EN ISO 19111-2:2012

SLOVENSKI STANDARD
01-junij-2012
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SDUDPHWULþQHYUHGQRVWL,62
Geographic information - Spatial referencing by coordinates - Part 2: Extension for
parametric values (ISO 19111-2:2009)
Geoinformation - Koordinatenreferenzsysteme - Teil 2: Erweiterung auf parametrisierte
Werte (ISO 19111-2:2009)
Information géographique - Système de références spatiales par coordonnées - Partie 2:
Supplément pour valeurs paramétriques (ISO 19111-2:2009)
Ta slovenski standard je istoveten z: EN ISO 19111-2:2012
ICS:
07.040 Astronomija. Geodezija. Astronomy. Geodesy.
Geografija Geography
35.240.70 Uporabniške rešitve IT v IT applications in science
znanosti
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 19111-2
NORME EUROPÉENNE
EUROPÄISCHE NORM
April 2012
ICS 35.240.70
English Version
Geographic information - Spatial referencing by coordinates -
Part 2: Extension for parametric values (ISO 19111-2:2009)
Information géographique - Système de références Geoinformation - Koordinatenreferenzsysteme - Teil 2:
spatiales par coordonnées - Partie 2: Supplément pour Erweiterung auf parametrisierte Werte (ISO 19111-2:2009)
valeurs paramétriques (ISO 19111-2:2009)
This European Standard was approved by CEN on 9 March 2012.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same
status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2012 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 19111-2:2012: E
worldwide for CEN national Members.

Contents Page
Foreword .3

Foreword
The text of ISO 19111-2:2009 has been prepared by Technical Committee ISO/TC 211 “Geographic
information/Geomatics” of the International Organization for Standardization (ISO) and has been taken over
as EN ISO 19111-2:2012 by Technical Committee CEN/TC 287 “Geographic Information” the secretariat of
which is held by BSI.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by October 2012, and conflicting national standards shall be withdrawn at
the latest by October 2012.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland, Turkey and the United Kingdom.
Endorsement notice
The text of ISO 19111-2:2009 has been approved by CEN as a EN ISO 19111-2:2012 without any
modification.
INTERNATIONAL ISO
STANDARD 19111-2
First edition
2009-08-15
Geographic information — Spatial
referencing by coordinates —
Part 2:
Extension for parametric values
Information géographique — Système de références spatiales par
coordonnées —
Partie 2: Supplément pour valeurs paramétriques

Reference number
ISO 19111-2:2009(E)
©
ISO 2009
ISO 19111-2:2009(E)
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ii © ISO 2009 – All rights reserved

ISO 19111-2:2009(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Conformance .1
3 Normative references.1
4 Terms and definitions .1
5 Conventions.2
5.1 Abbreviated terms.2
5.2 UML notation.2
5.3 Attribute status .2
6 Spatio-parametric referencing .3
6.1 Overview.3
6.2 Parametric coordinate reference system.3
6.3 Parametric coordinate system .4
6.4 Parametric datum .6
6.5 Spatio-parametric coordinate reference system.7
6.6 Spatio-parametric coordinate reference system with time.8
6.7 Transformation and conversion of parametric coordinate reference systems .8
Annex A (normative) Conformance .9
Annex B (informative) Examples .11
Bibliography.16

ISO 19111-2:2009(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 19111-2 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics.
ISO 19111 consists of the following parts, under the general title Geographic information — Spatial
referencing by coordinates:
⎯ Geographic information — Spatial referencing by coordinates
⎯ Part 2: Extension for parametric values
iv © ISO 2009 – All rights reserved

ISO 19111-2:2009(E)
Introduction
ISO 19111 describes the elements necessary to fully define various types of reference systems used for
spatial referencing by coordinates. In ISO 19111, a coordinate is one of n scalar values that define the position
of a point. ISO 19111 allows for coordinates which are angular, such as latitude and longitude, or linear, such
as easting and northing. It also describes the concept of a compound coordinate reference system, which
uses at least two independent coordinate reference systems to describe a three-dimensional spatial position.
Scientific communities, especially those concerned with the environmental sciences, frequently express
spatial position partially in terms of a parameter or function. Within these communities, this parameter or
function is treated as a coordinate. Its relationship with a spatial dimension will usually be non-linear.
Examples are widespread, but latitude, longitude and pressure is a commonly encountered example.
This part of ISO 19111 defines a parametric coordinate reference system using the concepts of ISO 19111.
The provisions of ISO 19111 are then used to include a parametric coordinate reference system as part of a
compound coordinate reference system. Optionally, time can also be included as an additional axis or as
axes.
INTERNATIONAL STANDARD ISO 19111-2:2009(E)

Geographic information — Spatial referencing by
coordinates —
Part 2:
Extension for parametric values
1 Scope
This part of ISO 19111 specifies the conceptual schema for the description of spatial referencing using
parametric values or functions. It applies the schema of ISO 19111 to combine a position referenced by
coordinates with a parametric value to form a spatio-parametric coordinate reference system (CRS). The
spatio-parametric CRS can optionally be extended to include time.
The intended users of this part of ISO 19111 are producers and users of environmental information.
Parameters which are attributes of spatial locations or features, but which are not involved in their spatial
referencing, are not addressed by this part of ISO 19111.
2 Conformance requirements
Any CRS for which conformance to this part of ISO 19111 is claimed shall be in accordance with Annex A.
3 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the cited edition applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 19111:2007, Geographic information — Spatial referencing by coordinates
4 Terms and definitions
For the purposes of this document the terms and definitions of ISO 19111 and the following apply.
4.1
parametric coordinate system
one-dimensional coordinate system where the axis units are parameter values which are not inherently spatial
4.2
parametric coordinate reference system
coordinate reference system based on a parametric datum
ISO 19111-2:2009(E)
4.3
parametric datum
datum describing the relationship of a parametric coordinate system to an object
NOTE The object is normally the Earth.
4.4
spatio-parametric coordinate reference system
compound coordinate reference system in which one constituent coordinate reference system is a parametric
coordinate reference system and one is a spatial coordinate reference system
NOTE Normally the spatial component is “horizontal” and the parametric component is “vertical”.
4.5
spatio-parametric-temporal coordinate reference system
compound coordinate reference system comprised of spatial, parametric and temporal coordinate reference
systems
5 Conventions
5.1 Abbreviated terms
CCRS Compound Coordinate Reference System
CRS Coordinate Reference System
CS Coordinate System
GML Geography Markup Language
UML Unified Modelling Language
5.2 UML notation
In this part of ISO 19111, the conceptual schema for describing spatio-parametric referencing is modelled with
the Unified Modelling Language (UML). The basic data types and UML diagram notations are defined in
ISO/TS 19103 and ISO/IEC 19501.
5.3 Attribute status
In this part of ISO 19111, attributes are given an obligation status:
Obligation Definition Meaning
M Mandatory This attribute shall be supplied.
O Optional This attribute may be supplied.

In Tables 1 to 3, the “Maximum occurrence” column indicates the maximum number of occurrences of
attribute values that are permissible, with “N” indicating no upper limit.
2 © ISO 2009 – All rights reserved

ISO 19111-2:2009(E)
6 Spatio-parametric referencing
6.1 Overview
ISO 19111 defines a coordinate reference system (CRS) as a coordinate system which is related to an object
(such as the Earth) by a datum. A coordinate system (CS) is a set of mathematical rules for specifying how
coordinates are to be assigned to points. A coordinate system will have one or more axes. A datum defines
the position of the origin, the scale, and the orientation of a coordinate system. ISO 19111 describes several
subtypes of coordinate reference system, coordinate system and datum. This part of ISO 19111 defines a
further subtype of each to accommodate parametric referencing.
6.2 Parametric coordinate reference system
A parametric coordinate reference system shall be a subtype of a single CRS. Figure 1 shows the UML
schema, which shall consist of one parametric coordinate system and one parametric datum, these elements
being according to 6.3 and 6.4.
Table 1 specifies the attributes of a parametric coordinate reference system inherited from SC_SingleCRS.
<>
SC_CRS
(from coordinate reference systems)
(ordered)
<> 0.* <>
CoordinateSystem 2.*
SC_CompoundCRS SC_SingleCRS
(from coordinate reference systems) +compoundCRS +componentReferenceSystem (from coordinate reference systems)
<>
SC_ParametricCRS
Figure 1 — UML schema for parametric CRS
ISO 19111-2:2009(E)
Table 1 — Defining elements of SC_ParametricCRS class
Description: One-dimensional coordinate reference system which uses parameter values or functions.
Stereotype: Type
Class attribute: Concrete
Inherited from: SC_SingleCRS
Association roles: (aggregation) datum to CD_ParametricDatum [1], association named DefiningDatum
(aggregation) coordinateSystem to CS_ParametricCS [1], association named CoordinateSystem
(associations inherited from SC_SingleCRS)
Public attributes: Six attributes inherited from SC_SingleCRS:
Attribute Maximum
UML identifier Data type Obligation Attribute description
name occurrence
CRS name Name RS_Identifier M 1 This is the primary name for the
CRS. Aliases and other identifiers
may be given through the
attributes alias and identifier.
CRS alias Alias GenericName O N An alias by which this CRS is
known.
CRS identifier Identifier RS_Identifier O N An identifier which references
elsewhere the CRS's defining
information; alternatively, an
identifier by which this CRS can be
referenced.
CRS scope Scope CharacterString M N Description of usage, or limitations
of usage, for which this CRS is
valid. If unknown, enter "not
known".
CRS validity domainOfValidity EX_Extent O N Area or region or timeframe in
which this CRS is valid.
CRS remarks Remarks CharacterString O 1 Comments or information on this
CRS, including data source
information.
6.3 Parametric coordinate system
A coordinate system shall be of the parametric type if a physical or material property or function is used as the
dimension. The parameter can be measured or could be a function defined in other contexts, but in parametric
coordinate systems it forms the coordinate system axis.
EXAMPLE 1 Pressure in meteorological applications
EXAMPLE 2 Density (isopycnals) in oceanographic applications.
A parametric coordinate system shall be a subtype of a coordinate system and shall be used as a part of a
parametric coordinate reference system. Figure 2 shows the UML schema and Table 2 describes the
attributes, inherited from CS_CoordinateSystem, as defined in ISO 19111.
A parametric coordinate reference system shall be one-dimensional and shall have one axis. The defining
elements are described in ISO 19111:2007, Tables 27 and 28.
4 © ISO 2009 – All rights reserved

ISO 19111-2:2009(E)
<> <>
0.* CoordinateSystem 1 0.*
SC_SingleCRS CS_CoordinateSystem
+referenceSystem +coordinateSystem +coordinateSystem
(from coordinate reference systems) (from coordinate systems)
1.*
+axis (ordered)
<>
CS_CoordinateSystemAxis
(from coordinate systems)
+axis 1
<> 0.* CoordinateSystem 1 <> 0.*
SC_ParametricCRS CS_ParametricCS
+referenceSystem +coordinateSystem +coordinateSystem

Figure 2 — UML schema for parametric coordinate system
Table 2 — Defining elements of CS_ParametricCoordinateSystem class
Description: One-dimensional coordinate reference system which uses parameter values or functions. The
values or functions can vary monotonically with height.
A ParametricCS shall have one axis association.
Stereotype: Type
Class attribute: Concrete
Inherited from: CS_CoordinateSystem
Association roles: (aggregation) coordinateSystem from SC_ParametricCRS [1], association named
CoordinateSystem (reverse: referenceSystem to SC_ParametricCRS [0.*] navigable only from
SC_ParametricCRS — see Table 1)
(associations inherited from CS_CoordinateSystem, including (aggregation) axis
to CS_CoordinateSystemAxis [1])
Public attributes: Four attributes inherited from CS_CoordinateSystem:
Attribute UML Maximum
Data type Obligation Attribute description
name identifier occurrence
CS name Name RS_Identifier M 1 This is the primary name for the coordinate
system. Aliases and other identifiers may
be given through the attributes alias and
identifier.
CS alias Alias GenericName
...