Polygon Concept

Description

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.)

Concept Definition

The Polygon Concept is defined as following:

there must be a specialization of traits::tag defining polygon_tag as type
there must be a specialization of traits::ring_type defining the type of its exterior ring and interior rings as type
this type defined by ring_type must fulfill the Ring Concept
there must be a specialization of 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
there must be a specialization of traits::exterior_ring with two functions named get, returning the exterior ring, one being const, the other being non const
there must be a specialization of traits::interior_rings with two functions named get, returning the interior rings, one being const, the other being non const

Rules

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).

Polygons are simple geometric objects (See also wiki but holes are allowed in Boost.Geometry polygons).
If the polygons underlying 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.
If the polygons underlying ring_type is defined as closed, all rings must be closed: the first point must be spatially equal to the last point.
The interior is a connected point set.
There should be no self intersections, but self tangencies (between exterior/interior rings) are allowed (as long as the interior is a connected point set.
There should be no cut lines, spikes or punctures.
The interior rings should be located within the exterior ring. Interior rings may not be located within each other.

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.

Available Models

polygon
a Boost.Polygon polygon_with_holes_data (requires #include boost/geometry/geometries/adapted/boost_polygon/polygon.hpp>)