SIST ISO 19125-1:2005
(Main)Geographic information -- Simple feature access -- Part 1: Common architecture
Geographic information -- Simple feature access -- Part 1: Common architecture
ISO 19125-1:2004 establishes a common architecture for geographic information and defines terms to use within the architecture. It also standardizes names and geometric definitions for Types for Geometry.
ISO 19125-1:2004 does not place any requirements on how to define the Geometry Types in the internal schema nor does it place any requirements on when or how or who defines the Geometry Types. ISO 19125-1:2004 does not attempt to standardize and does not depend upon any part of the mechanism by which Types are added and maintained.
Information géographique -- Accès aux entités simples -- Partie 1: Architecture commune
Geografske informacije – Dostop do enostavnih pojavov – 1. del: Skupna arhitektura
General Information
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INTERNATIONAL ISO
STANDARD 19125-1
First edition
2004-08-01
Corrected version
2004-11-01
Geographic information — Simple feature
access —
Part 1:
Common architecture
Information géographique — Accès aux entités simples —
Partie 1: Architecture commune
Reference number
ISO 19125-1:2004(E)
©
ISO 2004
---------------------- Page: 1 ----------------------
ISO 19125-1:2004(E)
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Published in Switzerland
ii © ISO 2004 – All rights reserved
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ISO 19125-1:2004(E)
Contents Page
Foreword. iv
Introduction . iv
1 Scope. 1
2 Conformance . 1
3 Normative references . 1
4 Terms and definitions. 1
5 Abbreviated terms. 4
6 Architecture . 5
6.1 Geometry object model . 5
6.2 Well-known Text Representation for Geometry. 21
6.3 Well-known Binary Representation for Geometry. 22
6.4 Well-known Text Representation of Spatial Reference Systems. 25
Annex A (informative) The correspondence of concepts of the common architecture with
concepts of the geometry model of ISO 19107. 28
Annex B (informative) Supported spatial reference data . 36
Bibliography . 42
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ISO 19125-1:2004(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 19125-1 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics from a
base document supplied by the Open GIS Consortium, Inc.
ISO 19125 consists of the following parts, under the general title Geographic information — Simple feature
access:
— Part 1: Common architecture
— Part 2: SQL option
This corrected version of ISO 19125-1:2004 incorporates the following corrections:
— a complete version of Figure 9, which was truncated in the original;
— removal from the Foreword of the reference to ISO 19125-3, which has now been deleted.
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ISO 19125-1:2004(E)
Introduction
This part of ISO 19125 describes the common architecture for simple feature geometry. The simple feature
geometry object model is Distributed Computing Platform neutral and uses UML notation. The base Geometry
class has subclasses for Point, Curve, Surface and GeometryCollection. Each geometric object is associated
with a Spatial Reference System, which describes the coordinate space in which the geometric object is
defined.
The extended Geometry model has specialized 0, 1 and 2-dimensional collection classes named MultiPoint,
MultiLineString and MultiPolygon for modelling 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.
The attributes, methods and assertions for each Geometry class are described in Figure 1 in 6.1.1. In
describing methods, this is used to refer to the receiver of the method (the object being messaged).
The SFA COM function “signatures” may use a different notation from SFA SQL. COM notation is more
familiar for COM programmers. However, UML notation is used throughout this part of ISO 19125. There may
also be methods used in this International Standard that differ from one part to another. Where this is the case,
the differences are shown within the part.
This part of ISO 19125 implements a profile of the spatial schema described in ISO 19107:2003, Geographic
information Spatial schema. Annex A provides a detailed mapping of the schema in this part of ISO 19125
with the schema described in ISO 19107:2003.
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INTERNATIONAL STANDARD ISO 19125-1:2004(E)
Geographic information — Simple feature access —
Part 1:
Common architecture
1 Scope
This part of ISO 19125 establishes a common architecture and defines terms to use within the architecture.
This part of ISO 19125 does not attempt to standardize and does not depend upon any part of the mechanism
by which Types are added and maintained, including the following:
a) syntax and functionality provided for defining types;
b) syntax and functionality provided for defining functions;
c) physical storage of type instances in the database;
d) specific terminology used to refer to User Defined Types, for example UDT.
This part of ISO 19125 does standardize names and geometric definitions for Types for Geometry.
This part of ISO 19125 does not place any requirements on how to define the Geometry Types in the internal
schema nor does it place any requirements on when or how or who defines the Geometry Types.
2 Conformance
In order to conform to this part of ISO 19125, an implementation shall satisfy the requirements of one or more
test suites specified in the other parts of ISO 19125.
3 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 19107:2003, Geographic information Spatial schema
ISO 19111:2003, Geographic information Spatial referencing by coordinates
4 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
4.1
boundary
set that represents the limit of an entity
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ISO 19125-1:2004(E)
NOTE Boundary is most commonly used in the context of geometry, where the set is a collection of points or a
collection of objects that represent those points. In other arenas, the term is used metaphorically to describe the transition
between an entity and the rest of its domain of discourse.
[ISO 19107]
4.2
buffer
geometric object (4.14) that contains all direct positions (4.7) whose distance from a specified geometric
object is less than or equal to a given distance
[ISO 19107]
4.3
coordinate
one of a sequence of n-numbers designating the position of a point (4.17) in n-dimensional space
NOTE In a coordinate reference system, the numbers must be qualified by units.
[adapted from ISO 19111]
4.4
coordinate dimension
number of measurements or axes needed to describe a position in a coordinate system (4.6)
[ISO 19107]
4.5
coordinate reference system
coordinate system (4.6) that is related to the real world by a datum
[adapted from ISO 19111]
4.6
coordinate system
set of mathematical rules for specifying how coordinates (4.3) are to be assigned to point (4.17)
[ISO 19111]
4.7
curve
1-dimensional geometric primitive (4.15), representing the continuous image of a line
NOTE The boundary of a curve is the set of points at either end of the curve. If the curve is a cycle, the two ends are
identical, and the curve (if topologically closed) is considered to not have a boundary. The first point is called the start
point, and the last is the end point. Connectivity of the curve is guaranteed by the “continuous image of a line” clause.
A topological theorem states that a continuous image of a connected set is connected.
[ISO 19107]
4.7
direct position
position described by a single set of coordinates (4.3) within a coordinate reference system (4.5)
[ISO 19107]
4.9
end point
last point (4.17) of a curve (4.7)
[ISO 19107]
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ISO 19125-1:2004(E)
4.10
exterior
difference between the universe and the closure
NOTE The concept of exterior is applicable to both topological and geometric complexes.
[ISO 19107]
4.11
feature
abstraction of real world phenomena
NOTE A feature may occur as a type or an instance. Feature type or feature instance is used when only one is meant.
[adapted from ISO 19101]
4.12
feature attribute
characteristic of a feature (4.11)
NOTE A feature attribute has a name, a data type, and a value domain associated to it. A feature attribute for a
feature instance also has an attribute value taken from the value domain.
[adapted from ISO 19101]
4.13
geometric complex
set of disjoint geometric primitives (4.15) where the boundary (4.1) of each geometric primitive can be
represented as the union of other geometric primitives of smaller dimension within the same set
NOTE The geometric primitives in the set are disjoint in the sense that no direct position is interior to more than one
geometric primitive. The set is closed under boundary operations, meaning that for each element in the geometric complex,
there is a collection (also a geometric complex) of geometric primitives that represents the boundary of that element.
Recall that the boundary of a point (the only 0D primitive object type in geometry) is empty. Thus, if the largest dimension
geometric primitive is a solid (3D), the composition of the boundary operator in this definition terminates after at most
3 steps. It is also the case that the boundary of any object is a cycle.
[ISO 19107]
4.14
geometric object
spatial object representing a geometric set
NOTE A geometric object consists of a geometric primitive, a collection of geometric primitives, or a geometric
complex treated as a single entity. A geometric object may be the spatial representation of an object such as a feature or a
significant part of a feature.
[ISO 19107]
4.15
geometric primitive
geometric object (4.14) representing a single, connected, homogeneous element of space
NOTE Geometric primitives are non-decomposed objects that represent information about geometric configuration.
They include points, curves, surfaces, and solids.
[ISO 19107]
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ISO 19125-1:2004(E)
4.16
interior
set of all direct positions (4.7) that are on a geometric object (4.14) but which are not on its boundary (4.1)
NOTE The interior of a topological object is the homomorphic image of the interior of any of its geometric realizations.
This is not included as a definition because it follows from a theorem of topology.
[ISO 19107]
4.17
point
0-dimensional geometric primitive (4.15), representing a position
NOTE The boundary of a point is the empty set.
[ISO 19107]
4.18
simple feature
feature (4.11) restricted to 2D geometry with linear interpolation between vertices, having both spatial and
non spatial attributes
4.19
start point
first point (4.17) of a curve (4.7)
[ISO 19107]
4.20
surface
2-dimensional geometric primitive (4.15), locally representing a continuous image of a region of a plane
NOTE The boundary of a surface is the set of oriented, closed curves that delineate the limits of the surface.
[adapted from ISO 19107]
5 Abbreviated terms
API Application Program Interface
COM Component Object Model
CORBA Common Object Request Broker Architecture
DCE Distributed Computing Environment
DCOM Distributed Component Objected Model
DE-9IM Dimensionally Extended Nine-Intersection Model
IEEE Institute of Electrical and Electronics Engineers, Inc.
NDR Little Endian byte order encoding
OLE Object Linking and Embedding
RPC Remote Procedure Call
SQL Structured Query Language
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ISO 19125-1:2004(E)
SRID Spatial Reference System Identifier
XDR Big Endian byte order encoding
UDT User Defined Type
UML Unified Modeling Language
WKB Well-Known Binary (representation for example, geometry)
6 Architecture
6.1 Geometry object model
6.1.1 Overview
This subclause describes the object model for simple feature geometry. The simple feature geometry object
model is Distributed Computing Platform neutral and uses UML notation. The object model for geometry
is shown in Figure 1. The base Geometry class has subclasses for Point, Curve, Surface and
GeometryCollection. Each geometric object is associated with a Spatial Reference System, which describes
the coordinate space in which the geometric object is defined.
Figure 1 — Geometry class hierarchy
Figure 1 is based on an extended Geometry model with specialized 0-, 1- and 2-dimensional collection
classes named MultiPoint, MultiLineString and MultiPolygon for modelling 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. Figure 1 shows
aggregation lines between the leaf-collection classes and their element classes; the aggregation lines for
non-leaf-collection classes are described in the text.
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ISO 19125-1:2004(E)
The attributes, methods and assertions for each Geometry class are described below. In describing methods,
this is used to refer to the receiver of the method (the object being messaged).
6.1.2 Geometry
6.1.2.1 Description
Geometry is the root class of the hierarchy. Geometry is an abstract (non-instantiable) class.
The instantiable subclasses of Geometry defined in this International Standard are restricted to 0, 1 and
2
2-dimensional geometric objects that exist in 2-dimensional coordinate space (ℜ ).
All instantiable Geometry classes described in this part of ISO 19125 are defined so that valid instances of a
Geometry class are topologically closed, i.e. all defined geometries include their boundary.
6.1.2.2 Basic methods on geometric objects
Dimension ( ):Integer — The inherent dimension of this geometric object, which must be less than or
equal to the coordinate dimension. This specification is restricted to geometries in 2-dimensional
coordinate space.
GeometryType ( ):String — Returns the name of the instantiable subtype of Geometry of which this
geometric object is a instantiable member. The name of the subtype of Geometry is returned as a string.
SRID ( ):Integer — Returns the Spatial Reference System ID for this geometric object.
Envelope( ):Geometry — The minimum bounding box for this Geometry, returned as a Geometry. The
polygon is defined by the corner points of the bounding box [(MINX, MINY), (MAXX, MINY), (MAXX,
MAXY), (MINX, MAXY), (MINX, MINY)].
AsText( ):String — Exports this geometric object to a specific Well-known Text Representation of
Geometry.
AsBinary( ):Binary — Exports this geometric object to a specific Well-known Binary Representation of
Geometry.
IsEmpty( ):Integer — Returns 1 (TRUE) if this geometric object is the empty Geometry. If true, then this
geometric object represents the empty point set, ∅, for the coordinate space.
IsSimple( ):Integer — Returns 1 (TRUE) if this geometric object has no anomalous geometric points,
such as self intersection or self tangency. The description of each instantiable geometric class will include
the specific conditions that cause an instance of that class to be classified as not simple.
Boundary( ):Geometry — Returns the closure of the combinatorial boundary of this geometric object
(Reference [1], section 3.12.2). Because the result of this function is a closure, and hence topologically
closed, the resulting boundary can be represented using representational Geometry primitives
(Reference [1], section 3.12.2).
6.1.2.3 Methods for testing spatial relations between geometric objects
The methods in this subclause are defined and described in more detail following the description of the sub-
types of Geometry.
Equals(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object is “spatially
equal” to anotherGeometry.
Disjoint(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object is “spatially
disjoint” from anotherGeometry.
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ISO 19125-1:2004(E)
Intersects(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
intersects” anotherGeometry.
Touches(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
touches” anotherGeometry.
Crosses(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
crosses’ anotherGeometry.
Within(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object is “spatially
within” anotherGeometry.
Contains(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
contains” anotherGeometry.
Overlaps(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
overlaps” anotherGeometry.
Relate(anotherGeometry:Geometry, intersectionPatternMatrix:String):Integer — Returns 1 (TRUE) if this
geometric object is spatially related to anotherGeometry by testing for intersections between the interior,
boundary and exterior of the two geometric objects as specified by the values in the
intersectionPatternMatrix.
6.1.2.4 Methods that support spatial analysis
Distance(anotherGeometry:Geometry):Double — Returns the shortest distance between any two Points
in the two geometric objects as calculated in the spatial reference system of this geometric object.
Buffer(distance:Double):Geometry — Returns a geometric object that represents all Points whose
distance from this geometric object is less than or equal to distance. Calculations are in the spatial
reference system of this geometric object.
ConvexHull( ):Geometry — Returns a geometric object that represents the convex hull of this geometric
object.
Intersection(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents the
Point set intersection of this geometric object with anotherGeometry.
Union(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents the Point
set union of this geometric object with anotherGeometry.
Difference(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents the
Point set difference of this geometric object with anotherGeometry.
SymDifference(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents
the Point set symmetric difference of this geometric object with anotherGeometry.
6.1.3 GeometryCollection
6.1.3.1 Description
A GeometryCollection is a geometric object that is a collection of 1 or more geometric objects.
All the elements in a GeometryCollection shall be in the same Spatial Reference. This is also the Spatial
Reference for the GeometryCollection.
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ISO 19125-1:2004(E)
GeometryCollection places no other constraints on its elements. Subclasses of GeometryCollection may
restrict membership based on dimension and may also place other constraints on the degree of spatial
overlap between elements.
6.1.3.2 Methods
NumGeometries( ):Integer — Returns the number of geometries in this GeometryCollection.
GeometryN(N:integer):Geometry — Returns the Nth geometry in this GeometryCollection.
6.1.4 Point
6.1.4.1 Description
A Point is a 0-dimensional geometric object and represents a single location in coordinate space. A Point has
an x-coordinate value and a y-coordinate value.
The boundary of a Point is the empty set.
6.1.4.2 Methods
X( ):Double — The x-coordinate value for this Point.
Y( ):Double — The y-coordinate value for this Point.
6.1.5 MultiPoint
A MultiPoint is a 0-dimensional GeometryCollection. The elements of a MultiPoint are restricted to Points. The
Points are not connected or ordered.
A MultiPoint is simple if no two Points in the MultiPoint are equal (have identical coordinate values).
The boundary of a MultiPoint is the empty set.
6.1.6 Curve
6.1.6.1 Description
A Curve is a 1-dimensional geometric object usually stored as a sequence of Points, with the subtype of
Curve specifying the form of the interpolation between Points. This part of ISO 19125 defines only one
subclass of Curve, LineString, which uses linear interpolation between Points.
A Curve is a 1-dimensional geometric object that is the homeomorphic image of a real, closed, interval D = [a,
2
b] = {x ∈ ℜ. a u x u b} under a mapping f:[a,b] → ℜ .
A Curve is simple if it does not pass through the same Point twice (Reference [1], section 3.12.7.3):
∀ c ∈ Curve, [a, b] = c.Domain,
c.IsSimple⇔ (∀ x1, x2 ∈ (a, b] x1 ≠ x2 ⇒ f(x1) ≠ f (x2)) ∧ (∀ x1, x2 ∈ [a, b) x1 ≠ x2 ⇒ f(x1) ≠ f(x2))
A Curve is closed if its start Point is equal to its end Point (Reference [1], section 3.12.7.3).
The boundary of a closed Curve is empty.
A Curve that is simple and closed is a Ring.
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ISO 19125-1:2004(E)
The boundary of a non-closed Curve consists of its two end Points (Reference [1], section 3.12.3.2).
A Curve is defined as topologically closed.
6.1.6.2 Methods
Length( ):Double — The length of this Curve in its associated spatial reference.
StartPoint( ):Point — The start Point of this Curve.
EndPoint( ):Point — The end Point of this Curve.
IsClosed( ):Integer — Returns 1 (TRUE) if this Curve is closed [StartPoint ( ) = EndPoint ( )].
IsRing( ):Integer — Returns 1 (TRUE) if this Curve is closed [StartPoint ( ) = EndPoint ( )] and this Curve
is simple (does not pass through the same Point more than once).
6.1.7 LineString, Line, LinearRing
6.1.7.1 Description
A LineString is a Curve with linear interpolation between Points. Each consecutive pair of Points defines a
Line segment.
A Line is a LineString with exactly 2 Points.
A LinearRing is a LineString that is both closed and simple. The Curve in Figure 2, item (c), is a closed
LineString that is a LinearRing. The Curve in Figure 2, item (d) is a closed LineString that is not a LinearRing.
Key
s start
e end
Figure 2 — Examples of LineStrings — Simple LineString (a), Non-simple LineString (b), Simple,
closed LineString (a LinearRing) (c), Non-simple closed LineString (d)
6.1.7.2 Methods
NumPoints( ):Integer — The number of Points in this LineString.
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ISO 19125-1:2004(E)
PointN(N:Integer):Point — Returns the specified Point N in this LineString.
6.1.8 MultiCurve
6.1.8.1 Description
A MultiCurve is a 1-dimensional GeometryCollection whose elements are Curves as in Figure 3.
MultiCurve is a non-instantiable class in this specification; it defines a set of methods for its subclasses and is
included for reasons of extensibility.
A MultiCurve 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.
The boundary of a MultiCurve is obtained by applying the “mod 2” union rule: A Point is in the boundary of a
MultiCurve if it is in the boundaries of an odd number of elements of the MultiCurve (Reference [1], section
3.12.3.2).
A MultiCurve is closed if all of its elements are closed. The boundary of a closed MultiCurve is always empty.
A MultiCurve is defined as topologically closed.
6.1.8.2 Methods
IsClosed( ):Integer — Returns 1 (TRUE) if this MultiCurve is closed [StartPoint ( ) = EndPoint ( ) for each
Curve in this MultiCurve].
Length( ):Double — The Length of this MultiCurve which is equal to the sum of the lengths of the element
Curves.
6.1.9 MultiLineString
A MultiLineString is a MultiCurve whose elements are LineStrings.
The boundaries for the MultiLineStrings in Figure 3 are (a){s1, e2}, (b) {s1, e1}, (c)∅.
Key
s start
e end
Figure 3 — Examples of MultiLineStrings — Simple MultiLineString (a), Non-simple MultiLineString
with 2 elements (b), Non-simple, closed MultiLineString with 2 elements (c)
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ISO 19125-1:2004(E)
6.1.10 Surface
6.1.10.1 Description
A Surface is a 2-dimensional geometric object.
A simple Surface consists of a single “patch” that is associated with one “exterior boundary” and 0 or more
“interior” boundaries. Simple Surfaces in 3-dimensional space are isomorphic to planar Surfaces. Polyhedral
Surfaces are formed by “stitching” together simple Surfaces along their boundaries, polyhedral Surfaces in
3-dimensional space may not be planar as a whole (Reference [1], sections 3.12.9.1, 3.12.9.3).
The boundary of a simple Surface is the set of closed Curves corresponding to its “exterior” and “interior”
boundaries (Reference [1], section 3.12.9.4).
The only instantiable subclass of Surface defined in this specification, Polygon, is a simple Surface that is
planar.
6.1.10.2 Methods
Area( ):Double — The area of this Surface, as measured in the spatial reference system of this Surface.
Centroid( ):Point — The mathematical centroid for this Surface as a Point. The result is not guaranteed
to be on this Surface.
PointOnSurface( ):Point — A Point guaranteed to be on this Surface.
6.1.11 Polygon
6.1.11.1 Description
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 as follows:
a) Polygons are topologically close
...
SLOVENSKI STANDARD
SIST ISO 19125-1:2005
01-februar-2005
Geografske informacije – Dostop do enostavnih pojavov – 1. del: Skupna
arhitektura
Geographic information -- Simple feature access -- Part 1: Common architecture
Information géographique -- Accès aux entités simples -- Partie 1: Architecture commune
Ta slovenski standard je istoveten z: ISO 19125-1:2004
ICS:
35.240.70 Uporabniške rešitve IT v IT applications in science
znanosti
SIST ISO 19125-1:2005 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 19125-1:2005
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SIST ISO 19125-1:2005
INTERNATIONAL ISO
STANDARD 19125-1
First edition
2004-08-01
Geographic information — Simple feature
access —
Part 1:
Common architecture
Information géographique — Accès aux entités simples —
Partie 1: Architecture commune
Reference number
ISO 19125-1:2004(E)
©
ISO 2004
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SIST ISO 19125-1:2005
ISO 19125-1:2004(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2004
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2004 – All rights reserved
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SIST ISO 19125-1:2005
ISO 19125-1:2004(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Conformance . 1
3 Normative references . 1
4 Terms and definitions. 1
5 Abbreviated terms. 4
6 Architecture . 5
6.1 Geometry object model . 5
6.2 Well-known Text Representation for Geometry. 21
6.3 Well-known Binary Representation for Geometry. 22
6.4 Well-known Text Representation of Spatial Reference Systems. 25
Annex A (informative) The correspondence of concepts of the common architecture with
concepts of the geometry model of ISO 19107. 28
Annex B (informative) Supported spatial reference data . 36
Bibliography . 42
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Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 19125-1 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics from a
base document supplied by the Open GIS Consortium, Inc.
ISO 19125 consists of the following parts, under the general title Geographic information — Simple feature
access:
— Part 1: Common architecture
— Part 2: SQL option
A Part 3: COM/OLE option is under preparation.
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Introduction
This part of ISO 19125 describes the common architecture for simple feature geometry. The simple feature
geometry object model is Distributed Computing Platform neutral and uses UML notation. The base Geometry
class has subclasses for Point, Curve, Surface and GeometryCollection. Each geometric object is associated
with a Spatial Reference System, which describes the coordinate space in which the geometric object is
defined.
The extended Geometry model has specialized 0, 1 and 2-dimensional collection classes named MultiPoint,
MultiLineString and MultiPolygon for modelling 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.
The attributes, methods and assertions for each Geometry class are described in Figure 1 in 6.1.1. In
describing methods, this is used to refer to the receiver of the method (the object being messaged).
The SFA COM function “signatures” may use a different notation from SFA SQL. COM notation is more
familiar for COM programmers. However, UML notation is used throughout this part of ISO 19125. There may
also be methods used in this International Standard that differ from one part to another. Where this is the case,
the differences are shown within the part.
This part of ISO 19125 implements a profile of the spatial schema described in ISO 19107:2003, Geographic
information Spatial schema. Annex A provides a detailed mapping of the schema in this part of ISO 19125
with the schema described in ISO 19107:2003.
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INTERNATIONAL STANDARD ISO 19125-1:2004(E)
Geographic information — Simple feature access —
Part 1:
Common architecture
1 Scope
This part of ISO 19125 establishes a common architecture and defines terms to use within the architecture.
This part of ISO 19125 does not attempt to standardize and does not depend upon any part of the mechanism
by which Types are added and maintained, including the following:
a) syntax and functionality provided for defining types;
b) syntax and functionality provided for defining functions;
c) physical storage of type instances in the database;
d) specific terminology used to refer to User Defined Types, for example UDT.
This part of ISO 19125 does standardize names and geometric definitions for Types for Geometry.
This part of ISO 19125 does not place any requirements on how to define the Geometry Types in the internal
schema nor does it place any requirements on when or how or who defines the Geometry Types.
2 Conformance
In order to conform to this part of ISO 19125, an implementation shall satisfy the requirements of one or more
test suites specified in the other parts of ISO 19125.
3 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 19107:2003, Geographic information Spatial schema
ISO 19111:2003, Geographic information Spatial referencing by coordinates
4 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
4.1
boundary
set that represents the limit of an entity
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NOTE Boundary is most commonly used in the context of geometry, where the set is a collection of points or a
collection of objects that represent those points. In other arenas, the term is used metaphorically to describe the transition
between an entity and the rest of its domain of discourse.
[ISO 19107]
4.2
buffer
geometric object (4.14) that contains all direct positions (4.7) whose distance from a specified geometric
object is less than or equal to a given distance
[ISO 19107]
4.3
coordinate
one of a sequence of n-numbers designating the position of a point (4.17) in n-dimensional space
NOTE In a coordinate reference system, the numbers must be qualified by units.
[adapted from ISO 19111]
4.4
coordinate dimension
number of measurements or axes needed to describe a position in a coordinate system (4.6)
[ISO 19107]
4.5
coordinate reference system
coordinate system (4.6) that is related to the real world by a datum
[adapted from ISO 19111]
4.6
coordinate system
set of mathematical rules for specifying how coordinates (4.3) are to be assigned to point (4.17)
[ISO 19111]
4.7
curve
1-dimensional geometric primitive (4.15), representing the continuous image of a line
NOTE The boundary of a curve is the set of points at either end of the curve. If the curve is a cycle, the two ends are
identical, and the curve (if topologically closed) is considered to not have a boundary. The first point is called the start
point, and the last is the end point. Connectivity of the curve is guaranteed by the “continuous image of a line” clause.
A topological theorem states that a continuous image of a connected set is connected.
[ISO 19107]
4.7
direct position
position described by a single set of coordinates (4.3) within a coordinate reference system (4.5)
[ISO 19107]
4.9
end point
last point (4.17) of a curve (4.7)
[ISO 19107]
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4.10
exterior
difference between the universe and the closure
NOTE The concept of exterior is applicable to both topological and geometric complexes.
[ISO 19107]
4.11
feature
abstraction of real world phenomena
NOTE A feature may occur as a type or an instance. Feature type or feature instance is used when only one is meant.
[adapted from ISO 19101]
4.12
feature attribute
characteristic of a feature (4.11)
NOTE A feature attribute has a name, a data type, and a value domain associated to it. A feature attribute for a
feature instance also has an attribute value taken from the value domain.
[adapted from ISO 19101]
4.13
geometric complex
set of disjoint geometric primitives (4.15) where the boundary (4.1) of each geometric primitive can be
represented as the union of other geometric primitives of smaller dimension within the same set
NOTE The geometric primitives in the set are disjoint in the sense that no direct position is interior to more than one
geometric primitive. The set is closed under boundary operations, meaning that for each element in the geometric complex,
there is a collection (also a geometric complex) of geometric primitives that represents the boundary of that element.
Recall that the boundary of a point (the only 0D primitive object type in geometry) is empty. Thus, if the largest dimension
geometric primitive is a solid (3D), the composition of the boundary operator in this definition terminates after at most
3 steps. It is also the case that the boundary of any object is a cycle.
[ISO 19107]
4.14
geometric object
spatial object representing a geometric set
NOTE A geometric object consists of a geometric primitive, a collection of geometric primitives, or a geometric
complex treated as a single entity. A geometric object may be the spatial representation of an object such as a feature or a
significant part of a feature.
[ISO 19107]
4.15
geometric primitive
geometric object (4.14) representing a single, connected, homogeneous element of space
NOTE Geometric primitives are non-decomposed objects that represent information about geometric configuration.
They include points, curves, surfaces, and solids.
[ISO 19107]
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4.16
interior
set of all direct positions (4.7) that are on a geometric object (4.14) but which are not on its boundary (4.1)
NOTE The interior of a topological object is the homomorphic image of the interior of any of its geometric realizations.
This is not included as a definition because it follows from a theorem of topology.
[ISO 19107]
4.17
point
0-dimensional geometric primitive (4.15), representing a position
NOTE The boundary of a point is the empty set.
[ISO 19107]
4.18
simple feature
feature (4.11) restricted to 2D geometry with linear interpolation between vertices, having both spatial and
non spatial attributes
4.19
start point
first point (4.17) of a curve (4.7)
[ISO 19107]
4.20
surface
2-dimensional geometric primitive (4.15), locally representing a continuous image of a region of a plane
NOTE The boundary of a surface is the set of oriented, closed curves that delineate the limits of the surface.
[adapted from ISO 19107]
5 Abbreviated terms
API Application Program Interface
COM Component Object Model
CORBA Common Object Request Broker Architecture
DCE Distributed Computing Environment
DCOM Distributed Component Objected Model
DE-9IM Dimensionally Extended Nine-Intersection Model
IEEE Institute of Electrical and Electronics Engineers, Inc.
NDR Little Endian byte order encoding
OLE Object Linking and Embedding
RPC Remote Procedure Call
SQL Structured Query Language
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SRID Spatial Reference System Identifier
XDR Big Endian byte order encoding
UDT User Defined Type
UML Unified Modeling Language
WKB Well-Known Binary (representation for example, geometry)
6 Architecture
6.1 Geometry object model
6.1.1 Overview
This subclause describes the object model for simple feature geometry. The simple feature geometry object
model is Distributed Computing Platform neutral and uses UML notation. The object model for geometry
is shown in Figure 1. The base Geometry class has subclasses for Point, Curve, Surface and
GeometryCollection. Each geometric object is associated with a Spatial Reference System, which describes
the coordinate space in which the geometric object is defined.
Figure 1 — Geometry class hierarchy
Figure 1 is based on an extended Geometry model with specialized 0-, 1- and 2-dimensional collection
classes named MultiPoint, MultiLineString and MultiPolygon for modelling 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. Figure 1 shows
aggregation lines between the leaf-collection classes and their element classes; the aggregation lines for
non-leaf-collection classes are described in the text.
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The attributes, methods and assertions for each Geometry class are described below. In describing methods,
this is used to refer to the receiver of the method (the object being messaged).
6.1.2 Geometry
6.1.2.1 Description
Geometry is the root class of the hierarchy. Geometry is an abstract (non-instantiable) class.
The instantiable subclasses of Geometry defined in this International Standard are restricted to 0, 1 and
2
2-dimensional geometric objects that exist in 2-dimensional coordinate space (ℜ ).
All instantiable Geometry classes described in this part of ISO 19125 are defined so that valid instances of a
Geometry class are topologically closed, i.e. all defined geometries include their boundary.
6.1.2.2 Basic methods on geometric objects
Dimension ( ):Integer — The inherent dimension of this geometric object, which must be less than or
equal to the coordinate dimension. This specification is restricted to geometries in 2-dimensional
coordinate space.
GeometryType ( ):String — Returns the name of the instantiable subtype of Geometry of which this
geometric object is a instantiable member. The name of the subtype of Geometry is returned as a string.
SRID ( ):Integer — Returns the Spatial Reference System ID for this geometric object.
Envelope( ):Geometry — The minimum bounding box for this Geometry, returned as a Geometry. The
polygon is defined by the corner points of the bounding box [(MINX, MINY), (MAXX, MINY), (MAXX,
MAXY), (MINX, MAXY), (MINX, MINY)].
AsText( ):String — Exports this geometric object to a specific Well-known Text Representation of
Geometry.
AsBinary( ):Binary — Exports this geometric object to a specific Well-known Binary Representation of
Geometry.
IsEmpty( ):Integer — Returns 1 (TRUE) if this geometric object is the empty Geometry. If true, then this
geometric object represents the empty point set, ∅, for the coordinate space.
IsSimple( ):Integer — Returns 1 (TRUE) if this geometric object has no anomalous geometric points,
such as self intersection or self tangency. The description of each instantiable geometric class will include
the specific conditions that cause an instance of that class to be classified as not simple.
Boundary( ):Geometry — Returns the closure of the combinatorial boundary of this geometric object
(Reference [1], section 3.12.2). Because the result of this function is a closure, and hence topologically
closed, the resulting boundary can be represented using representational Geometry primitives
(Reference [1], section 3.12.2).
6.1.2.3 Methods for testing spatial relations between geometric objects
The methods in this subclause are defined and described in more detail following the description of the sub-
types of Geometry.
Equals(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object is “spatially
equal” to anotherGeometry.
Disjoint(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object is “spatially
disjoint” from anotherGeometry.
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Intersects(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
intersects” anotherGeometry.
Touches(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
touches” anotherGeometry.
Crosses(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
crosses’ anotherGeometry.
Within(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object is “spatially
within” anotherGeometry.
Contains(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
contains” anotherGeometry.
Overlaps(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
overlaps” anotherGeometry.
Relate(anotherGeometry:Geometry, intersectionPatternMatrix:String):Integer — Returns 1 (TRUE) if this
geometric object is spatially related to anotherGeometry by testing for intersections between the interior,
boundary and exterior of the two geometric objects as specified by the values in the
intersectionPatternMatrix.
6.1.2.4 Methods that support spatial analysis
Distance(anotherGeometry:Geometry):Double — Returns the shortest distance between any two Points
in the two geometric objects as calculated in the spatial reference system of this geometric object.
Buffer(distance:Double):Geometry — Returns a geometric object that represents all Points whose
distance from this geometric object is less than or equal to distance. Calculations are in the spatial
reference system of this geometric object.
ConvexHull( ):Geometry — Returns a geometric object that represents the convex hull of this geometric
object.
Intersection(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents the
Point set intersection of this geometric object with anotherGeometry.
Union(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents the Point
set union of this geometric object with anotherGeometry.
Difference(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents the
Point set difference of this geometric object with anotherGeometry.
SymDifference(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents
the Point set symmetric difference of this geometric object with anotherGeometry.
6.1.3 GeometryCollection
6.1.3.1 Description
A GeometryCollection is a geometric object that is a collection of 1 or more geometric objects.
All the elements in a GeometryCollection shall be in the same Spatial Reference. This is also the Spatial
Reference for the GeometryCollection.
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GeometryCollection places no other constraints on its elements. Subclasses of GeometryCollection may
restrict membership based on dimension and may also place other constraints on the degree of spatial
overlap between elements.
6.1.3.2 Methods
NumGeometries( ):Integer — Returns the number of geometries in this GeometryCollection.
GeometryN(N:integer):Geometry — Returns the Nth geometry in this GeometryCollection.
6.1.4 Point
6.1.4.1 Description
A Point is a 0-dimensional geometric object and represents a single location in coordinate space. A Point has
an x-coordinate value and a y-coordinate value.
The boundary of a Point is the empty set.
6.1.4.2 Methods
X( ):Double — The x-coordinate value for this Point.
Y( ):Double — The y-coordinate value for this Point.
6.1.5 MultiPoint
A MultiPoint is a 0-dimensional GeometryCollection. The elements of a MultiPoint are restricted to Points. The
Points are not connected or ordered.
A MultiPoint is simple if no two Points in the MultiPoint are equal (have identical coordinate values).
The boundary of a MultiPoint is the empty set.
6.1.6 Curve
6.1.6.1 Description
A Curve is a 1-dimensional geometric object usually stored as a sequence of Points, with the subtype of
Curve specifying the form of the interpolation between Points. This part of ISO 19125 defines only one
subclass of Curve, LineString, which uses linear interpolation between Points.
A Curve is a 1-dimensional geometric object that is the homeomorphic image of a real, closed, interval D = [a,
2
b] = {x ∈ ℜ. a u x u b} under a mapping f:[a,b] → ℜ .
A Curve is simple if it does not pass through the same Point twice (Reference [1], section 3.12.7.3):
∀ c ∈ Curve, [a, b] = c.Domain,
c.IsSimple⇔ (∀ x1, x2 ∈ (a, b] x1 ≠ x2 ⇒ f(x1) ≠ f (x2)) ∧ (∀ x1, x2 ∈ [a, b) x1 ≠ x2 ⇒ f(x1) ≠ f(x2))
A Curve is closed if its start Point is equal to its end Point (Reference [1], section 3.12.7.3).
The boundary of a closed Curve is empty.
A Curve that is simple and closed is a Ring.
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The boundary of a non-closed Curve consists of its two end Points (Reference [1], section 3.12.3.2).
A Curve is defined as topologically closed.
6.1.6.2 Methods
Length( ):Double — The length of this Curve in its associated spatial reference.
StartPoint( ):Point — The start Point of this Curve.
EndPoint( ):Point — The end Point of this Curve.
IsClosed( ):Integer — Returns 1 (TRUE) if this Curve is closed [StartPoint ( ) = EndPoint ( )].
IsRing( ):Integer — Returns 1 (TRUE) if this Curve is closed [StartPoint ( ) = EndPoint ( )] and this Curve
is simple (does not pass through the same Point more than once).
6.1.7 LineString, Line, LinearRing
6.1.7.1 Description
A LineString is a Curve with linear interpolation between Points. Each consecutive pair of Points defines a
Line segment.
A Line is a LineString with exactly 2 Points.
A LinearRing is a LineString that is both closed and simple. The Curve in Figure 2, item (c), is a closed
LineString that is a LinearRing. The Curve in Figure 2, item (d) is a closed LineString that is not a LinearRing.
Key
s start
e end
Figure 2 — Examples of LineStrings — Simple LineString (a), Non-simple LineString (b), Simple,
closed LineString (a LinearRing) (c), Non-simple closed LineString (d)
6.1.7.2 Methods
NumPoints( ):Integer — The number of Points in this LineString.
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PointN(N:Integer):Point — Returns the specified Point N in this LineString.
6.1.8 MultiCurve
6.1.8.1 Description
A MultiCurve is a 1-dimensional GeometryCollection whose elements are Curves as in Figure 3.
MultiCurve is a non-instantiable class in this specification; it defines a set of methods for its subclasses and is
included for reasons of extensibility.
A MultiCurve 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.
The boundary of a MultiCurve is obtained by applying the “mod 2” union rule: A Point is in the boundary of a
MultiCurve if it is in the boundaries of an odd number of elements of the MultiCurve (Reference [1], section
3.12.3.2).
A MultiCurve is closed if all of its elements are closed. The boundary of a closed MultiCurve is always empty.
A MultiCurve is defined as topologically closed.
6.1.8.2 Methods
IsClosed( ):Integer — Returns 1 (TRUE) if this MultiCurve is closed [StartPoint ( ) = EndPoint ( ) for each
Curve in this MultiCurve].
Length( ):Double — The Length of this MultiCurve which is equal to the sum of the lengths of the element
Curves.
6.1.9 MultiLineString
A MultiLineString is a MultiCurve whose elements are LineStrings.
The boundaries for the MultiLineStrings in Figure 3 are (a){s1, e2}, (b) {s1, e1}, (c)∅.
Key
s start
e end
Figure 3 — Examples of MultiLineStrings — Simple MultiLineString (a), Non-simple MultiLineString
with 2 elements (b), Non-simple, closed MultiLineString with 2 elements (c)
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6.1.10 Surface
6.1.10.1 Description
A Surface is a 2-dimensional geometric object.
A simple Surface consists of a single “patch” that is associated with one “exterior boundary” and 0 or more
“interior” boundaries. Simple Surfaces in 3-dimensional space are isomorphic to planar Surfaces. Polyhedral
Surfaces are formed by “stitching” together simple Surfaces along their boundaries, polyhedral Surfaces in
3-dimensional space may not be planar as a whole (Refe
...
INTERNATIONAL ISO
STANDARD 19125-1
First edition
2004-08-01
Corrected version
2004-11-01
Geographic information — Simple feature
access —
Part 1:
Common architecture
Information géographique — Accès aux entités simples —
Partie 1: Architecture commune
Reference number
ISO 19125-1:2004(E)
©
ISO 2004
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ISO 19125-1:2004(E)
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Published in Switzerland
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ISO 19125-1:2004(E)
Contents Page
Foreword. iv
Introduction . iv
1 Scope. 1
2 Conformance . 1
3 Normative references . 1
4 Terms and definitions. 1
5 Abbreviated terms. 4
6 Architecture . 5
6.1 Geometry object model . 5
6.2 Well-known Text Representation for Geometry. 21
6.3 Well-known Binary Representation for Geometry. 22
6.4 Well-known Text Representation of Spatial Reference Systems. 25
Annex A (informative) The correspondence of concepts of the common architecture with
concepts of the geometry model of ISO 19107. 28
Annex B (informative) Supported spatial reference data . 36
Bibliography . 42
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ISO 19125-1:2004(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 19125-1 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics from a
base document supplied by the Open GIS Consortium, Inc.
ISO 19125 consists of the following parts, under the general title Geographic information — Simple feature
access:
— Part 1: Common architecture
— Part 2: SQL option
This corrected version of ISO 19125-1:2004 incorporates the following corrections:
— a complete version of Figure 9, which was truncated in the original;
— removal from the Foreword of the reference to ISO 19125-3, which has now been deleted.
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ISO 19125-1:2004(E)
Introduction
This part of ISO 19125 describes the common architecture for simple feature geometry. The simple feature
geometry object model is Distributed Computing Platform neutral and uses UML notation. The base Geometry
class has subclasses for Point, Curve, Surface and GeometryCollection. Each geometric object is associated
with a Spatial Reference System, which describes the coordinate space in which the geometric object is
defined.
The extended Geometry model has specialized 0, 1 and 2-dimensional collection classes named MultiPoint,
MultiLineString and MultiPolygon for modelling 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.
The attributes, methods and assertions for each Geometry class are described in Figure 1 in 6.1.1. In
describing methods, this is used to refer to the receiver of the method (the object being messaged).
The SFA COM function “signatures” may use a different notation from SFA SQL. COM notation is more
familiar for COM programmers. However, UML notation is used throughout this part of ISO 19125. There may
also be methods used in this International Standard that differ from one part to another. Where this is the case,
the differences are shown within the part.
This part of ISO 19125 implements a profile of the spatial schema described in ISO 19107:2003, Geographic
information Spatial schema. Annex A provides a detailed mapping of the schema in this part of ISO 19125
with the schema described in ISO 19107:2003.
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INTERNATIONAL STANDARD ISO 19125-1:2004(E)
Geographic information — Simple feature access —
Part 1:
Common architecture
1 Scope
This part of ISO 19125 establishes a common architecture and defines terms to use within the architecture.
This part of ISO 19125 does not attempt to standardize and does not depend upon any part of the mechanism
by which Types are added and maintained, including the following:
a) syntax and functionality provided for defining types;
b) syntax and functionality provided for defining functions;
c) physical storage of type instances in the database;
d) specific terminology used to refer to User Defined Types, for example UDT.
This part of ISO 19125 does standardize names and geometric definitions for Types for Geometry.
This part of ISO 19125 does not place any requirements on how to define the Geometry Types in the internal
schema nor does it place any requirements on when or how or who defines the Geometry Types.
2 Conformance
In order to conform to this part of ISO 19125, an implementation shall satisfy the requirements of one or more
test suites specified in the other parts of ISO 19125.
3 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 19107:2003, Geographic information Spatial schema
ISO 19111:2003, Geographic information Spatial referencing by coordinates
4 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
4.1
boundary
set that represents the limit of an entity
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ISO 19125-1:2004(E)
NOTE Boundary is most commonly used in the context of geometry, where the set is a collection of points or a
collection of objects that represent those points. In other arenas, the term is used metaphorically to describe the transition
between an entity and the rest of its domain of discourse.
[ISO 19107]
4.2
buffer
geometric object (4.14) that contains all direct positions (4.7) whose distance from a specified geometric
object is less than or equal to a given distance
[ISO 19107]
4.3
coordinate
one of a sequence of n-numbers designating the position of a point (4.17) in n-dimensional space
NOTE In a coordinate reference system, the numbers must be qualified by units.
[adapted from ISO 19111]
4.4
coordinate dimension
number of measurements or axes needed to describe a position in a coordinate system (4.6)
[ISO 19107]
4.5
coordinate reference system
coordinate system (4.6) that is related to the real world by a datum
[adapted from ISO 19111]
4.6
coordinate system
set of mathematical rules for specifying how coordinates (4.3) are to be assigned to point (4.17)
[ISO 19111]
4.7
curve
1-dimensional geometric primitive (4.15), representing the continuous image of a line
NOTE The boundary of a curve is the set of points at either end of the curve. If the curve is a cycle, the two ends are
identical, and the curve (if topologically closed) is considered to not have a boundary. The first point is called the start
point, and the last is the end point. Connectivity of the curve is guaranteed by the “continuous image of a line” clause.
A topological theorem states that a continuous image of a connected set is connected.
[ISO 19107]
4.7
direct position
position described by a single set of coordinates (4.3) within a coordinate reference system (4.5)
[ISO 19107]
4.9
end point
last point (4.17) of a curve (4.7)
[ISO 19107]
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4.10
exterior
difference between the universe and the closure
NOTE The concept of exterior is applicable to both topological and geometric complexes.
[ISO 19107]
4.11
feature
abstraction of real world phenomena
NOTE A feature may occur as a type or an instance. Feature type or feature instance is used when only one is meant.
[adapted from ISO 19101]
4.12
feature attribute
characteristic of a feature (4.11)
NOTE A feature attribute has a name, a data type, and a value domain associated to it. A feature attribute for a
feature instance also has an attribute value taken from the value domain.
[adapted from ISO 19101]
4.13
geometric complex
set of disjoint geometric primitives (4.15) where the boundary (4.1) of each geometric primitive can be
represented as the union of other geometric primitives of smaller dimension within the same set
NOTE The geometric primitives in the set are disjoint in the sense that no direct position is interior to more than one
geometric primitive. The set is closed under boundary operations, meaning that for each element in the geometric complex,
there is a collection (also a geometric complex) of geometric primitives that represents the boundary of that element.
Recall that the boundary of a point (the only 0D primitive object type in geometry) is empty. Thus, if the largest dimension
geometric primitive is a solid (3D), the composition of the boundary operator in this definition terminates after at most
3 steps. It is also the case that the boundary of any object is a cycle.
[ISO 19107]
4.14
geometric object
spatial object representing a geometric set
NOTE A geometric object consists of a geometric primitive, a collection of geometric primitives, or a geometric
complex treated as a single entity. A geometric object may be the spatial representation of an object such as a feature or a
significant part of a feature.
[ISO 19107]
4.15
geometric primitive
geometric object (4.14) representing a single, connected, homogeneous element of space
NOTE Geometric primitives are non-decomposed objects that represent information about geometric configuration.
They include points, curves, surfaces, and solids.
[ISO 19107]
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4.16
interior
set of all direct positions (4.7) that are on a geometric object (4.14) but which are not on its boundary (4.1)
NOTE The interior of a topological object is the homomorphic image of the interior of any of its geometric realizations.
This is not included as a definition because it follows from a theorem of topology.
[ISO 19107]
4.17
point
0-dimensional geometric primitive (4.15), representing a position
NOTE The boundary of a point is the empty set.
[ISO 19107]
4.18
simple feature
feature (4.11) restricted to 2D geometry with linear interpolation between vertices, having both spatial and
non spatial attributes
4.19
start point
first point (4.17) of a curve (4.7)
[ISO 19107]
4.20
surface
2-dimensional geometric primitive (4.15), locally representing a continuous image of a region of a plane
NOTE The boundary of a surface is the set of oriented, closed curves that delineate the limits of the surface.
[adapted from ISO 19107]
5 Abbreviated terms
API Application Program Interface
COM Component Object Model
CORBA Common Object Request Broker Architecture
DCE Distributed Computing Environment
DCOM Distributed Component Objected Model
DE-9IM Dimensionally Extended Nine-Intersection Model
IEEE Institute of Electrical and Electronics Engineers, Inc.
NDR Little Endian byte order encoding
OLE Object Linking and Embedding
RPC Remote Procedure Call
SQL Structured Query Language
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ISO 19125-1:2004(E)
SRID Spatial Reference System Identifier
XDR Big Endian byte order encoding
UDT User Defined Type
UML Unified Modeling Language
WKB Well-Known Binary (representation for example, geometry)
6 Architecture
6.1 Geometry object model
6.1.1 Overview
This subclause describes the object model for simple feature geometry. The simple feature geometry object
model is Distributed Computing Platform neutral and uses UML notation. The object model for geometry
is shown in Figure 1. The base Geometry class has subclasses for Point, Curve, Surface and
GeometryCollection. Each geometric object is associated with a Spatial Reference System, which describes
the coordinate space in which the geometric object is defined.
Figure 1 — Geometry class hierarchy
Figure 1 is based on an extended Geometry model with specialized 0-, 1- and 2-dimensional collection
classes named MultiPoint, MultiLineString and MultiPolygon for modelling 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. Figure 1 shows
aggregation lines between the leaf-collection classes and their element classes; the aggregation lines for
non-leaf-collection classes are described in the text.
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The attributes, methods and assertions for each Geometry class are described below. In describing methods,
this is used to refer to the receiver of the method (the object being messaged).
6.1.2 Geometry
6.1.2.1 Description
Geometry is the root class of the hierarchy. Geometry is an abstract (non-instantiable) class.
The instantiable subclasses of Geometry defined in this International Standard are restricted to 0, 1 and
2
2-dimensional geometric objects that exist in 2-dimensional coordinate space (ℜ ).
All instantiable Geometry classes described in this part of ISO 19125 are defined so that valid instances of a
Geometry class are topologically closed, i.e. all defined geometries include their boundary.
6.1.2.2 Basic methods on geometric objects
Dimension ( ):Integer — The inherent dimension of this geometric object, which must be less than or
equal to the coordinate dimension. This specification is restricted to geometries in 2-dimensional
coordinate space.
GeometryType ( ):String — Returns the name of the instantiable subtype of Geometry of which this
geometric object is a instantiable member. The name of the subtype of Geometry is returned as a string.
SRID ( ):Integer — Returns the Spatial Reference System ID for this geometric object.
Envelope( ):Geometry — The minimum bounding box for this Geometry, returned as a Geometry. The
polygon is defined by the corner points of the bounding box [(MINX, MINY), (MAXX, MINY), (MAXX,
MAXY), (MINX, MAXY), (MINX, MINY)].
AsText( ):String — Exports this geometric object to a specific Well-known Text Representation of
Geometry.
AsBinary( ):Binary — Exports this geometric object to a specific Well-known Binary Representation of
Geometry.
IsEmpty( ):Integer — Returns 1 (TRUE) if this geometric object is the empty Geometry. If true, then this
geometric object represents the empty point set, ∅, for the coordinate space.
IsSimple( ):Integer — Returns 1 (TRUE) if this geometric object has no anomalous geometric points,
such as self intersection or self tangency. The description of each instantiable geometric class will include
the specific conditions that cause an instance of that class to be classified as not simple.
Boundary( ):Geometry — Returns the closure of the combinatorial boundary of this geometric object
(Reference [1], section 3.12.2). Because the result of this function is a closure, and hence topologically
closed, the resulting boundary can be represented using representational Geometry primitives
(Reference [1], section 3.12.2).
6.1.2.3 Methods for testing spatial relations between geometric objects
The methods in this subclause are defined and described in more detail following the description of the sub-
types of Geometry.
Equals(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object is “spatially
equal” to anotherGeometry.
Disjoint(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object is “spatially
disjoint” from anotherGeometry.
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Intersects(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
intersects” anotherGeometry.
Touches(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
touches” anotherGeometry.
Crosses(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
crosses’ anotherGeometry.
Within(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object is “spatially
within” anotherGeometry.
Contains(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
contains” anotherGeometry.
Overlaps(anotherGeometry:Geometry):Integer — Returns 1 (TRUE) if this geometric object “spatially
overlaps” anotherGeometry.
Relate(anotherGeometry:Geometry, intersectionPatternMatrix:String):Integer — Returns 1 (TRUE) if this
geometric object is spatially related to anotherGeometry by testing for intersections between the interior,
boundary and exterior of the two geometric objects as specified by the values in the
intersectionPatternMatrix.
6.1.2.4 Methods that support spatial analysis
Distance(anotherGeometry:Geometry):Double — Returns the shortest distance between any two Points
in the two geometric objects as calculated in the spatial reference system of this geometric object.
Buffer(distance:Double):Geometry — Returns a geometric object that represents all Points whose
distance from this geometric object is less than or equal to distance. Calculations are in the spatial
reference system of this geometric object.
ConvexHull( ):Geometry — Returns a geometric object that represents the convex hull of this geometric
object.
Intersection(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents the
Point set intersection of this geometric object with anotherGeometry.
Union(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents the Point
set union of this geometric object with anotherGeometry.
Difference(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents the
Point set difference of this geometric object with anotherGeometry.
SymDifference(anotherGeometry:Geometry):Geometry — Returns a geometric object that represents
the Point set symmetric difference of this geometric object with anotherGeometry.
6.1.3 GeometryCollection
6.1.3.1 Description
A GeometryCollection is a geometric object that is a collection of 1 or more geometric objects.
All the elements in a GeometryCollection shall be in the same Spatial Reference. This is also the Spatial
Reference for the GeometryCollection.
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GeometryCollection places no other constraints on its elements. Subclasses of GeometryCollection may
restrict membership based on dimension and may also place other constraints on the degree of spatial
overlap between elements.
6.1.3.2 Methods
NumGeometries( ):Integer — Returns the number of geometries in this GeometryCollection.
GeometryN(N:integer):Geometry — Returns the Nth geometry in this GeometryCollection.
6.1.4 Point
6.1.4.1 Description
A Point is a 0-dimensional geometric object and represents a single location in coordinate space. A Point has
an x-coordinate value and a y-coordinate value.
The boundary of a Point is the empty set.
6.1.4.2 Methods
X( ):Double — The x-coordinate value for this Point.
Y( ):Double — The y-coordinate value for this Point.
6.1.5 MultiPoint
A MultiPoint is a 0-dimensional GeometryCollection. The elements of a MultiPoint are restricted to Points. The
Points are not connected or ordered.
A MultiPoint is simple if no two Points in the MultiPoint are equal (have identical coordinate values).
The boundary of a MultiPoint is the empty set.
6.1.6 Curve
6.1.6.1 Description
A Curve is a 1-dimensional geometric object usually stored as a sequence of Points, with the subtype of
Curve specifying the form of the interpolation between Points. This part of ISO 19125 defines only one
subclass of Curve, LineString, which uses linear interpolation between Points.
A Curve is a 1-dimensional geometric object that is the homeomorphic image of a real, closed, interval D = [a,
2
b] = {x ∈ ℜ. a u x u b} under a mapping f:[a,b] → ℜ .
A Curve is simple if it does not pass through the same Point twice (Reference [1], section 3.12.7.3):
∀ c ∈ Curve, [a, b] = c.Domain,
c.IsSimple⇔ (∀ x1, x2 ∈ (a, b] x1 ≠ x2 ⇒ f(x1) ≠ f (x2)) ∧ (∀ x1, x2 ∈ [a, b) x1 ≠ x2 ⇒ f(x1) ≠ f(x2))
A Curve is closed if its start Point is equal to its end Point (Reference [1], section 3.12.7.3).
The boundary of a closed Curve is empty.
A Curve that is simple and closed is a Ring.
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The boundary of a non-closed Curve consists of its two end Points (Reference [1], section 3.12.3.2).
A Curve is defined as topologically closed.
6.1.6.2 Methods
Length( ):Double — The length of this Curve in its associated spatial reference.
StartPoint( ):Point — The start Point of this Curve.
EndPoint( ):Point — The end Point of this Curve.
IsClosed( ):Integer — Returns 1 (TRUE) if this Curve is closed [StartPoint ( ) = EndPoint ( )].
IsRing( ):Integer — Returns 1 (TRUE) if this Curve is closed [StartPoint ( ) = EndPoint ( )] and this Curve
is simple (does not pass through the same Point more than once).
6.1.7 LineString, Line, LinearRing
6.1.7.1 Description
A LineString is a Curve with linear interpolation between Points. Each consecutive pair of Points defines a
Line segment.
A Line is a LineString with exactly 2 Points.
A LinearRing is a LineString that is both closed and simple. The Curve in Figure 2, item (c), is a closed
LineString that is a LinearRing. The Curve in Figure 2, item (d) is a closed LineString that is not a LinearRing.
Key
s start
e end
Figure 2 — Examples of LineStrings — Simple LineString (a), Non-simple LineString (b), Simple,
closed LineString (a LinearRing) (c), Non-simple closed LineString (d)
6.1.7.2 Methods
NumPoints( ):Integer — The number of Points in this LineString.
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PointN(N:Integer):Point — Returns the specified Point N in this LineString.
6.1.8 MultiCurve
6.1.8.1 Description
A MultiCurve is a 1-dimensional GeometryCollection whose elements are Curves as in Figure 3.
MultiCurve is a non-instantiable class in this specification; it defines a set of methods for its subclasses and is
included for reasons of extensibility.
A MultiCurve 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.
The boundary of a MultiCurve is obtained by applying the “mod 2” union rule: A Point is in the boundary of a
MultiCurve if it is in the boundaries of an odd number of elements of the MultiCurve (Reference [1], section
3.12.3.2).
A MultiCurve is closed if all of its elements are closed. The boundary of a closed MultiCurve is always empty.
A MultiCurve is defined as topologically closed.
6.1.8.2 Methods
IsClosed( ):Integer — Returns 1 (TRUE) if this MultiCurve is closed [StartPoint ( ) = EndPoint ( ) for each
Curve in this MultiCurve].
Length( ):Double — The Length of this MultiCurve which is equal to the sum of the lengths of the element
Curves.
6.1.9 MultiLineString
A MultiLineString is a MultiCurve whose elements are LineStrings.
The boundaries for the MultiLineStrings in Figure 3 are (a){s1, e2}, (b) {s1, e1}, (c)∅.
Key
s start
e end
Figure 3 — Examples of MultiLineStrings — Simple MultiLineString (a), Non-simple MultiLineString
with 2 elements (b), Non-simple, closed MultiLineString with 2 elements (c)
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ISO 19125-1:2004(E)
6.1.10 Surface
6.1.10.1 Description
A Surface is a 2-dimensional geometric object.
A simple Surface consists of a single “patch” that is associated with one “exterior boundary” and 0 or more
“interior” boundaries. Simple Surfaces in 3-dimensional space are isomorphic to planar Surfaces. Polyhedral
Surfaces are formed by “stitching” together simple Surfaces along their boundaries, polyhedral Surfaces in
3-dimensional space may not be planar as a whole (Reference [1], sections 3.12.9.1, 3.12.9.3).
The boundary of a simple Surface is the set of closed Curves corresponding to its “exterior” and “interior”
boundaries (Reference [1], section 3.12.9.4).
The only instantiable subclass of Surface defined in this specification, Polygon, is a simple Surface that is
planar.
6.1.10.2 Methods
Area( ):Double — The area of this Surface, as measured in the spatial reference system of this Surface.
Centroid( ):Point — The mathematical centroid for this Surface as a Point. The result is not guaranteed
to be on this Surface.
PointOnSurface( ):Point — A Point guaranteed to be on this Surface.
6.1.11 Polygon
6.1.11.1 Description
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 as follows:
a) Po
...
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