ISO 19111-2:2009

Geographic information — Spatial referencing by coordinates — Part 2: Extension for parametric values

ISO 19111-2:2009 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 ISO 19111-2:2009 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 ISO 19111-2:2009.

Information géographique — Système de références spatiales par coordonnées — Partie 2: Supplément pour valeurs paramétriques

Geografske informacije - Lociranje s koordinatami - 2. del: Razširitev za parametrične vrednosti

General Information

• Status: Withdrawn
• Publication Date: 13-Aug-2009
• Withdrawal Date: 13-Aug-2009
• ICS: 35.240.70 - IT applications in science
• Technical Committee: ISO/TC 211 - Geographic information/Geomatics
• Drafting Committee: ISO/TC 211/WG 9 - Information management
• Current Stage: 9599 - Withdrawal of International Standard
• Completion Date: 31-Jan-2019
• Ref Project: SIST ISO 19111-2:2009 - Geographic information - Spatial referencing by coordinates - Part 2: Extension for parametric values

Relations

• Revised: ISO 19111:2019 - Geographic information — Referencing by coordinates
• Effective Date: 24-Jun-2017
• Revised: ISO 19111:2003 - Geographic information — Spatial referencing by coordinates
• Effective Date: 15-Apr-2008

Standards Content (Sample)

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

---------------------- Page: 1 ----------------------
ISO 19111-2:2009(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.


COPYRIGHT PROTECTED DOCUMENT


©  ISO 2009
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 [e-mail]
Web www.iso.org
Published in Switzerland

ii © ISO 2009 – All rights reserved

---------------------- Page: 2 ----------------------
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 2009 – All rights reserved iii

---------------------- Page: 3 ----------------------
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

---------------------- Page: 4 ----------------------
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.

© ISO 2009 – All rights reserved v

---------------------- Page: 5 ----------------------
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 2009 – All rights reserved 1

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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

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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 2009 – All rights reserved 3

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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

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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 O N An alias by which this coordinate system is
known.
CS identifier identifier RS_Identifier O N An identifier which references elsewhere
the coordinate system's defining
information; alternatively, an identifier by
which this coordinate system can be
referenced.
CS remarks remarks CharacterString O 1 Comments or information on this
coordinate system, including data source
information.

© ISO 2009 – All rights reserved 5

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ISO 19111-2:2009(E)
6.4 Parametric datum
A parametric datum shall be a subtype of a datum. It shall be used as a part of a parametric coordinate
reference system. Figure 3 shows the UML schema. Table 3 describes the attributes, inherited from
CD_Datum, as defined in ISO 19111.
<> <>
0.* DefiningDatum 0.*
SC_SingleCRS CD_Datum
(from coordinate reference systems) +referenceSystem +datum (from datums)
0.* DefiningDatum 1
<> <>
SC_ParametricCRS CD_ParametricDatum
+referenceSystem +datum

Figure 3 — UML schema for parametric datum
6 © ISO 2009 – All rights reserved

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ISO 19111-2:2009(E)
Table 3 — Defining elements of CD_ParametricDatum class
Description: A textual description and/or a set of parameters identifying a particular reference surface used as
the origin of a parametric coordinate system, including its position with respect to the Earth
Stereotype: Type
Class attribute: Concrete
Inherited from: CD_Datum
Association roles: (aggregation) datum to CD_ParametricDatum [1], association named DefiningDatum (reverse:
referenceSystem to SC_ParametricCRS [0.*] navigable only from SC_ParametricCRS — see
Table 1)
Public attributes: Eight attributes inherited from CD_Datum:
Maximum
Attribute name UML identifier Data type Obligation Attribute description
occurrence
Datum name Name RS_Identifier M 1 This is the primary name for the datum.
Aliases and other identifiers may be
given through the attributes alias and
identifier.
Datum alias Alias GenericName O N An alias by which this datum is known.
Datum identifier Identifier RS_Identifier O N An identifier which references
elsewhere the datum's defining
information; alternatively, an identifier
by which this datum can be referenced.
Datum anchor anchorDefinition CharacterString O 1 The datum definition: a description,
possibly including coordinates of an
identified point or points, of the
relationship used to anchor the
coordinate system to the Earth or
alternative object.
For a parametric datum, the anchor
...

SLOVENSKI STANDARD
SIST ISO 19111-2:2009
01-december-2009
*HRJUDIVNHLQIRUPDFLMH/RFLUDQMHVNRRUGLQDWDPLGHO5D]ãLULWHY]D
SDUDPHWULþQHYUHGQRVWL
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
Ta slovenski standard je istoveten z: ISO 19111-2:2009
ICS:
35.240.70 Uporabniške rešitve IT v IT applications in science
znanosti
SIST ISO 19111-2:2009 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

SIST ISO 19111-2:2009

---------------------- Page: 2 ----------------------

SIST ISO 19111-2:2009

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

---------------------- Page: 3 ----------------------

SIST ISO 19111-2:2009
ISO 19111-2:2009(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.


COPYRIGHT PROTECTED DOCUMENT


©  ISO 2009
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 [e-mail]
Web www.iso.org
Published in Switzerland

ii © ISO 2009 – All rights reserved

---------------------- Page: 4 ----------------------

SIST ISO 19111-2:2009
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 2009 – All rights reserved iii

---------------------- Page: 5 ----------------------

SIST ISO 19111-2:2009
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

---------------------- Page: 6 ----------------------

SIST ISO 19111-2:2009
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.

© ISO 2009 – All rights reserved v

---------------------- Page: 7 ----------------------

SIST ISO 19111-2:2009

---------------------- Page: 8 ----------------------

SIST ISO 19111-2:2009
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 2009 – All rights reserved 1

---------------------- Page: 9 ----------------------

SIST ISO 19111-2:2009
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

---------------------- Page: 10 ----------------------

SIST ISO 19111-2:2009
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 2009 – All rights reserved 3

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SIST ISO 19111-2:2009
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

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SIST ISO 19111-2:2009
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 O N An alias by which this coordinate system is
known.
CS identifier identifier RS_Identifier O N An identifier which references elsewhere
the coordinate system's defining
information; alternatively, an identifier by
which this coordinate system can be
referenced.
CS remarks remarks CharacterString O 1 Comments or information on this
coordinate system, including data source
information.

© ISO 2009 – All rights reserved 5

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SIST ISO 19111-2:2009
ISO 19111-2:2009(E)
6.4 Parametric datum
A parametric datum shall be a subtype of a datum. It shall be used as a part of a parametric coordinate
reference system. Figure 3 shows the UML schema. Table 3 describes the attributes, inherited from
CD_Datum, as defined in ISO 19111.
<> <>
0.* DefiningDatum 0.*
SC_SingleCRS CD_Datum
(from coordinate reference systems) +referenceSystem +datum (from datums)
0.* DefiningDatum 1
<> <>
SC_ParametricCRS CD_ParametricDatum
+referenceSystem +datum

Figure 3 — UML schema for parametric datum
6 © ISO 2009 – All rights reserved

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SIST ISO 19111-2:2009
ISO 19111-2:2009(E)
Table 3 — Defining elements of CD_ParametricDatum class
Description: A textual description and/or a set of parameters identifying a particular reference surface used as
the origin of a parametric coordinate system, including its position with respect to the Earth
Stereotype: Type
Class attribute: Concrete
Inherited from: CD_Datum
Association roles: (aggregation) datum to CD_ParametricDatum [1], association named DefiningDatum (reverse:
referenceSystem to SC_ParametricCRS [0.*] navigable only from SC_ParametricCRS — see
Table 1)
Public attributes: Eight attributes inherited from CD_Datum:
Maximum
Attribute name UML identifier Data type Obligation Attribute description
occurrence
Datum name Name RS_Identifier M 1 This is the primary name for the datum.
Aliases and other identifiers may be
given through the attributes alias and
identifier.
D
...

NORME ISO
INTERNATIONALE 19111-2
Première édition
2009-08-15
Information géographique — Système de
références spatiales par coordonnées —
Partie 2:
Supplément pour valeurs paramétriques
Geographic information — Spatial referencing by coordinates —
Part 2: Extension for parametric values
Numéro de référence
ISO 19111-2:2009(F)
©
ISO 2009

---------------------- Page: 1 ----------------------
ISO 19111-2:2009(F)
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2009
Droits de reproduction réservés. Sauf prescription différente, aucune partie de cette publication ne peut être reproduite ni utilisée sous
quelque forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie et les microfilms, sans l’accord écrit
de l’ISO à l’adresse ci-après ou du comité membre de l’ISO dans le pays du demandeur.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
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Version française parue en 2012
Publié en Suisse
ii © ISO 2009 – Tous droits réservés

---------------------- Page: 2 ----------------------
ISO 19111-2:2009(F)
Sommaire Page
Avant-propos .iv
Introduction . v
1 Domaine d’application . 1
2 Exigences relatives à la conformité . 1
3 Références normatives . 1
4 Termes et définitions . 1
5 Conventions . 2
5.1 Termes abrégés . 2
5.2 Notation UML . 2
5.3 État des attributs . 2
6 Système de références spatio-paramétriques . 2
6.1 Présentation . 2
6.2 Système de coordonnées de référence paramétriques . 3
6.3 Système de coordonnées paramétriques . 4
6.4 Référence paramétrique . 5
6.5 Système de coordonnées de référence spatio-paramétriques . 7
6.6 Système de coordonnées de référence spatio-paramétriques en fonction du temps . 8
6.7 Transformation et conversion de systèmes de coordonnées de référence paramétriques . 8
Annexe A (normative) Conformité . 9
Annexe B (informative) Exemples . 11
Bibliographie .17
© ISO 2009 – Tous droits réservés iii

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ISO 19111-2:2009(F)
Avant-propos
L’ISO (Organisation internationale de normalisation) est une fédération mondiale d’organismes nationaux de
normalisation (comités membres de l’ISO). L’élaboration des Normes internationales est en général confiée aux
comités techniques de l’ISO. Chaque comité membre intéressé par une étude a le droit de faire partie du comité
technique créé à cet effet. Les organisations internationales, gouvernementales et non gouvernementales,
en liaison avec l’ISO participent également aux travaux. L’ISO collabore étroitement avec la Commission
électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.
Les Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI, Partie 2.
La tâche principale des comités techniques est d’élaborer les Normes internationales. Les projets de Normes
internationales adoptés par les comités techniques sont soumis aux comités membres pour vote. Leur publication
comme Normes internationales requiert l’approbation de 75 % au moins des comités membres votants.
L’attention est appelée sur le fait que certains des éléments du présent document peuvent faire l’objet de droits
de propriété intellectuelle ou de droits analogues. L’ISO ne saurait être tenue pour responsable de ne pas avoir
identifié de tels droits de propriété et averti de leur existence.
L’ISO 19111-2 a été élaborée par le comité technique ISO/TC 211, Information géographique/Géomatique.
L’ISO 19111 comprend les parties suivantes, présentées sous le titre général Information géographique —
Système de références spatiales par coordonnées:
— Information géographique — Système de références spatiales par coordonnées
— Partie 2: Supplément pour valeurs paramétriques
iv © ISO 2009 – Tous droits réservés

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ISO 19111-2:2009(F)
Introduction
L‘ISO 19111 décrit les éléments nécessaires pour définir intégralement les différents types de systèmes
de références utilisés pour un référencement spatial par coordonnées. Dans l’ISO 19111, une coordonnée
est une valeur parmi n valeurs scalaires qui définissent la position d’un point. L’ISO 19111 tient compte des
coordonnées angulaires, comme latitude et longitude, ou linéaires, comme abscisse et ordonnée. Elle décrit
également le concept d’un système de coordonnées de référence combiné, qui utilise au moins deux systèmes
de coordonnées de référence indépendants pour décrire une position tridimensionnelle dans l’espace.
Les communautés scientifiques, en particulier celles concernés par les sciences de l’environnement, n’expriment
fréquemment une position dans l’espace que partiellement, en termes de paramètre ou de fonction. Au sein
de ces communautés, ce paramètre ou fonction est traité comme une coordonnée. Sa relation avec une
dimension spatiale sera habituellement non linéaire. Les exemples sont répandus, mais latitude, longitude et
pression représentent un exemple rencontré communément.
La présente partie de l’ISO 19111 définit un système de coordonnées de référence paramétriques utilisant
les concepts de l’ISO 19111. Les dispositions de l’ISO 19111 sont alors utilisées pour inclure un système de
coordonnées de référence paramétriques dans le cadre d’un système de coordonnées de référence combiné.
Éventuellement, le temps peut également être inclus comme axe(s) supplémentaire(s).
© ISO 2009 – Tous droits réservés v

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NORME INTERNATIONALE ISO 19111-2:2009(F)
Information géographique — Système de références spatiales
par coordonnées —
Partie 2:
Supplément pour valeurs paramétriques
1 Domaine d’application
La présente partie de l’ISO 19111 spécifie le schéma conceptuel pour la description d’un système de références
spatiales utilisant des valeurs ou fonctions paramétriques. Il applique le schéma de l’ISO 19111 pour combiner
une position référencée par des coordonnées avec une valeur paramétrique pour former un système de
coordonnées de référence (CRS, coordinate reference system) spatio-paramétriques. Le système CRS spatio-
paramétriques peut éventuellement être étendu pour inclure le temps.
Les utilisateurs visés de la présente partie de l’ISO 19111 sont les créateurs et utilisateurs d’informations liées
à l’environnement.
Les paramètres qui sont des attributs d’emplacements ou entités spatiaux, mais qui ne sont pas impliqués dans
leur système de références spatiales, ne sont pas abordés dans la présente partie de l’ISO 19111.
2 Exigences relatives à la conformité
Tout système CRS pour lequel la conformité à la présente partie de l’ISO 19111 est revendiquée doit être
conforme à l’Annexe A.
3 Références normatives
Les documents de référence suivants sont indispensables à l’application du présent document. Pour les
références datées, seule l’édition citée s’applique. Pour les références non datées, la dernière édition du
document de référence s’applique (y compris les éventuels amendements).
ISO 19111:2007, Information géographique — Système de références spatiales par coordonnées
4 Termes et définitions
Pour les besoins du présent document, les termes et définitions donnés dans l’ISO 19111 ainsi que les suivants
s’appliquent.
4.1
système de coordonnées paramétriques
système de coordonnées unidimensionnel où les unités de l’axe sont des valeurs de paramètres qui ne sont
pas spatiales de manière inhérente
4.2
système de coordonnées de référence paramétriques
système de coordonnées de référence basé sur une référence paramétrique
4.3
référence paramétrique
référence décrivant la relation d’un système de coordonnées paramétriques avec un objet
NOTE L’objet est normalement la Terre.
© ISO 2009 – Tous droits réservés 1

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ISO 19111-2:2009(F)
4.4
système de coordonnées de référence spatio-paramétriques
système de coordonnées de référence combiné dans lequel un système de coordonnées de référence le
composant est un système de coordonnées de référence paramétriques et l’autre est un système de
coordonnées de référence spatiales
NOTE Normalement la composante spatiale est «horizontale» et la composante paramétrique est «verticale».
4.5
système de coordonnées de référence spatio-paramétriques-temporelles
système de coordonnées de référence combiné comprenant des systèmes de coordonnées de référence
spatiales, paramétriques et temporelles
5 Conventions
5.1 Termes abrégés
CCRS Système de coordonnées de référence combiné (Compound Coordinate Reference System)
CRS Système de coordonnées de référence (Coordinate Reference System)
CS Système de coordonnées (Coordinate System)
GML Langage de balisage géographique (Geography Markup Language)
UML Langage de modélisation unifié (Unified Modelling Language)
5.2 Notation UML
Dans la présente partie de l’ISO 19111, le schéma conceptuel pour la description d’un système de références
spatio-paramétriques est modélisé avec le langage de modélisation unifié (UML). Les types de données de
base et les notations de diagramme d’UML sont définis dans l’ISO/TS 19103 et l’ISO/CEI 19501.
5.3 État des attributs
Dans la présente partie de l’ISO 19111, les attributs ont un état de contrainte:
Contrainte Définition Signification
O Obligatoire Cet attribut doit être fourni.
F Facultatif Il n’est pas obligatoire de fournir cet attribut.
Dans les Tableaux 1 à 3, la colonne «Occurrences maximales» indique le nombre maximal autorisé
d’occurrences des valeurs d’attributs, «N» signifiant l’absence de limite maximale.
6 Système de références spatio-paramétriques
6.1 Présentation
L’ISO 19111 définit un système de coordonnées de référence (CRS) comme un système de coordonnées lié
à un objet (comme la Terre) par une référence. Un système de coordonnées (CS) est un ensemble de règles
mathématiques servant à spécifier comment des coordonnées doivent être affectées à des points. Un système
de coordonnées aura un ou plusieurs axes. Une référence définit la position de l’origine, l’échelle et l’orientation
d’un système de coordonnées. L’ISO 19111 décrit plusieurs sous-types d’un système de coordonnées de
référence, d’un système de coordonnées et de référence. La présente partie de l’ISO 19111 définit un sous-type
supplémentaire pour chacun de ces éléments afin de s’adapter à un système de références paramétriques.
2 © ISO 2009 – Tous droits réservés

---------------------- Page: 7 ----------------------
ISO 19111-2:2009(F)
6.2 Système de coordonnées de référence paramétriques
Un système de coordonnées de référence paramétriques doit être un sous-type d’un CRS simple. La Figure 1
montre le schéma UML, qui doit être composé d’un système de coordonnées paramétriques et d’une référence
paramétrique, ces éléments étant conformes à 6.3 et 6.4.
Le Tableau 1 spécifie les attributs d’un système de coordonnées de référence paramétriques hérité de
SC_SingleCRS.
<>
SC_CRS
(à partir des systèmes de coordonnées de référence)
(ordered)
<> <>
0.*
CoordinateSystem 2.*
SC_CompoundCRS SC_SingleCRS
(à partir des systèmes +compoundCRS +componentReferenceSystem (à partir des systèmes
de coordonnées de référence) de coordonnées de référence)
<>
SC_ParametricCRS
Figure 1 — Schéma UML pour un système CRS paramétriques
© ISO 2009 – Tous droits réservés 3

---------------------- Page: 8 ----------------------
ISO 19111-2:2009(F)
Tableau 1 — Définition des éléments de la classe SC_ParametricCRS
Description: Système de coordonnées de référence unidimensionnel qui utilise des valeurs ou fonctions de
paramètres.
Stéréotype: Type
Attribut de classe: Concrete
Héritage: SC_SingleCRS
Rôles d’association: (agrégation) référence à CD_ParametricDatum [1], association nommée DefiningDatum
(agrégation) coordinateSystem à CS_ParametricCS [1], association nommée
CoordinateSystem (associations héritées de SC_SingleCRS)
Attributs publics: Six attributs hérités de SC_SingleCRS:
Nom de Identificateur Occurrences
Type de données Contrainte Description de l’attribut
l’attribut UML maximales
Nom du CRS Name RS_Identifier O 1 Il s’agit du nom principal du CRS. Les
alias et les autres identificateurs peuvent
être donnés par l’alias et l’identificateur
des attributs.
Alias du CRS Alias GenericName F N Alias identifiant le CRS.
Identificateur Identifier RS_Identifier F N Identificateur qui référence à un autre
du CRS endroit les informations relatives à
la définition du CRS ou identificateur
permettant de référencer ce CRS.
Domaine Scope CharacterString O N Description de l’utilisation, ou limites de
d’application l’utilisation, pour laquelle ce CRS est
du CRS valide. Si cette information est inconnue,
entrer «not known» («inconnu»).
Validité domainOfValidity EX_Extent F N Zone, région ou intervalle de temps
du CRS dans lequel le CRS est valide.
Remarques Remarks CharacterString F 1 Commentaires ou informations
relatives concernant ce CRS, notamment les
au CRS informations relatives à la source des
données.
6.3 Système de coordonnées paramétriques
Un système de coordonnées doit être du type paramétrique si une propriété ou fonction physique ou matérielle
est utilisée comme dimension. Le paramètre peut être mesuré ou pourrait être une fonction définie dans d’autres
contextes, mais dans des systèmes de coordonnées paramétriques, il constitue l’axe du système de coordonnées.
EXEMPLE 1 La pression dans les applications météorologiques
EXEMPLE 2 La densité (isopycnique) dans les applications océanographiques.
Un système de coordonnées paramétriques doit être un sous-type d’un système de coordonnées et doit être
utilisé dans le cadre d’un système de coordonnées de référence paramétriques. La Figure 2 montre le schéma
UML et le Tableau 2 décrit les attributs, hérités de CS_CoordinateSystem, tels que définis dans l’ISO 19111.
Un système de coordonnées de référence paramétriques doit être unidimensionnel et doit n’avoir qu’un axe. La
définition des éléments est décrite dans l’ISO 19111:2007, Tableaux 27 et 28.
4 © ISO 2009 – Tous droits réservés

---------------------- Page: 9 ----------------------
ISO 19111-2:2009(F)
<> <>
0.* CoordinateSystem 1 0.*
SC_SingleCRS CS_CoordinateSystem
(à partir des systèmes +referenceSystem +coordinateSystem (à partir des systèmes de coordonnées) +coordinateSystem
de coordonnées de référence)
1.*
+axis (ordered)
<>
CS_CoordinateSystemAxis
(à partir des systèmes de coordonnées)
+axis 1
<> 0.* CoordinateSystem 1 <> 0.*
SC_ParametricCRS CS_ParametricCS
+referenceSystem +coordinateSystem +coordinateSystem
Figure 2 — Schéma UML pour un système de coordonnées paramétriques
Tableau 2 — Définition des éléments de la classe CS_ParametricCoordinateSystem class
Description: Système de coordonnées de référence unidimensionnel qui utilise des valeurs ou fonctions de
paramètres. Les valeurs ou fonctions peuvent varier de façon régulière avec la hauteur.
Un ParametricCS doit disposer d’une association d’axes.
Stéréotype: Type
Attribut de classe: Concrete
Héritage: CS_CoordinateSystem
Rôles d’association: (agrégation) coordinateSystem depuis SC_ParametricCRS [1], association nommée
CoordinateSystem (inversé: referenceSystem à SC_ParametricCRS [0.*] accessible uniquement
depuis SC_ParametricCRS — voir Tableau 1) (associations héritées de CS_CoordinateSystem,
incluant (agrégation) axe vers CS_CoordinateSystemAxis [1])
Attributs publics: Quatre attributs hérités de CS_CoordinateSystem:
Nom de Identificateur Occurrences
Type de données Contrainte Description de l’attribut
l’attribut UML maximales
Nom du CS Name RS_Identifier O 1 Il s’agit du nom principal du système
de coordonnées. Les alias et les autres
identificateurs peuvent être donnés par
l’alias et l’identificateur des attributs.
Alias du CS Alias GenericName F N Alias identifiant le système de
coordonnées.
Identificateur identifier RS_Identifier F N Identificateur qui référence à un autre
du CS endroit les informations relatives à la
définition du système de coordonnées
ou identificateur permettant de
référencer ce système de coordonnées.
Remarques remarks CharacterString F 1 Commentaires ou informations
relatives au concernant ce système de
CS coordonnées, notamment les
informations relatives à la source des
données.
6.4 Référence paramétrique
Une référence paramétrique doit être un sous-type d’une référence. Elle doit être utilisée dans le cadre d’un
système de coordonnées de référence paramétriques. La Figure 3 représente le schéma UML. Le Tableau 3
décrit les attributs, hérités de CD_Datum, tels que définis dans l’ISO 19111.
© ISO 2009 – Tous droits réservés 5

---------------------- Page: 10 ----------------------
ISO 19111-2:2009(F)
<> <>
0.* DefiningDatum 0.*
SC_SingleCRS CD_Datum
(à partir des systèmes de coordonnées de référence) +referenceSystem +datum (à partir des référence)
0.* DefiningDatum 1
<> <>
SC_ParametricCRS CD_ParametricDatum
+referenceSystem +datum
Figure 3 — Schéma UML pour une référence paramétrique
6 © ISO 2009 – Tous droits réservés

---------------------- Page: 11 ----------------------
ISO 19111-2:2009(F)
Tableau 3 — Définition des éléments de la classe CD_ParametricDatum class
Description: Description textuelle et/ou ensemble de paramètres identifiant une surface de référence
spécifique comme origine d’un système de coordonnées paramétriques, y compris sa position
par rapport à la Terre
Stéréotype: Type
Attribut de classe: Concrete
Héritage: CD_Datum
Rôles d’association: (agrégation) référence à CD_ParametricDatum [1], association nommée DefiningDatum
(inversé: referenceSystem à SC_ParametricCRS [0.*] accessible uniquement depuis
SC_ParametricCRS — voir Tableau 1)
Attributs publics: Huit attributs hérités de CD_Datum:
Nom de Identificateur Occurrences
Type de données Contrainte Description de l’attribut
l’attribut UML maximales
Nom de la Name RS_Identifier O 1 Il s’agit du nom principal de la
référence référence. Les alias et les autres
identificateurs peuvent être donnés par
l’alias et l’identificateur des attributs.
Alias de la Alias GenericName F N Alias identifiant la référence.
référence
Identificateur Identifier RS_Identifier F N Identificateur qui référence à un autre
de la endroit les informations relatives
référence à la définition de la référence ou
identificateur permettant de référencer
cette référence.
Point anchorDefinition CharacterString F 1 Définition de la référence: description,
d’ancrage de incluant éventuellement les
la référence coordonnées d’un ou plusieurs points
identifiés, de la relation utilisée pour
fixer le système de coordonnées à la
Terre ou à un autre objet.
Pour une référence paramétrique,
le point d’ancrage peut être une
surface physique identifiée, associée
à l’orientation définie par rapport à la
surface.
Époque de realizationEpoch Date F 1 Point temporel après lequel cette
réalisation de définition de référence est valide. Ce
la référence point temporel peut être donné avec
n’importe quelle précision.
Domaine Scope CharacterString O N Description de l’utilisation, ou
d’application limites de l’utilisation, pour laquelle
de la cette référence est valide. Si cette
référence information est inconnue, entrer «not
known» («inconnu»).
Validité de la domainOfValidity EX_Extent F 1 Zone, région ou intervalle de temps
référence dans lequel la référence est valide.
Remarques Remarks CharacterString F 1 Commentaires ou informations
relatives à la concernant cette ré
...

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Information géographique - Système de références spatiales par coordonnées - Partie 2: Supplément pour valeurs paramétriquesGeographic information - Spatial referencing by coordinates - Part 2: Extension for parametric values35.240.70Uporabniške rešitve IT v znanostiIT applications in scienceICS:Ta slovenski standard je istoveten z:ISO/PRF 19111-2oSIST ISO/PRF 19111-2:2009en01-julij-2009oSIST ISO/PRF 19111-2:2009SLOVENSKI
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oSIST ISO/PRF 19111-2:2009



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INTERNATIONAL STANDARD ISO19111-2First edition2009-##-##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
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ii PROOF/ÉPREUVE © ISO 2009 – All rights reserved
oSIST ISO/PRF 19111-2:2009



ISO 19111-2:2009(E) © ISO 2009 – All rights reserved PROOF/ÉPREUVE iiiContents 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
oSIST ISO/PRF 19111-2:2009



ISO 19111-2:2009(E) iv PROOF/ÉPREUVE © ISO 2009 – All rights reserved 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 oSIST ISO/PRF 19111-2:2009



ISO 19111-2:2009(E) © ISO 2009 – All rights reserved PROOF/ÉPREUVE vIntroduction 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.
oSIST ISO/PRF 19111-2:2009



oSIST ISO/PRF 19111-2:2009



INTERNATIONAL STANDARD ISO 19111-2:2009(E) © ISO 2009 – All rights reserved PROOF/ÉPREUVE 1Geographic 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 oSIST ISO/PRF 19111-2:2009



ISO 19111-2:2009(E) 2 PROOF/ÉPREUVE © ISO 2009 – All rights reserved 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. oSIST ISO/PRF 19111-2:2009



ISO 19111-2:2009(E) © ISO 2009 – All rights reserved PROOF/ÉPREUVE 36 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)CoordinateSystem<>SC_CompoundCRS(from coordinate reference systems)<>SC_SingleCRS(from coordinate reference systems)<>SC_ParametricCRS+compoundCRS+componentReferenceSystem0.*2.*(ordered) Figure 1 — UML schema for parametric CRS oSIST ISO/PRF 19111-2:2009



ISO 19111-2:2009(E) 4 PROOF/ÉPREUVE © ISO 2009 – All rights reserved 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 name UML identifier Data type Obligation Maximum occurrence Attribute description 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. oSIST ISO/PRF 19111-2:2009



ISO 19111-2:2009(E) © ISO 2009 – All rights reserved PROOF/ÉPREUVE 5CoordinateSystem<>SC_SingleCRS(from coordinate reference systems)<>CS_ParametricCS+referenceSystem0.*1(ordered)<>CS_CoordinateSystem(from coordinate systems)<>CS_CoordinateSystemAxis(from coordinate systems)<>SC_ParametricCRS+coordinateSystem+coordinateSystem0.*1.*+axis+axisCoordinateSystem+referenceSystem0.*1+coordinateSystem+coordinateSystem0.*1 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 name UML identifier Data type ObligationMaximum occurrence Attribute description 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 O N An alias by which this coordinate system is known. CS identifier identifier RS_Identifier O N An identifier which references elsewhere the coordinate system's defining information; alternatively, an identifier by which this coordinate system can be referenced. CS remarks remarks CharacterString O 1 Comments or information on this coordinate system, including data source information.
oSIST ISO/PRF 19111-2:2009



ISO 19111-2:2009(E) 6 PROOF/ÉPREUVE © ISO 2009 – All rights reserved 6.4 Parametric datum A parametric datum shall be a subtype of a datum. It shall be used as a part of a parametric coordinate reference system. Figure 3 shows the UML schema. Table 3 describes the attributes, inherited from CD_Datum, as defined in ISO 19111. DefiningDatum<>SC_SingleCRS(from coordinate reference systems)<>CD_ParametricDatum+referenceSystem0.*0.*<>CD_Datum(from datums)<>SC_ParametricCRS+datumDefiningDatum+referenceSystem0.*1+datum Figure 3 — UML schema for parametric datum oSIST ISO/PRF 19111-2:2009



ISO 19111-2:2009(E) © ISO 2009 – All rights reserved PROOF/ÉPREUVE 7Table 3 — Defining elements of CD_ParametricDatum class Description: A textual description and/or a set of parameters identifying a particular reference surface used as the origin of a parametric coordinate system, including its position with respect to the Earth Stereotype: Type Class attribute:
Concrete Inherited from: CD_Datum Association roles: (aggregation) datum to CD_ParametricDatum [1], association named DefiningDatum (reverse: referenceSystem to SC_ParametricCRS [0.*] navigable only from SC_ParametricCRS —see Table 1) Public attributes: Eight attributes inherited from CD_Datum: Attribute name UML identifier Data type ObligationMaxi
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