162 4 Geometry standards
A multi curve is simple if and only if all of its elements are simple and the only
intersections between any two elements occur at points that are on the boundaries of
both elements.
A multi curve is closed if all of its elements are closed. The boundary of a closed
multi curve is always empty.
4.4.3 Polygon and MultiPolygon
A surface (class Surface) consists of one or many polygons (class Polygon).
A polygon (class Polygon) is a planar area defined by one exterior boundary and
zero or more interior boundaries. Each interior boundary defines a hole in the polygon.
The most important mIes that define valid polygons are as follows:
• Polygons are topologically closed.
• The boundary of a polygon consists of a set of linear rings (class LinearRing)
that make up its exterior and interior boundaries.
• The interior of every polygon is a connected point set. This is the area within
the polygon.
• The exterior of a polygon with one or more holes is not connected. Each hole
defines a connected component of the exterior.
(1)
(2)
(3)
Fig. 4.56. Polygons with 1, 2, and 3 LinearRings respectively (IS054 2000)
(1)
(2)
(3)
(4)
Fig. 4.57. Examples of objects not representable as a single instance ofPolygon (IS054 2000)