13.4.2.1 The Geometry Class Hierarchy

The geometry classes define a hierarchy as follows:

• Geometry (noninstantiable)

  • Point (instantiable)

  • Curve (noninstantiable)

    • LineString (instantiable)

      • Line

      • LinearRing

  • Surface (noninstantiable)

    • Polygon (instantiable)

  • GeometryCollection (instantiable)

    • MultiPoint (instantiable)

    • MultiCurve (noninstantiable)

      • MultiLineString (instantiable)

    • MultiSurface (noninstantiable)

      • MultiPolygon (instantiable)

It is not possible to create objects in noninstantiable classes. It is possible to create objects in instantiable classes. All classes have properties, and instantiable classes may also have assertions (rules that define valid class instances).

Geometry is the base class. It is an abstract class. The instantiable subclasses of Geometry are restricted to zero-, one-, and two-dimensional geometric objects that exist in two-dimensional coordinate space. All instantiable geometry classes are defined so that valid instances of a geometry class are topologically closed (that is, all defined geometries include their boundary).

The base Geometry class has subclasses for Point, Curve, Surface, and GeometryCollection:

• Point represents zero-dimensional objects.

• Curve represents one-dimensional objects, and has subclass LineString, with sub-subclasses Line and LinearRing.

• Surface is designed for two-dimensional objects and has subclass Polygon.

• GeometryCollection has specialized zero-, one-, and two-dimensional collection classes named MultiPoint, MultiLineString, and MultiPolygon for modeling geometries corresponding to collections of Points, LineStrings, and Polygons, respectively. MultiCurve and MultiSurface are introduced as abstract superclasses that generalize the collection interfaces to handle Curves and Surfaces.

Geometry, Curve, Surface, MultiCurve, and MultiSurface are defined as noninstantiable classes. They define a common set of methods for their subclasses and are included for extensibility.

Point, LineString, Polygon, GeometryCollection, MultiPoint, MultiLineString, and MultiPolygon are instantiable classes.