ISO 19111:2003
(Main)Geographic information — Spatial referencing by coordinates
Geographic information — Spatial referencing by coordinates
ISO 19111:2003 defines the conceptual schema for the description of spatial referencing by coordinates. It describes the minimum data required to define one-, two- and three-dimensional coordinate reference systems. It allows additional descriptive information to be provided. It also describes the information required to change coordinate values from one coordinate reference system to another. ISO 19111:2003 is applicable to producers and users of geographic information. Although it is applicable to digital geographic data, its principles can be extended to many other forms of geographic data such as maps, charts, and text documents.
Information géographique — Système de références spatiales par coordonnées
Geografske informacije - Lociranje s koordinatami
General Information
Relations
Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 19111
First edition
2003-02-15
Geographic information — Spatial
referencing by coordinates
Information géographique — Système de références spatiales par
coordonnées
Reference number
ISO 19111:2003(E)
©
ISO 2003
---------------------- Page: 1 ----------------------
ISO 19111:2003(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 2003
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 2003 — All rights reserved
---------------------- Page: 2 ----------------------
ISO 19111:2003(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Conformance requirements . 1
3 Normative references . 1
4 Terms and definitions. 1
5 Conventions . 5
5.1 Symbols and abbreviated terms. 5
5.2 UML notation . 6
6 Definition of the conceptual schema for coordinate reference systems . 7
6.1 Introduction . 7
6.2 Coordinate reference system. 7
6.2.1 Type of coordinate reference system . 7
6.2.2 Single coordinate reference system . 8
6.2.3 Compound coordinate reference system. 8
6.3 Datum . 9
6.3.1 Types of datums. 9
6.3.2 Datum description. 10
6.3.3 Prime meridian . 10
6.3.4 Ellipsoid . 11
6.4 Coordinate system. 11
6.5 Coordinate operation — coordinate conversion and coordinate transformation. 12
6.5.1 General. 12
6.5.2 Coordinate conversion (including map projection) . 13
6.5.3 Coordinate transformation. 14
6.5.4 Requirements for describing a coordinate operation. 14
6.5.5 Concatenated coordinate operation . 16
6.6 Citations. 17
6.7 Accuracy and precision of coordinates, coordinate operations, and parameters. 18
6.8 Attributes to describe a coordinate reference system. 19
Annex A (normative) Conformance . 22
Annex B (normative) UML schemas . 24
Annex C (informative) Decision trees. 27
Annex D (informative) Geodetic relationships. 29
Annex E (informative) Examples. 35
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ISO 19111:2003(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 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics.
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ISO 19111:2003(E)
Introduction
Geographic information contains spatial references which relate the features represented in the data to
positions in the real world. Spatial references fall into two categories:
those using coordinates;
those based on geographic identifiers.
This International Standard deals only with spatial referencing by coordinates. Spatial referencing by
geographic identifiers is the subject of ISO 19112, Geographic information ― Spatial referencing by
geographic identifiers.
Coordinates are unambiguous only when the coordinate reference system to which those coordinates are
related has been fully defined. A coordinate reference system is a coordinate system which has a reference to
the Earth. This International Standard describes the elements that are necessary to define fully various types
of coordinate systems and coordinate reference systems applicable to geographic information. The subset of
elements required is partially dependent upon the type of coordinates. This International Standard also
includes optional fields to allow for the inclusion of non-essential coordinate reference system information. The
elements are intended to be both machine and human readable. A set of coordinates on the same coordinate
reference system requires one coordinate reference system description.
In addition to describing a coordinate reference system, this International Standard provides for the
description of a coordinate transformation or coordinate conversion between two different coordinate
reference systems. With such information, geographic data referred to different coordinate reference systems
can be merged together for integrated manipulation. Alternatively, an audit trail of coordinate reference system
manipulations can be maintained.
© ISO 2003 — All rights reserved v
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INTERNATIONAL STANDARD ISO 19111:2003(E)
Geographic information — Spatial referencing by coordinates
1 Scope
This International Standard defines the conceptual schema for the description of spatial referencing by
coordinates. It describes the minimum data required to define one-, two- and three-dimensional coordinate
reference systems. It allows additional descriptive information to be provided. It also describes the information
required to change coordinate values from one coordinate reference system to another.
This International Standard is applicable to producers and users of geographic information. Although it is
applicable to digital geographic data, its principles can be extended to many other forms of geographic data
such as maps, charts, and text documents.
2 Conformance requirements
This International Standard defines two classes of conformance, Class A for conformance of coordinate
reference systems and Class B for coordinate operations between two coordinate reference systems. Any
coordinate reference system claiming conformance to this International Standard shall satisfy the
requirements given in Annex A, Clause A.1. Any coordinate operation claiming conformance to this
International Standard shall satisfy the requirements given in Annex A, Clause A.2.
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 1000, SI units and recommendations for use of their multiples and of certain other units
1)
ISO/TS 19103:— , Geographic information — Conceptual schema language
ISO 19113:2002, Geographic information — Quality principles
1)
ISO 19114:— , Geographic information — Quality evaluation procedures
4 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
4.1
Cartesian coordinate system
coordinate system which gives the position of points relative to n mutually perpendicular axes
1)
To be published.
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ISO 19111:2003(E)
NOTE n is 1, 2 or 3 for the purposes of this International Standard.
4.2
compound coordinate reference system
coordinate reference system using two other independent coordinate reference systems to describe a position
EXAMPLE One coordinate reference system based on a two- or three-dimensional coordinate system and the other
coordinate reference system based on a gravity-related height system.
4.3
coordinate
one of a sequence of n numbers designating the position of a point in n-dimensional space
NOTE 1 In a coordinate reference system, the numbers must be qualified by units.
NOTE 2 A coordinate operation is performed on coordinates in a source system resulting in coordinates in a target
system.
4.4
coordinate conversion
change of coordinates, based on a one-to-one relationship, from one coordinate system to another based
on the same datum
EXAMPLE Between geodetic and Cartesian coordinate systems or between geodetic coordinates and projected
coordinates, or change of units such as from radians to degrees or feet to metres.
NOTE A coordinate conversion uses parameters which have constant values.
4.5
coordinate operation
change of coordinates, based on a one-to-one relationship, from one coordinate reference system to
another
NOTE Supertype of coordinate transformation and coordinate conversion.
4.6
coordinate reference system
coordinate system that is related to the real world by a datum
NOTE For geodetic and vertical datums, it will be related to the Earth.
4.7
coordinate system
set of mathematical rules for specifying how coordinates are to be assigned to points
4.8
coordinate transformation
change of coordinates from one coordinate reference system to another coordinate reference system
based on a different datum through a one-to-one relationship
NOTE A coordinate transformation uses parameters which are derived empirically by a set of points with known
coordinates in both coordinate reference systems.
4.9
datum
parameter or set of parameters that serve as a reference or basis for the calculation of other parameters
NOTE A datum defines the position of the origin, the scale, and the orientation of the axes of a coordinate system.
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ISO 19111:2003(E)
4.10
easting
E
distance in a coordinate system, eastwards (positive) or westwards (negative) from a north-south reference
line
4.11
ellipsoid
surface formed by the rotation of an ellipse about a main axis
NOTE In this International Standard, ellipsoids are always oblate, meaning that the axis of rotation is always the
minor axis.
4.12
ellipsoidal height
geodetic height
h
distance of a point from the ellipsoid measured along the perpendicular from the ellipsoid to this point
positive if upwards or outside of the ellipsoid
NOTE Only used as part of a three-dimensional geodetic coordinate system and never on its own.
4.13
engineering datum
local datum
datum describing the relationship of a coordinate system to a local reference
NOTE Engineering datum excludes both geodetic and vertical datums.
EXAMPLE A system for identifying relative positions within a few kilometres of the reference point.
4.14
flattening
f
ratio of the difference between the semi-major (a) and semi-minor axis (b) of an ellipsoid to the semi-major
axis: f = (a − b)/a
NOTE Sometimes inverse flattening 1/f = a/(a − b) is given instead; 1/f is also known as reciprocal flattening.
4.15
geodetic coordinate system
ellipsoidal coordinate system
coordinate system in which position is specified by geodetic latitude, geodetic longitude and (in the three-
dimensional case) ellipsoidal height
4.16
geodetic datum
datum describing the relationship of a coordinate system to the Earth
NOTE In most cases, the geodetic datum includes an ellipsoid definition.
4.17
geodetic latitude
ellipsoidal latitude
ϕ
angle from the equatorial plane to the perpendicular to the ellipsoid through a given point, northwards treated
as positive
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ISO 19111:2003(E)
4.18
geodetic longitude
ellipsoidal longitude
λ
angle from the prime meridian plane to the meridian plane of a given point, eastward treated as positive
4.19
geoid
level surface which best fits mean sea level either locally or globally
NOTE “Level surface” means an equipotential surface of the Earth’s gravity field which is everywhere perpendicular
to the direction of gravity.
4.20
gravity-related height
H
height dependent on the Earth’s gravity field
NOTE In particular, orthometric height or normal height, which are both approximations of the distance of a point
above the mean sea level.
4.21
Greenwich meridian
meridian that passes through the position of the Airy Transit Circle at the Royal Observatory Greenwich,
United Kingdom
NOTE Most geodetic datums use the Greenwich meridian as the prime meridian. Its precise position differs slightly
between different datums.
4.22
height
h, H
distance of a point from a chosen reference surface along a line perpendicular to that surface
NOTE 1 See ellipsoidal height and gravity-related height.
NOTE 2 Height of a point outside the surface treated as positive; negative height is also called depth.
4.23
map projection
coordinate conversion from a geodetic coordinate system to a plane
4.24
mean sea level
average level of the surface of the sea over all stages of tide and seasonal variations
NOTE Mean sea level in a local context normally means mean sea level for the region calculated from observations
at one or more points over a given period of time. Mean sea level in a global context differs from a global geoid by not
more than 2 m.
4.25
meridian
intersection of an ellipsoid by a plane containing the semi-minor axis of the ellipsoid
NOTE This term is often used for the pole-to-pole arc rather than the complete closed figure.
4.26
northing
N
distance in a coordinate system, northwards (positive) or southwards (negative) from an east-west reference
line
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ISO 19111:2003(E)
4.27
polar coordinate system
coordinate system in which position is specified by distance and direction from the origin
NOTE In three dimensions also called spherical coordinate system.
4.28
prime meridian
zero meridian
meridian from which the longitudes of other meridians are quantified
4.29
projected coordinate system
two-dimensional coordinate system resulting from a map projection
4.30
semi-major axis
a
longest radius of an ellipsoid
NOTE For an ellipsoid representing the Earth, it is the radius of the equator.
4.31
semi-minor axis
b
shortest radius of an ellipsoid
NOTE For an ellipsoid representing the Earth, it is the distance from the centre of the ellipsoid to either pole.
4.32
spatial reference
description of position in the real world
NOTE This may take the form of a label, code or set of coordinates.
4.33
vertical datum
datum describing the relation of gravity-related heights to the Earth
NOTE In most cases the vertical datum will be related to a defined mean sea level based on water level observations
over a long time period. Ellipsoidal heights are treated as related to a three-dimensional ellipsoidal coordinate system
referenced to a geodetic datum. Vertical datums include sounding datums (used for hydrographic purposes), in which
case the heights may be negative heights or depths.
5 Conventions
5.1 Symbols and abbreviated terms
a semi-major axis
b semi-minor axis
CCRS Compound coordinate reference system
E easting
h ellipsoidal height
N northing
SC Spatial referencing by Coordinates
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ISO 19111:2003(E)
SI le Système International d’unités
UML Unified Modeling Language
λ geodetic longitude
ϕ geodetic latitude
x, y, z Cartesian coordinates in a geodetic datum
i, j, k Cartesian coordinates in a engineering datum
r, Ω, θ spherical polar coordinates
5.2 UML notation
The diagrams that appear in this International Standard are presented using the Unified Modeling Language
(UML) static structure diagram with the ISO Interface Definition Language (IDL) basic type definitions and the
UML Object Constraint Language (OCL) as the conceptual schema language. The UML notations used in this
International Standard are described in Figure 1.
Figure 1 — UML notation
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ISO 19111:2003(E)
6 Definition of the conceptual schema for coordinate reference systems
6.1 Introduction
Location or position on or near the Earth's surface may be described using coordinates. Coordinates are
unambiguous only when the coordinate reference system to which those coordinates are related has been
fully defined. Each position shall be described by a set of coordinates in a coordinate reference system.
Coordinates supplied in a dataset shall belong to the same coordinate reference system. A description of this
coordinate reference system shall be supplied with the dataset. Coordinate data shall be accompanied by
information sufficient to make the coordinates unambiguous. This information varies by coordinate system
type and datum type.
In the clauses below, attributes are given a requirement status:
Requirement Definition Comment
M mandatory This attribute shall be supplied.
C conditional This attribute shall be supplied if the condition (given in the attribute
description) is true. It may be supplied if the condition is false.
O optional This attribute may be supplied.
The Maximum Occurrence column in the following tables indicates the maximum number of occurrences of
attribute values that are permissible, with N indicating no upper limit. The conceptual schema for describing
coordinate reference systems is modelled with the Unified Modeling Language (UML) in Annex B. In case of
inconsistency between the metadata textual description and the UML model (re: Annex B), the textual
description shall prevail. The basic data types are defined in ISO/TS 19103.
6.2 Coordinate reference system
6.2.1 Type of coordinate reference system
A coordinate reference system may be either single or compound. A single coordinate reference system is
defined in 6.2.2 and a compound coordinate reference system is defined in 6.2.3. The requirements for
describing the type of coordinate reference system shall be in accordance with Table 1.
Table 1 — Requirements for describing the type of coordinate reference system
Element name UML Data type Obligation Maximum Description
identifier occurrence
Coordinate reference typeCode SC_TypeCode M 1 Code denoting the type of coordinate
system type code reference system:
1 — a single coordinate reference
system
2 — a compound coordinate reference
system
Coordinate reference remarks CharacterString O 1 Comments on the coordinate
system remarks reference system including source
information.
To determine whether the coordinate reference system is compound or single, decision tree 1 in Annex C may
be used (see Figure C.1).
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ISO 19111:2003(E)
6.2.2 Single coordinate reference system
A position of a feature can be given by a set of coordinates. Coordinates are unambiguous if the coordinate
reference system to which those coordinates are related has been fully defined.
A coordinate reference system is realized by a set of coordinates. The realization is sometimes known as a
reference frame.
A coordinate reference system shall be defined by one datum and by one coordinate system; see Figure 2.
Figure 2 — Coordinate reference system
For the purposes of this International Standard, a coordinate reference system shall not change with time.
When a reference frame changes with time, a new datum and coordinate reference system shall be created,
with date of realization of the datum and coordinate reference system included in their names or identifiers.
The requirements for describing a coordinate reference system shall be in accordance with Table 2.
Table 2 — Requirements for describing a coordinate reference system
Element name UML Data type Obligation Maximum Description
identifier occurrence
Coordinate reference CRSID RS_Identifier M 1 Identifier of the coordinate reference
system identifier system.
Coordinate reference alias CharacterString O N Alternative name or identifier by which
system alias this coordinate reference system is
known.
Coordinate reference validArea EX_Extent O 1 Area for which the coordinate
system valid area reference system is valid.
Coordinate reference scope CharacterString O N Application for which the coordinate
system scope reference system is valid.
6.2.3 Compound coordinate reference system
The horizontal and vertical components of a description of position in three dimensions may sometimes come
from different coordinate reference systems rather than through a single three-dimensional coordinate
reference system. This is always the case for positions where vertical coordinates are related to mean sea
level. This shall be handled through a compound coordinate reference system (CCRS) which identifies the two
coordinate reference systems utilized, see Figure 3. Vertical datum and gravity-related height are an example
of a datum and coordinate system for coordinate reference system 2.
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ISO 19111:2003(E)
Figure 3 — Compound coordinate reference system
The requirements for describing a compound coordinate reference system shall be in accordance with Table 3.
Each of the two coordinate reference systems shall then be described in the normal way.
The compound coordinate reference system identifier may be a concatenation of the coordinate reference
system identifiers for the component coordinate reference systems.
Table 3 — Requirements for describing a compound coordinate reference system
Element name UML Data type Obligation Maximum Description
identifier occurrence
Compound coordinate CCRSID RS_Identifier O 1 Identifier of the compound coordinate
reference system reference system.
identifier
Compound coordinate alias CharacterString O N Alternative name or identifier by which
reference system alias this compound coordinate reference
system is known.
Compound coordinate validArea EX_Extent O 1 Area for which the compound
reference system valid coordinate reference system is valid.
area
Compound coordinate scope CharacterString O N Application for which the compound
reference system coordinate reference system is valid.
scope
6.3 Datum
6.3.1 Types of datums
A datum is geodetic, vertical or engineering. A geodetic datum gives the relationship of a coordinate system to
the Earth and is used as the basis for two- or three-dimensional systems. In most cases, it shall require an
ellipsoid definition. A vertical datum gives the relationship of gravity-related heights to a surface known as the
geoid. The geoid is a surface close to mean sea level. In this International Standard, a datum shall be
engineering if it is neither geodetic nor vertical.
For geographic information purposes it is necessary to identify a datum, but the definition of the datum itself is
optional.
If the type of coordinate reference system is not known, decision tree 2 in Annex C may be used in the
determination of the datum type (see Figure C.2).
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ISO 19111:2003(E)
6.3.2 Datum description
If a coordinate reference system citation is not supplied, then a datum description in accordance with Table 4
shall be supplied.
Table 4 — Requirements for describing a datum
Element name UML Data type Obligation Maximum Description
identifier occurrence
Datum identifier datumID RS_Identifier M 1 Identifier of the datum.
Datum alias alias CharacterString O N Alternative name or names by which
this datum is known.
Datum type type CharacterString O 1 Type of datum. Valid values are:
— geodetic,
— vertical, or
— engineering
Datum anchor point point CharacterString O 1 Description including coordinates of the
point or points used to anchor the
datum to the Earth.
Datum realization realization Date O 1 Epoch of realization of the datum.
epoch Epoch
Datum valid area validArea EX_Extent O 1 Area for which the datum is valid.
Datum scope scope CharacterString O N Application for which the datum is valid.
Datum remarks remarks CharacterString O 1 Comments on the datum including
source information.
When the datum type is geodetic, then certain prime meridian and ellipsoid attributes as described below shall
be mandatory regardless of whether a value for datum type has been provided or not.
6.3.3 Prime meridian
A p
...
SLOVENSKI STANDARD
SIST ISO 19111:2003
01-november-2003
Geografske informacije - Lociranje s koordinatami
Geographic information -- Spatial referencing by coordinates
Information géographique -- Système de références spatiales par coordonnées
Ta slovenski standard je istoveten z: ISO 19111:2003
ICS:
07.040 Astronomija. Geodezija. Astronomy. Geodesy.
Geografija Geography
35.240.70 Uporabniške rešitve IT v IT applications in science
znanosti
SIST ISO 19111:2003 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 19111:2003
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SIST ISO 19111:2003
INTERNATIONAL ISO
STANDARD 19111
First edition
2003-02-15
Geographic information — Spatial
referencing by coordinates
Information géographique — Système de références spatiales par
coordonnées
Reference number
ISO 19111:2003(E)
©
ISO 2003
---------------------- Page: 3 ----------------------
SIST ISO 19111:2003
ISO 19111:2003(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 2003
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 2003 — All rights reserved
---------------------- Page: 4 ----------------------
SIST ISO 19111:2003
ISO 19111:2003(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Conformance requirements . 1
3 Normative references . 1
4 Terms and definitions. 1
5 Conventions . 5
5.1 Symbols and abbreviated terms. 5
5.2 UML notation . 6
6 Definition of the conceptual schema for coordinate reference systems . 7
6.1 Introduction . 7
6.2 Coordinate reference system. 7
6.2.1 Type of coordinate reference system . 7
6.2.2 Single coordinate reference system . 8
6.2.3 Compound coordinate reference system. 8
6.3 Datum . 9
6.3.1 Types of datums. 9
6.3.2 Datum description. 10
6.3.3 Prime meridian . 10
6.3.4 Ellipsoid . 11
6.4 Coordinate system. 11
6.5 Coordinate operation — coordinate conversion and coordinate transformation. 12
6.5.1 General. 12
6.5.2 Coordinate conversion (including map projection) . 13
6.5.3 Coordinate transformation. 14
6.5.4 Requirements for describing a coordinate operation. 14
6.5.5 Concatenated coordinate operation . 16
6.6 Citations. 17
6.7 Accuracy and precision of coordinates, coordinate operations, and parameters. 18
6.8 Attributes to describe a coordinate reference system. 19
Annex A (normative) Conformance . 22
Annex B (normative) UML schemas . 24
Annex C (informative) Decision trees. 27
Annex D (informative) Geodetic relationships. 29
Annex E (informative) Examples. 35
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SIST ISO 19111:2003
ISO 19111:2003(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 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics.
iv © ISO 2003 — All rights reserved
---------------------- Page: 6 ----------------------
SIST ISO 19111:2003
ISO 19111:2003(E)
Introduction
Geographic information contains spatial references which relate the features represented in the data to
positions in the real world. Spatial references fall into two categories:
those using coordinates;
those based on geographic identifiers.
This International Standard deals only with spatial referencing by coordinates. Spatial referencing by
geographic identifiers is the subject of ISO 19112, Geographic information ― Spatial referencing by
geographic identifiers.
Coordinates are unambiguous only when the coordinate reference system to which those coordinates are
related has been fully defined. A coordinate reference system is a coordinate system which has a reference to
the Earth. This International Standard describes the elements that are necessary to define fully various types
of coordinate systems and coordinate reference systems applicable to geographic information. The subset of
elements required is partially dependent upon the type of coordinates. This International Standard also
includes optional fields to allow for the inclusion of non-essential coordinate reference system information. The
elements are intended to be both machine and human readable. A set of coordinates on the same coordinate
reference system requires one coordinate reference system description.
In addition to describing a coordinate reference system, this International Standard provides for the
description of a coordinate transformation or coordinate conversion between two different coordinate
reference systems. With such information, geographic data referred to different coordinate reference systems
can be merged together for integrated manipulation. Alternatively, an audit trail of coordinate reference system
manipulations can be maintained.
© ISO 2003 — All rights reserved v
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SIST ISO 19111:2003
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SIST ISO 19111:2003
INTERNATIONAL STANDARD ISO 19111:2003(E)
Geographic information — Spatial referencing by coordinates
1 Scope
This International Standard defines the conceptual schema for the description of spatial referencing by
coordinates. It describes the minimum data required to define one-, two- and three-dimensional coordinate
reference systems. It allows additional descriptive information to be provided. It also describes the information
required to change coordinate values from one coordinate reference system to another.
This International Standard is applicable to producers and users of geographic information. Although it is
applicable to digital geographic data, its principles can be extended to many other forms of geographic data
such as maps, charts, and text documents.
2 Conformance requirements
This International Standard defines two classes of conformance, Class A for conformance of coordinate
reference systems and Class B for coordinate operations between two coordinate reference systems. Any
coordinate reference system claiming conformance to this International Standard shall satisfy the
requirements given in Annex A, Clause A.1. Any coordinate operation claiming conformance to this
International Standard shall satisfy the requirements given in Annex A, Clause A.2.
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 1000, SI units and recommendations for use of their multiples and of certain other units
1)
ISO/TS 19103:— , Geographic information — Conceptual schema language
ISO 19113:2002, Geographic information — Quality principles
1)
ISO 19114:— , Geographic information — Quality evaluation procedures
4 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
4.1
Cartesian coordinate system
coordinate system which gives the position of points relative to n mutually perpendicular axes
1)
To be published.
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NOTE n is 1, 2 or 3 for the purposes of this International Standard.
4.2
compound coordinate reference system
coordinate reference system using two other independent coordinate reference systems to describe a position
EXAMPLE One coordinate reference system based on a two- or three-dimensional coordinate system and the other
coordinate reference system based on a gravity-related height system.
4.3
coordinate
one of a sequence of n numbers designating the position of a point in n-dimensional space
NOTE 1 In a coordinate reference system, the numbers must be qualified by units.
NOTE 2 A coordinate operation is performed on coordinates in a source system resulting in coordinates in a target
system.
4.4
coordinate conversion
change of coordinates, based on a one-to-one relationship, from one coordinate system to another based
on the same datum
EXAMPLE Between geodetic and Cartesian coordinate systems or between geodetic coordinates and projected
coordinates, or change of units such as from radians to degrees or feet to metres.
NOTE A coordinate conversion uses parameters which have constant values.
4.5
coordinate operation
change of coordinates, based on a one-to-one relationship, from one coordinate reference system to
another
NOTE Supertype of coordinate transformation and coordinate conversion.
4.6
coordinate reference system
coordinate system that is related to the real world by a datum
NOTE For geodetic and vertical datums, it will be related to the Earth.
4.7
coordinate system
set of mathematical rules for specifying how coordinates are to be assigned to points
4.8
coordinate transformation
change of coordinates from one coordinate reference system to another coordinate reference system
based on a different datum through a one-to-one relationship
NOTE A coordinate transformation uses parameters which are derived empirically by a set of points with known
coordinates in both coordinate reference systems.
4.9
datum
parameter or set of parameters that serve as a reference or basis for the calculation of other parameters
NOTE A datum defines the position of the origin, the scale, and the orientation of the axes of a coordinate system.
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4.10
easting
E
distance in a coordinate system, eastwards (positive) or westwards (negative) from a north-south reference
line
4.11
ellipsoid
surface formed by the rotation of an ellipse about a main axis
NOTE In this International Standard, ellipsoids are always oblate, meaning that the axis of rotation is always the
minor axis.
4.12
ellipsoidal height
geodetic height
h
distance of a point from the ellipsoid measured along the perpendicular from the ellipsoid to this point
positive if upwards or outside of the ellipsoid
NOTE Only used as part of a three-dimensional geodetic coordinate system and never on its own.
4.13
engineering datum
local datum
datum describing the relationship of a coordinate system to a local reference
NOTE Engineering datum excludes both geodetic and vertical datums.
EXAMPLE A system for identifying relative positions within a few kilometres of the reference point.
4.14
flattening
f
ratio of the difference between the semi-major (a) and semi-minor axis (b) of an ellipsoid to the semi-major
axis: f = (a − b)/a
NOTE Sometimes inverse flattening 1/f = a/(a − b) is given instead; 1/f is also known as reciprocal flattening.
4.15
geodetic coordinate system
ellipsoidal coordinate system
coordinate system in which position is specified by geodetic latitude, geodetic longitude and (in the three-
dimensional case) ellipsoidal height
4.16
geodetic datum
datum describing the relationship of a coordinate system to the Earth
NOTE In most cases, the geodetic datum includes an ellipsoid definition.
4.17
geodetic latitude
ellipsoidal latitude
ϕ
angle from the equatorial plane to the perpendicular to the ellipsoid through a given point, northwards treated
as positive
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4.18
geodetic longitude
ellipsoidal longitude
λ
angle from the prime meridian plane to the meridian plane of a given point, eastward treated as positive
4.19
geoid
level surface which best fits mean sea level either locally or globally
NOTE “Level surface” means an equipotential surface of the Earth’s gravity field which is everywhere perpendicular
to the direction of gravity.
4.20
gravity-related height
H
height dependent on the Earth’s gravity field
NOTE In particular, orthometric height or normal height, which are both approximations of the distance of a point
above the mean sea level.
4.21
Greenwich meridian
meridian that passes through the position of the Airy Transit Circle at the Royal Observatory Greenwich,
United Kingdom
NOTE Most geodetic datums use the Greenwich meridian as the prime meridian. Its precise position differs slightly
between different datums.
4.22
height
h, H
distance of a point from a chosen reference surface along a line perpendicular to that surface
NOTE 1 See ellipsoidal height and gravity-related height.
NOTE 2 Height of a point outside the surface treated as positive; negative height is also called depth.
4.23
map projection
coordinate conversion from a geodetic coordinate system to a plane
4.24
mean sea level
average level of the surface of the sea over all stages of tide and seasonal variations
NOTE Mean sea level in a local context normally means mean sea level for the region calculated from observations
at one or more points over a given period of time. Mean sea level in a global context differs from a global geoid by not
more than 2 m.
4.25
meridian
intersection of an ellipsoid by a plane containing the semi-minor axis of the ellipsoid
NOTE This term is often used for the pole-to-pole arc rather than the complete closed figure.
4.26
northing
N
distance in a coordinate system, northwards (positive) or southwards (negative) from an east-west reference
line
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4.27
polar coordinate system
coordinate system in which position is specified by distance and direction from the origin
NOTE In three dimensions also called spherical coordinate system.
4.28
prime meridian
zero meridian
meridian from which the longitudes of other meridians are quantified
4.29
projected coordinate system
two-dimensional coordinate system resulting from a map projection
4.30
semi-major axis
a
longest radius of an ellipsoid
NOTE For an ellipsoid representing the Earth, it is the radius of the equator.
4.31
semi-minor axis
b
shortest radius of an ellipsoid
NOTE For an ellipsoid representing the Earth, it is the distance from the centre of the ellipsoid to either pole.
4.32
spatial reference
description of position in the real world
NOTE This may take the form of a label, code or set of coordinates.
4.33
vertical datum
datum describing the relation of gravity-related heights to the Earth
NOTE In most cases the vertical datum will be related to a defined mean sea level based on water level observations
over a long time period. Ellipsoidal heights are treated as related to a three-dimensional ellipsoidal coordinate system
referenced to a geodetic datum. Vertical datums include sounding datums (used for hydrographic purposes), in which
case the heights may be negative heights or depths.
5 Conventions
5.1 Symbols and abbreviated terms
a semi-major axis
b semi-minor axis
CCRS Compound coordinate reference system
E easting
h ellipsoidal height
N northing
SC Spatial referencing by Coordinates
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SI le Système International d’unités
UML Unified Modeling Language
λ geodetic longitude
ϕ geodetic latitude
x, y, z Cartesian coordinates in a geodetic datum
i, j, k Cartesian coordinates in a engineering datum
r, Ω, θ spherical polar coordinates
5.2 UML notation
The diagrams that appear in this International Standard are presented using the Unified Modeling Language
(UML) static structure diagram with the ISO Interface Definition Language (IDL) basic type definitions and the
UML Object Constraint Language (OCL) as the conceptual schema language. The UML notations used in this
International Standard are described in Figure 1.
Figure 1 — UML notation
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6 Definition of the conceptual schema for coordinate reference systems
6.1 Introduction
Location or position on or near the Earth's surface may be described using coordinates. Coordinates are
unambiguous only when the coordinate reference system to which those coordinates are related has been
fully defined. Each position shall be described by a set of coordinates in a coordinate reference system.
Coordinates supplied in a dataset shall belong to the same coordinate reference system. A description of this
coordinate reference system shall be supplied with the dataset. Coordinate data shall be accompanied by
information sufficient to make the coordinates unambiguous. This information varies by coordinate system
type and datum type.
In the clauses below, attributes are given a requirement status:
Requirement Definition Comment
M mandatory This attribute shall be supplied.
C conditional This attribute shall be supplied if the condition (given in the attribute
description) is true. It may be supplied if the condition is false.
O optional This attribute may be supplied.
The Maximum Occurrence column in the following tables indicates the maximum number of occurrences of
attribute values that are permissible, with N indicating no upper limit. The conceptual schema for describing
coordinate reference systems is modelled with the Unified Modeling Language (UML) in Annex B. In case of
inconsistency between the metadata textual description and the UML model (re: Annex B), the textual
description shall prevail. The basic data types are defined in ISO/TS 19103.
6.2 Coordinate reference system
6.2.1 Type of coordinate reference system
A coordinate reference system may be either single or compound. A single coordinate reference system is
defined in 6.2.2 and a compound coordinate reference system is defined in 6.2.3. The requirements for
describing the type of coordinate reference system shall be in accordance with Table 1.
Table 1 — Requirements for describing the type of coordinate reference system
Element name UML Data type Obligation Maximum Description
identifier occurrence
Coordinate reference typeCode SC_TypeCode M 1 Code denoting the type of coordinate
system type code reference system:
1 — a single coordinate reference
system
2 — a compound coordinate reference
system
Coordinate reference remarks CharacterString O 1 Comments on the coordinate
system remarks reference system including source
information.
To determine whether the coordinate reference system is compound or single, decision tree 1 in Annex C may
be used (see Figure C.1).
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6.2.2 Single coordinate reference system
A position of a feature can be given by a set of coordinates. Coordinates are unambiguous if the coordinate
reference system to which those coordinates are related has been fully defined.
A coordinate reference system is realized by a set of coordinates. The realization is sometimes known as a
reference frame.
A coordinate reference system shall be defined by one datum and by one coordinate system; see Figure 2.
Figure 2 — Coordinate reference system
For the purposes of this International Standard, a coordinate reference system shall not change with time.
When a reference frame changes with time, a new datum and coordinate reference system shall be created,
with date of realization of the datum and coordinate reference system included in their names or identifiers.
The requirements for describing a coordinate reference system shall be in accordance with Table 2.
Table 2 — Requirements for describing a coordinate reference system
Element name UML Data type Obligation Maximum Description
identifier occurrence
Coordinate reference CRSID RS_Identifier M 1 Identifier of the coordinate reference
system identifier system.
Coordinate reference alias CharacterString O N Alternative name or identifier by which
system alias this coordinate reference system is
known.
Coordinate reference validArea EX_Extent O 1 Area for which the coordinate
system valid area reference system is valid.
Coordinate reference scope CharacterString O N Application for which the coordinate
system scope reference system is valid.
6.2.3 Compound coordinate reference system
The horizontal and vertical components of a description of position in three dimensions may sometimes come
from different coordinate reference systems rather than through a single three-dimensional coordinate
reference system. This is always the case for positions where vertical coordinates are related to mean sea
level. This shall be handled through a compound coordinate reference system (CCRS) which identifies the two
coordinate reference systems utilized, see Figure 3. Vertical datum and gravity-related height are an example
of a datum and coordinate system for coordinate reference system 2.
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Figure 3 — Compound coordinate reference system
The requirements for describing a compound coordinate reference system shall be in accordance with Table 3.
Each of the two coordinate reference systems shall then be described in the normal way.
The compound coordinate reference system identifier may be a concatenation of the coordinate reference
system identifiers for the component coordinate reference systems.
Table 3 — Requirements for describing a compound coordinate reference system
Element name UML Data type Obligation Maximum Description
identifier occurrence
Compound coordinate CCRSID RS_Identifier O 1 Identifier of the compound coordinate
reference system reference system.
identifier
Compound coordinate alias CharacterString O N Alternative name or identifier by which
reference system alias this compound coordinate reference
system is known.
Compound coordinate validArea EX_Extent O 1 Area for which the compound
reference system valid coordinate reference system is valid.
area
Compound coordinate scope CharacterString O N Application for which the compound
reference system coordinate reference system is valid.
scope
6.3 Datum
6.3.1 Types of datums
A datum is geodetic, vertical or engineering. A geodetic datum gives the relationship of a coordinate system to
the Earth and is used as the basis for two- or three-dimensional systems. In most cases, it shall require an
ellipsoid definition. A vertical datum gives the relationship of gravity-related heights to a surface known as the
geoid. The geoid is a surface close to mean sea level. In this International Standard, a datum shall be
engineering if it is neither geodetic nor vertical.
For geographic information purposes it is necessary to identify a datum, but the definition of the datum itself is
optional.
If the type of coordinate reference system is not known, decision tree 2 in Annex C may be used in the
determination of the datum type (see Figure C.2).
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6.3.2 Datum description
If a coordinate reference system citation is not supplied, then a datum description in accordance with Table 4
shall b
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