockwise, it is vice versa.
ring_typeis 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.