The set of geometry types proposed by OGC's SQL with Geometry Types environment is based on the OpenGIS Geometry Model. In this model, each geometric object has the following general properties:
It is associated with a Spatial Reference System, which describes the coordinate space in which the object is defined.
It belongs to some geometry class.
The geometry classes define a hierarchy as follows:
Geometry (non-instantiable)
Point (instantiable)
Curve (non-instantiable)
LineString (instantiable)
Line
LinearRing
Surface (non-instantiable)
Polygon (instantiable)
GeometryCollection (instantiable)
MultiPoint (instantiable)
MultiCurve (non-instantiable)
MultiLineString
(instantiable)
MultiSurface (non-instantiable)
MultiPolygon (instantiable)
It is not possible to create objects in non-instantiable 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 non-instantiable
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.
Geometry is the root class of the hierarchy.
It is a non-instantiable class but has a number of properties
that are common to all geometry values created from any of the
Geometry subclasses. These properties are
described in the following list. Particular subclasses have
their own specific properties, described later.
Geometry Properties
A geometry value has the following properties:
Its type. Each geometry belongs to one of the instantiable classes in the hierarchy.
Its SRID, or Spatial Reference Identifier. This value identifies the geometry's associated Spatial Reference System that describes the coordinate space in which the geometry object is defined.
In MySQL, the SRID value is just an integer associated with the geometry value. All calculations are done assuming Euclidean (planar) geometry.
Its coordinates in its Spatial Reference System, represented as double-precision (eight-byte) numbers. All non-empty geometries include at least one pair of (X,Y) coordinates. Empty geometries contain no coordinates.
Coordinates are related to the SRID. For example, in different coordinate systems, the distance between two objects may differ even when objects have the same coordinates, because the distance on the planar coordinate system and the distance on the geocentric system (coordinates on the Earth's surface) are different things.
Its interior, boundary, and exterior.
Every geometry occupies some position in space. The exterior of a geometry is all space not occupied by the geometry. The interior is the space occupied by the geometry. The boundary is the interface between the geometry's interior and exterior.
Its MBR (Minimum Bounding Rectangle), or Envelope. This is the bounding geometry, formed by the minimum and maximum (X,Y) coordinates:
((MINX MINY, MAXX MINY, MAXX MAXY, MINX MAXY, MINX MINY))
Whether the value is simple
or non-simple. Geometry
values of types (LineString,
MultiPoint,
MultiLineString) are either simple or
non-simple. Each type determines its own assertions for
being simple or non-simple.
Whether the value is closed
or not closed. Geometry
values of types (LineString,
MultiString) are either closed or not
closed. Each type determines its own assertions for being
closed or not closed.
Whether the value is empty
or non-empty A geometry is
empty if it does not have any points. Exterior, interior,
and boundary of an empty geometry are not defined (that is,
they are represented by a NULL value). An
empty geometry is defined to be always simple and has an
area of 0.
Its dimension. A geometry can have a dimension of –1, 0, 1, or 2:
–1 for an empty geometry.
0 for a geometry with no length and no area.
1 for a geometry with non-zero length and zero area.
2 for a geometry with non-zero area.
Point objects have a dimension of zero.
LineString objects have a dimension of 1.
Polygon objects have a dimension of 2.
The dimensions of MultiPoint,
MultiLineString, and
MultiPolygon objects are the same as the
dimensions of the elements they consist of.
A Point is a geometry that represents a
single location in coordinate space.
Point
Examples
Imagine a large-scale map of the world with many cities. A
Point object could represent each city.
On a city map, a Point object could
represent a bus stop.
Point
Properties
X-coordinate value.
Y-coordinate value.
Point is defined as a zero-dimensional
geometry.
The boundary of a Point is the empty set.
A Curve is a one-dimensional geometry,
usually represented by a sequence of points. Particular
subclasses of Curve define the type of
interpolation between points. Curve is a
non-instantiable class.
Curve
Properties
A Curve has the coordinates of its
points.
A Curve is defined as a one-dimensional
geometry.
A Curve is simple if it does not pass
through the same point twice.
A Curve is closed if its start point is
equal to its endpoint.
The boundary of a closed Curve is empty.
The boundary of a non-closed Curve
consists of its two endpoints.
A Curve that is simple and closed is a
LinearRing.
A LineString is a Curve
with linear interpolation between points.
LineString
Examples
On a world map, LineString objects could
represent rivers.
In a city map, LineString objects could
represent streets.
LineString
Properties
A LineString has coordinates of segments,
defined by each consecutive pair of points.
A LineString is a Line
if it consists of exactly two points.
A LineString is a
LinearRing if it is both closed and
simple.
A Surface is a two-dimensional geometry. It
is a non-instantiable class. Its only instantiable subclass is
Polygon.
Surface
Properties
A Surface is defined as a two-dimensional
geometry.
The OpenGIS specification defines a simple
Surface as a geometry that consists of a
single “patch” that is associated with a single
exterior boundary and zero or more interior boundaries.
The boundary of a simple Surface is the
set of closed curves corresponding to its exterior and
interior boundaries.
A Polygon is a planar
Surface representing a multisided geometry.
It is defined by a single exterior boundary and zero or more
interior boundaries, where each interior boundary defines a hole
in the Polygon.
Polygon
Examples
On a region map, Polygon objects could
represent forests, districts, and so on.
Polygon
Assertions
The boundary of a Polygon consists of a
set of LinearRing objects (that is,
LineString objects that are both simple
and closed) that make up its exterior and interior
boundaries.
A Polygon has no rings that cross. The
rings in the boundary of a Polygon may
intersect at a Point, but only as a
tangent.
A Polygon has no lines, spikes, or
punctures.
A Polygon has an interior that is a
connected point set.
A Polygon may have holes. The exterior of
a Polygon with holes is not connected.
Each hole defines a connected component of the exterior.
The preceding assertions make a Polygon a
simple geometry.
A GeometryCollection is a geometry that is a
collection of one or more geometries of any class.
All the elements in a GeometryCollection must
be in the same Spatial Reference System (that is, in the same
coordinate system). There are no other constraints on the
elements of a GeometryCollection, although
the subclasses of GeometryCollection
described in the following sections may restrict membership.
Restrictions may be based on:
Element type (for example, a MultiPoint
may contain only Point elements)
Dimension
Constraints on the degree of spatial overlap between elements
A MultiPoint is a geometry collection
composed of Point elements. The points are
not connected or ordered in any way.
MultiPoint
Examples
On a world map, a MultiPoint could
represent a chain of small islands.
On a city map, a MultiPoint could
represent the outlets for a ticket office.
MultiPoint
Properties
A MultiPoint is a zero-dimensional
geometry.
A MultiPoint is simple if no two of its
Point values are equal (have identical
coordinate values).
The boundary of a MultiPoint is the empty
set.
A MultiCurve is a geometry collection
composed of Curve elements.
MultiCurve is a non-instantiable class.
MultiCurve
Properties
A MultiCurve is a one-dimensional
geometry.
A MultiCurve is simple if and only if all
of its elements are simple; the only intersections between
any two elements occur at points that are on the boundaries
of both elements.
A MultiCurve boundary is obtained by
applying the “mod 2 union rule” (also known as
the “odd-even rule”): A point is in the
boundary of a MultiCurve if it is in the
boundaries of an odd number of MultiCurve
elements.
A MultiCurve is closed if all of its
elements are closed.
The boundary of a closed MultiCurve is
always empty.
A MultiLineString is a
MultiCurve geometry collection composed of
LineString elements.
MultiLineString
Examples
On a region map, a MultiLineString could
represent a river system or a highway system.
A MultiSurface is a geometry collection
composed of surface elements. MultiSurface is
a non-instantiable class. Its only instantiable subclass is
MultiPolygon.
MultiSurface
Assertions
Two MultiSurface surfaces have no
interiors that intersect.
Two MultiSurface elements have boundaries
that intersect at most at a finite number of points.
A MultiPolygon is a
MultiSurface object composed of
Polygon elements.
MultiPolygon
Examples
On a region map, a MultiPolygon could
represent a system of lakes.
MultiPolygon
Assertions
A MultiPolygon has no two
Polygon elements with interiors that
intersect.
A MultiPolygon has no two
Polygon elements that cross (crossing is
also forbidden by the previous assertion), or that touch at
an infinite number of points.
A MultiPolygon may not have cut lines,
spikes, or punctures. A MultiPolygon is a
regular, closed point set.
A MultiPolygon that has more than one
Polygon has an interior that is not
connected. The number of connected components of the
interior of a MultiPolygon is equal to
the number of Polygon values in the
MultiPolygon.
MultiPolygon
Properties
A MultiPolygon is a two-dimensional
geometry.
A MultiPolygon boundary is a set of
closed curves (LineString values)
corresponding to the boundaries of its
Polygon elements.
Each Curve in the boundary of the
MultiPolygon is in the boundary of
exactly one Polygon element.
Every Curve in the boundary of an
Polygon element is in the boundary of the
MultiPolygon.