A Polygon is a planar Surface, defined by 1 exterior boundary and 0 or more interior boundaries. Each interior boundary defines a hole in the Polygon. The assertions for polygons (the rules that define valid polygons) are: 1. Polygons are topologically closed. 2. The boundary of a Polygon consists of a set of LinearRings that make up its exterior and interior boundaries. 3. No two rings in the boundary cross, the rings in the boundary of a Polygon may intersect at a Point but only as a tangent : ∀ P ∈ Polygon, ∀ c1, c2 ∈ P.Boundary(), c1 ≠ c2, ∀ p, q ∈ Point, p, q ∈ c1, p ≠ q, [ p ∈ c2 ⇒ q ∉ c2] 4. A Polygon may not have cut lines, spikes or punctures: ∀ P ∈ Polygon, P = Closure(Interior(P)) 5. The Interior of every Polygon is a connected point set. 6. The Exterior of a Polygon with 1 or more holes is not connected. Each hole defines a connected component of the Exterior. In the above assertions, Interior, Closure and Exterior have the standard topological definitions. The combination of 1 and 3 make a Polygon a Regular Closed point set. Polygons are simple geometries.

public interface IPolygon

Public Interface IPolygon

public interface class IPolygon

type IPolygon =  interface end