ISO 19162:2015

Geographic information - Well-known text representation of coordinate reference systems

ISO 19162:2015 defines the structure and content of a text string implementation of the abstract model for coordinate reference systems described in ISO 19111:2007 and ISO 19111-2:2009. The string defines frequently needed types of coordinate reference systems and coordinate operations in a self-contained form that is easily readable by machines and by humans. The essence is its simplicity; as a consequence there are some constraints upon the more open content allowed in ISO 19111:2007. To retain simplicity in the well-known text (WKT) description of coordinate reference systems and coordinate operations, the scope of this International Standard excludes parameter grouping and pass-through coordinate operations. The text string provides a means for humans and machines to correctly and unambiguously interpret and utilise a coordinate reference system definition with look-ups or cross references only to define coordinate operation mathematics. Because it omits metadata about the source of the data and may omit metadata about the applicability of the information, the WKT string is not suitable for the storage of definitions of coordinate reference systems or coordinate operations.

Information géographique — Représentation textuelle bien lisible de systèmes de référence par coordonnées

Geografske informacije - Koordinatni referenčni sistemi, podani kot tekst

Ta mednarodni standard določa strukturo in vsebino implementacije besedilnih nizov abstraktnega modela za koordinatne referenčne sisteme, opisane v standardih ISO 19111:2007 in ISO 19111-2:2009. Niz določa pogosto potrebne vrste koordinatnih referenčnih sistemov in koordinatnih operacij v samostojni obliki, ki jo stroji in ljudje zlahka preberejo. Bistvo je njegova preprostost; posledično za bolj odprto vsebino, ki jo omogoča standard ISO 19111:2007, veljajo nekatere omejitve. Za ohranjanje preprostosti opisa koordinatnih referenčnih sistemov in koordinatnih operacij, podanih kot besedilo (WKT), področje uporabe tega standarda ne vključuje razvrščanja parametrov in prehodnih koordinatnih operacij.
Besedilni niz omogoča ljudem in strojem pravilno in nedvoumno interpretacijo in uporabo definicije koordinatnega referenčnega sistema s poizvedbami ali sklici samo za opredelitev matematike koordinatnih operacij. Ker izpušča metapodatke o viru podatkov in morda izpušča metapodatke o uporabnosti informacij, niz WKT ni primeren za shranjevanje definicij koordinatnih referenčnih sistemov ali koordinatnih operacij.

General Information

• Status: Withdrawn
• Publication Date: 13-Aug-2015
• Withdrawal Date: 13-Aug-2015
• 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
• Start Date: 11-Jul-2019
• Completion Date: 13-Dec-2025
• Ref Project: SIST ISO 19162:2017 - Geographic information -- Well-known text representation of coordinate reference systems

Relations

• Revised: ISO 19162:2019 - Geographic information - Well-known text representation of coordinate reference systems
• Effective Date: 23-Apr-2020

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 19162
First edition
2015-08-15
Geographic information — Well-
known text representation of
coordinate reference systems
Information géographique — Représentation textuelle bien lisible de
systèmes de référence par coordonnées
Reference number
©
ISO 2015
© ISO 2015, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2015 – All rights reserved

Contents Page
Foreword . vii
Introduction . viii
1 Scope . 1
2 Conformance requirements . 1
3 Normative references . 2
4 Definitions and abbreviations . 2
4.1 Definitions . 2
4.2 Abbreviations . 8
5 Backus-Naur Form notation and syntax . 8
6 WKT string form . 9
6.1 Overview . 9
6.2 Encoding . 9
6.3 Characters used in WKT . 9
6.3.1 Basic characters . 9
6.3.2 Numbers . 11
6.3.3 Date and time . 11
6.3.4 CRS WKT characters . 12
6.3.5 Double quote . 13
6.4 Delimiter . 13
6.5 Case sensitivity . 13
6.6 Reserved keywords . 13
6.7 Backward compatibility . 15
7 WKT representation of common attributes . 15
7.1 Introduction . 15
7.2 Name . 15
7.3 Scope, extent, identifier and remark . 15
7.3.1 Introduction . 15
7.3.2 Scope . 16
7.3.3 Extent . 16
7.3.4 Identifier . 18
7.3.5 Remark. 19
7.4 Unit and unit conversion factor . 20
7.5 Coordinate system . 21
7.5.1 Syntax . 21
7.5.2 Coordinate system type and dimension . 22
7.5.3 Axis name and abbreviation . 23
7.5.4 Axis direction . 24
7.5.5 Axis order . 25
7.5.6 Axis unit and coordinate system unit . 25
7.5.7 Examples of WKT describing coordinate systems . 26
8 WKT representation of geodetic coordinate reference systems . 28
8.1 Overview . 28
8.2 Geodetic datum . 28
8.2.1 Ellipsoid . 28
8.2.2 Prime meridian . 29
8.2.3 Datum . 30
8.3 Coordinate systems for geodetic CRSs . 31
8.4 Examples of WKT describing a geodetic CRS . 31
9 WKT representation of projected CRSs .32
9.1 Overview .32
9.2 Base CRS .32
9.2.1 General .32
9.2.2 Ellipsoidal CS unit .33
9.3 Map projection .33
9.3.1 Introduction .33
9.3.2 Map projection name and identifier .34
9.3.3 Map projection method .34
9.3.4 Map projection parameter .35
9.4 Coordinate systems for projected CRSs .35
9.5 Examples of WKT describing a projected CRS .35
10 WKT representation of vertical CRSs .36
10.1 Overview .36
10.2 Vertical datum .37
10.3 Vertical coordinate system .37
10.4 Example of WKT describing a vertical CRS .37
11 WKT representation of engineering CRSs .37
11.1 Overview .37
11.2 Engineering datum .38
11.3 Coordinate systems for engineering CRSs .38
11.4 Examples of WKT describing an engineering CRS .38
12 WKT representation of image CRSs .39
12.1 Overview .39
12.2 Image datum .39
12.3 Coordinate systems for image CRSs.40
13 WKT representation of parametric CRSs .40
13.1 Overview .40
13.2 Parametric datum.40
13.3 Parametric coordinate system .40
13.4 Example of WKT describing a parametric CRS .41
14 WKT representation of temporal CRSs .41
14.1 Overview .41
14.2 Temporal datum .41
14.3 Temporal coordinate system .41
14.4 Example of WKT describing a temporal CRS .41
15 WKT representation of derived CRSs .42
15.1 Overview .42
15.2 Derived CRS conversion .42
15.2.1 Introduction .42
15.2.2 Derived CRS conversion method .43
15.2.3 Derived CRS conversion parameter .43
15.2.4 Derived CRS conversion parameter file .44
15.2.5 Derived CRS conversion example .44
15.3 Derived CRS of type geodetic .44
15.3.1 Representation .44
15.3.2 Example of WKT describing a derived geodetic CRS .45
15.4 Derived CRS of type vertical .45
15.5 Derived CRS of type engineering .46
15.5.1 Representation .46
15.5.2 Examples of WKT describing a derived engineering CRS .47
15.6 Derived CRS of type parametric .48
15.7 Derived CRS of type temporal .48
16 WKT representation of compound coordinate reference systems .49
16.1 Overview .49
16.2 Examples of WKT describing a compound CRS .50
iv © ISO 2015 – All rights reserved

17 WKT representation of coordinate operations . 51
17.1 Coordinate operations . 51
17.2 Coordinate operation components . 51
17.2.1 Source and target CRS . 51
17.2.2 Coordinate operation name and identifier . 51
17.2.3 Coordinate operation method . 52
17.2.4 Coordinate operation parameter . 52
17.2.5 Coordinate operation parameter file . 53
17.2.6 Interpolation CRS . 53
17.2.7 Coordinate operation accuracy . 53
17.2.8 Other coordinate operation attributes . 53
17.3 Examples of WKT describing a coordinate operation . 54
18 WKT representation of CRS and coordinate operation couplets . 55
18.1 Bound CRS . 55
18.2 Bound CRS components . 56
18.2.1 Abridged coordinate transformation . 56
18.2.2 Coordinate operation method in abridged coordinate transformations . 56
18.2.3 Abridged coordinate transformation parameter . 57
18.2.4 Coordinate operation parameter file . 57
18.3 Examples of WKT describing a Bound CRS . 58
Annex A (normative) Abstract test suite . 59
A.1 Conformance of a WKT string describing a geodetic CRS . 59
A.2 Conformance of a WKT string describing a projected CRS . 59
A.3 Conformance of a WKT string describing a vertical CRS . 60
A.4 Conformance of a WKT string describing an engineering CRS . 60
A.5 Conformance of a WKT string describing an image CRS . 61
A.6 Conformance of a WKT string describing a parametric CRS . 61
A.7 Conformance of a WKT string describing a temporal CRS . 62
A.8 Conformance of a WKT string describing a derived CRS . 62
A.9 Conformance of a WKT string describing a compound CRS . 63
A.10 Conformance of a WKT string describing a coordinate operation . 63
A.11 Conformance of a WKT string describing a Bound CRS . 64
Annex B (informative) Recommended practice for implementation . 65
B.1 Introduction . 65
B.2 Keywords . 65
B.2.1 Keyword case sensitivity . 65
B.2.2 Alternative keywords . 65
B.2.3 Handling of unrecognised keywords . 65
B.3 Characters . 65
B.3.1 Handling of unrecognised characters . 65
B.3.2 String length . 65
B.4 White space . 66
B.4.1 Insertion of white space. 66
B.4.2 Parsing of white space outside of quoted text . 66
B.4.3 Parsing of white space within quoted text . 66
B.5 Identifiers . 66
B.5.1 Use of identifier . 66
B.5.2 Using names to interpret identity . 66
B.6 Numbers . 67
B.6.1 Precision . 67
B.6.2 Defining parameters for a sphere . 67
B.6.3 Implied units . 67
B.7 Attribute order . 67
B.8 Version of CRS WKT . 67
Annex C (informative) Mapping of concepts from previous versions of CRS WKT . 68
C.1 BNF . 68
C.2 Backward compatibility of CRS common attributes . 68
C.2.1 Name . 68
C.2.2 ID (Authority) .68
C.3 Backward compatibility of coordinate reference system components .69
C.3.1 Ellipsoid .69
C.3.2 Prime meridian .69
C.3.3 Datum .69
C.3.4 Map projection .70
C.3.5 Coordinate system .71
C.4 Backward compatibility of coordinate reference systems .72
C.4.1 Geodetic CRS .72
C.4.2 Projected CRS .73
C.4.3 Vertical CRS and engineering (local) CRS .73
C.4.4 Compound CRS .74
C.4.5 Fitted CS .74
C.5 Backward compatibility of coordinate operations .74
C.6 Mapping of tokens and keywords from previous versions of CRS WKT to this
International Standard .75
Annex D (informative) Triaxial ellipsoid .79
Annex E (informative) Identifiers for coordinate operation methods and parameters .80
E.1 Introduction .80
E.2 Map projection methods .81
E.3 Map projection parameters .81
E.4 Coordinate transformation methods .83
E.5 Coordinate transformation parameters .83
Bibliography .85

vi © ISO 2015 – 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
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.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of
ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2. www.iso.org/directives
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. Details of any patent
rights identified during the development of the document will be in the Introduction and/or on the ISO list of
patent declarations received. www.iso.org/patents
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment,
as well as information about ISO's adherence to the WTO principles in the Technical Barriers to Trade (TBT)
see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 211, jointly with the Open Geospatial Consortium
(OGC).
Introduction
Well-known Text (WKT) offers a compact machine- and human-readable representation of geometric objects.
WKT may also be used for succinctly describing the critical elements of coordinate reference system (CRS)
definitions.
WKT was described in the Open Geospatial Consortium implementation specifications 99-036 through 06-
103r4 and International Standard ISO 19125-1:2004, “Geographic information – Simple feature access – Part
1: Common architecture”. The WKT representation of coordinate reference systems was subsequently
extended in Open Geospatial Consortium implementation specification 01-009 "Coordinate Transformation
Services" and this extension was later adopted in the Open Geospatial Consortium GeoAPI 3.0
implementation standard 09-083r3 and GeoPackage 1.0 implementation standard 12-128r10. The WKT
representation of coordinate reference systems as defined in ISO 19125-1:2004 and OGC specification 01-
009 is inconsistent with the terminology and technical provisions of ISO 19111:2007 and OGC Abstract
Specification topic 2 (08-015r2), “Geographic information – Spatial referencing by coordinates”.
This International Standard provides an updated version of WKT representation of coordinate reference
systems that follows the provisions of ISO 19111:2007 and ISO 19111-2:2009. It extends earlier WKT to allow
for the description of coordinate operations. This International Standard defines the structure and content of
well-known text strings. It does not prescribe how implementations should read or write these strings.

viii © ISO 2015 – All rights reserved

INTERNATIONAL STANDARD ISO 19162:2015(E)

Geographic information — Well-known text representation of
coordinate reference systems
1 Scope
This International Standard defines the structure and content of a text string implementation of the abstract
model for coordinate reference systems described in ISO 19111:2007 and ISO 19111-2:2009. The string
defines frequently needed types of coordinate reference systems and coordinate operations in a self-
contained form that is easily readable by machines and by humans. The essence is its simplicity; as a
consequence there are some constraints upon the more open content allowed in ISO 19111:2007. To retain
simplicity in the well-known text (WKT) description of coordinate reference systems and coordinate operations,
the scope of this International Standard excludes parameter grouping and pass-through coordinate operations.
The text string provides a means for humans and machines to correctly and unambiguously interpret and
utilise a coordinate reference system definition with look-ups or cross references only to define coordinate
operation mathematics. Because it omits metadata about the source of the data and may omit metadata about
the applicability of the information, the WKT string is not suitable for the storage of definitions of coordinate
reference systems or coordinate operations.
2 Conformance requirements
This International Standard defines eleven classes of conformance (see Annex A) in three groups:
1) Any WKT string claiming conformance of coordinate reference system definition shall satisfy the
requirements in Annex A as shown in Table 1.
Table 1 — Conformance requirements for coordinate reference systems
Conformance
Coordinate reference system
requirements
type
given in
geodetic A.1
projected A.2
vertical A.3
engineering A.4
image A.5
parametric A.6
temporal A.7
derived geodetic
derived vertical
derived engineering A.8
derived parametric
derived temporal
compound A.9
2) Any WKT string claiming conformance of coordinate operation definition shall satisfy the
requirements given in A.10.
3) Any WKT string claiming conformance of coordinate transformation bound to a coordinate reference
system definition shall satisfy the requirements given in A.11.
Conformance is applicable to the WKT string. Recommended practices for implementations writing or reading
coordinate reference system WKT strings are given in Annex B.
3 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 8601:2004, Data elements and interchange formats — Information interchange — Representation of
dates and times
ISO/IEC 9075-1:2011, Information technology ― Database languages ― SQL ― Part 1: Framework
(SQL/Framework)
ISO/IEC 9075-2:2011, Information technology ― Database languages ― SQL ― Part 2: Foundation
(SQL/Foundation)
ISO/IEC 10646:2012, Information technology ― Universal Coded Character Set (UCS)
ISO 19111:2007, Geographic information ― Spatial referencing by coordinates
ISO 19111-2:2009, Geographic information ― Spatial referencing by coordinates ― Part 2: Extension for
parametric values
4 Definitions and abbreviations
4.1 Definitions
For the purposes of this document, the following terms and definitions apply.
4.1.1
affine coordinate system
coordinate system (4.1.8) in Euclidean space with straight axes that are not necessarily mutually
perpendicular
[SOURCE: ISO 19111:2007, 4.1]
4.1.2
bearing
horizontal angle at a point relative to a specified direction
Note 1 to entry: The direction is usually specified to be north. In some communities the term bearing refers specifically
to grid north and directions relative to true north are then termed ‘azimuth’; in other communities a bearing refers
specifically to true north. In this International Standard bearing is used for any specified reference direction. The angle
may be reckoned positive clockwise or positive counter-clockwise depending upon the application.
2 © ISO 2015 – All rights reserved

4.1.3
Cartesian coordinate system
coordinate system (4.1.8) which gives the position of points relative to n mutually perpendicular axes that each
has zero curvature
Note 1 to entry: n is 2 or 3 for the purposes of this International Standard.
4.1.4
compound coordinate reference system
coordinate reference system (4.1.7) using at least two independent coordinate reference systems
Note 1 to entry: Coordinate reference systems are independent of each other if coordinate values in one cannot be
converted or transformed into coordinate values in the other.
[SOURCE: ISO 19111:2007, 4.3]
4.1.5
coordinate conversion
coordinate operation (4.1.6) in which both coordinate reference systems (4.1.7) are based on the same datum
(4.1.11)
EXAMPLE Conversion from an ellipsoidal coordinate reference system based on the WGS 84 datum to a Cartesian
coordinate reference system also based on the WGS 84 datum, or change of units such as from radians to degrees or feet
to metres.
Note 1 to entry: A coordinate conversion uses parameters which have specified values that are not determined
empirically.
[SOURCE: ISO 19111:2007, 4.6]
4.1.6
coordinate operation
change of coordinates, based on a one-to-one relationship, from one coordinate reference system (4.1.7) to
another
Note 1 to entry: Supertype of coordinate transformation (4.1.9) and coordinate conversion (4.1.5).
[SOURCE: ISO 19111:2007, 4.7]
4.1.7
coordinate reference system
coordinate system (4.1.8) that is related to an object by a datum (4.1.11)
Note 1 to entry: For geodetic and vertical datums (4.1.19, 4.1.39), the object will be the Earth.
[SOURCE: ISO 19111:2007, 4.8]
4.1.8
coordinate system
set of mathematical rules for specifying how coordinates are to be assigned to points
[SOURCE: ISO 19111:2007, 4.10]
4.1.9
coordinate transformation
coordinate operation (4.1.6) in which the two coordinate reference systems (4.1.7) are based on different
datums (4.1.11)
Note 1 to entry: A coordinate transformation uses parameters which are derived empirically by a set of points with
known coordinates in both coordinate reference systems.
[SOURCE: ISO 19111:2007, 4.11]
4.1.10
cylindrical coordinate system
three-dimensional coordinate system (4.1.8) with two distance and one angular coordinates
[SOURCE: ISO 19111:2007, 4.13]
4.1.11
datum
parameter or set of parameters that define the position of the origin, the scale, and the orientation of a
coordinate system (4.1.8)
[SOURCE: ISO 19111:2007, 4.14]
4.1.12
ellipsoid
surface formed by the rotation of an ellipse about a main axis
Note 1 to entry: In this International Standard, ellipsoids are always oblate, meaning that the axis of rotation is always
the minor axis.
[SOURCE: ISO 19111:2007, 4.17]
4.1.13
ellipsoidal coordinate system
geodetic coordinate system
coordinate system (4.1.8) in which position is specified by geodetic latitude (4.1.20), geodetic longitude
(4.1.21) and (in the three-dimensional case) ellipsoidal height (4.1.14)
[SOURCE: ISO 19111:2007, 4.18]
4.1.14
ellipsoidal height
geodetic height
h
distance of a point from the ellipsoid (4.1.12) measured along the perpendicular from the ellipsoid to this point,
positive if upwards or outside of the ellipsoid
Note 1 to entry: Only used as part of a three-dimensional ellipsoidal coordinate system (4.1.13) and never on its own.
[SOURCE: ISO 19111:2007, 4.19]
4.1.15
engineering coordinate reference system
coordinate reference system (4.1.7) based on an engineering datum (4.1.16)
EXAMPLES Local engineering and architectural grids; coordinate reference system local to a ship or an orbiting
spacecraft.
[SOURCE: ISO 19111:2007, 4.20]
4.1.16
engineering datum
local datum
datum (4.1.11) describing the relationship of a coordinate system (4.1.8) to a local reference
4 © ISO 2015 – All rights reserved

Note 1 to entry: Engineering datum excludes both geodetic and vertical datums (4.1.19, 4.1.39).
EXAMPLE A system for identifying relative positions within a few kilometres of the reference point.
[SOURCE: ISO 19111:2007, 4.21]
4.1.17
flattening
f
ratio of the difference between the semi-major axis (a) (4.1.32) and semi-minor axis (b) (4.1.33) of an ellipsoid
(4.1.12) to the semi-major axis; f = (a – b)/a
Note 1 to entry: Sometimes inverse flattening 1/f = a/(a−b) is given instead; 1/f is also known as reciprocal flattening.
[SOURCE: ISO 19111:2007, 4.22, modified – The first occurrence of the words “semi-major” have been
expanded to “semi-major axis”.]
4.1.18
geodetic coordinate reference system
coordinate reference system (4.1.7) based on a geodetic datum (4.1.19)
[SOURCE: ISO 19111:2007, 4.23]
4.1.19
geodetic datum
datum (4.1.11) describing the relationship of a two- or three-dimensional coordinate system (4.1.8) to the
Earth
[SOURCE: ISO 19111:2007, 4.24]
4.1.20
geodetic latitude
ellipsoidal latitude

angle from the equatorial plane to the perpendicular to the ellipsoid (4.1.12) through a given point, northwards
treated as positive
[SOURCE: ISO 19111:2007, 4.25]
4.1.21
geodetic longitude
ellipsoidal longitude

angle from the prime meridian (4.1.30) plane to the meridian plane of a given point, eastward treated as
positive
[SOURCE: ISO 19111:2007, 4.26]
4.1.22
image coordinate reference system
coordinate reference system (4.1.7) based on an image datum (4.1.23)
[SOURCE: ISO 19111:2007, 4.30]
4.1.23
image datum
engineering datum (4.1.16) which defines the relationship of a coordinate system (4.1.8) to an image
[SOURCE: ISO 19111:2007, 4.31]
4.1.24
linear coordinate system
one-dimensional coordinate system (4.1.8) in which a linear feature forms the axis
EXAMPLES Distances along a pipeline; depths down a deviated oil well bore.
[SOURCE: ISO 19111:2007, 4.32]
4.1.25
map projection
coordinate conversion (4.1.4) from an ellipsoidal coordinate system (4.1.13) to a plane
[SOURCE: ISO 19111:2007, 4.33]
4.1.26
parametric coordinate reference system
coordinate reference system (4.1.7) based on a parametric datum (4.1.28)
[SOURCE: ISO 19111-2:2009, 4.2]
4.1.27
parametric coordinate system
one-dimensional coordinate system (4.1.8) where the axis units are parameter values which are not inherently
spatial
[SOURCE: ISO 19111-2:2009, 4.1]
4.1.28
parametric datum
datum (4.1.11) describing the relationship of a parametric coordinate system (4.1.27) to an object
Note 1 to entry: The object is normally the Earth.
[SOURCE: ISO 19111-2:2009, 4.3]
4.1.29
polar coordinate system
two-dimensional coordinate system (4.1.8) in which position is specified by distance and direction from the
origin
Note 1 to entry: For the three-dimensional case, see spherical coordinate system (4.1.35).
[SOURCE: ISO 19111:2007, 4.37]
4.1.30
prime meridian
zero meridian
meridian from which the longitudes of other meridians are quantified
[SOURCE: ISO 19111:2007, 4.38]
4.1.31
projected coordinate reference system
coordinate reference system (4.1.7) derived from a two-dimensional geodetic coordinate reference system
(4.1.18) by applying a map projection (4.1.25)
[SOURCE: ISO 19111:2007, 4.39]
6 © ISO 2015 – All rights reserved
...

SLOVENSKI STANDARD
01-junij-2017
*HRJUDIVNHLQIRUPDFLMH.RRUGLQDWQLUHIHUHQþQLVLVWHPLSRGDQLNRWWHNVW
Geographic information -- Well-known text representation of coordinate reference
systems
Information géographique -- Représentation textuelle bien lisible de systèmes de
référence par coordonnées
Ta slovenski standard je istoveten z: ISO 19162:2015
ICS:
07.040 Astronomija. Geodezija. Astronomy. Geodesy.
Geografija Geography
35.240.70 Uporabniške rešitve IT v IT applications in science
znanosti
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

INTERNATIONAL ISO
STANDARD 19162
First edition
2015-08-15
Geographic information — Well-
known text representation of
coordinate reference systems
Information géographique — Représentation textuelle bien lisible de
systèmes de référence par coordonnées
Reference number
©
ISO 2015
© ISO 2015, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2015 – All rights reserved

Contents Page
Foreword . vii
Introduction . viii
1 Scope . 1
2 Conformance requirements . 1
3 Normative references . 2
4 Definitions and abbreviations . 2
4.1 Definitions . 2
4.2 Abbreviations . 8
5 Backus-Naur Form notation and syntax . 8
6 WKT string form . 9
6.1 Overview . 9
6.2 Encoding . 9
6.3 Characters used in WKT . 9
6.3.1 Basic characters . 9
6.3.2 Numbers . 11
6.3.3 Date and time . 11
6.3.4 CRS WKT characters . 12
6.3.5 Double quote . 13
6.4 Delimiter . 13
6.5 Case sensitivity . 13
6.6 Reserved keywords . 13
6.7 Backward compatibility . 15
7 WKT representation of common attributes . 15
7.1 Introduction . 15
7.2 Name . 15
7.3 Scope, extent, identifier and remark . 15
7.3.1 Introduction . 15
7.3.2 Scope . 16
7.3.3 Extent . 16
7.3.4 Identifier . 18
7.3.5 Remark. 19
7.4 Unit and unit conversion factor . 20
7.5 Coordinate system . 21
7.5.1 Syntax . 21
7.5.2 Coordinate system type and dimension . 22
7.5.3 Axis name and abbreviation . 23
7.5.4 Axis direction . 24
7.5.5 Axis order . 25
7.5.6 Axis unit and coordinate system unit . 25
7.5.7 Examples of WKT describing coordinate systems . 26
8 WKT representation of geodetic coordinate reference systems . 28
8.1 Overview . 28
8.2 Geodetic datum . 28
8.2.1 Ellipsoid . 28
8.2.2 Prime meridian . 29
8.2.3 Datum . 30
8.3 Coordinate systems for geodetic CRSs . 31
8.4 Examples of WKT describing a geodetic CRS . 31
9 WKT representation of projected CRSs .32
9.1 Overview .32
9.2 Base CRS .32
9.2.1 General .32
9.2.2 Ellipsoidal CS unit .33
9.3 Map projection .33
9.3.1 Introduction .33
9.3.2 Map projection name and identifier .34
9.3.3 Map projection method .34
9.3.4 Map projection parameter .35
9.4 Coordinate systems for projected CRSs .35
9.5 Examples of WKT describing a projected CRS .35
10 WKT representation of vertical CRSs .36
10.1 Overview .36
10.2 Vertical datum .37
10.3 Vertical coordinate system .37
10.4 Example of WKT describing a vertical CRS .37
11 WKT representation of engineering CRSs .37
11.1 Overview .37
11.2 Engineering datum .38
11.3 Coordinate systems for engineering CRSs .38
11.4 Examples of WKT describing an engineering CRS .38
12 WKT representation of image CRSs .39
12.1 Overview .39
12.2 Image datum .39
12.3 Coordinate systems for image CRSs.40
13 WKT representation of parametric CRSs .40
13.1 Overview .40
13.2 Parametric datum.40
13.3 Parametric coordinate system .40
13.4 Example of WKT describing a parametric CRS .41
14 WKT representation of temporal CRSs .41
14.1 Overview .41
14.2 Temporal datum .41
14.3 Temporal coordinate system .41
14.4 Example of WKT describing a temporal CRS .41
15 WKT representation of derived CRSs .42
15.1 Overview .42
15.2 Derived CRS conversion .42
15.2.1 Introduction .42
15.2.2 Derived CRS conversion method .43
15.2.3 Derived CRS conversion parameter .43
15.2.4 Derived CRS conversion parameter file .44
15.2.5 Derived CRS conversion example .44
15.3 Derived CRS of type geodetic .44
15.3.1 Representation .44
15.3.2 Example of WKT describing a derived geodetic CRS .45
15.4 Derived CRS of type vertical .45
15.5 Derived CRS of type engineering .46
15.5.1 Representation .46
15.5.2 Examples of WKT describing a derived engineering CRS .47
15.6 Derived CRS of type parametric .48
15.7 Derived CRS of type temporal .48
16 WKT representation of compound coordinate reference systems .49
16.1 Overview .49
16.2 Examples of WKT describing a compound CRS .50
iv © ISO 2015 – All rights reserved

17 WKT representation of coordinate operations . 51
17.1 Coordinate operations . 51
17.2 Coordinate operation components . 51
17.2.1 Source and target CRS . 51
17.2.2 Coordinate operation name and identifier . 51
17.2.3 Coordinate operation method . 52
17.2.4 Coordinate operation parameter . 52
17.2.5 Coordinate operation parameter file . 53
17.2.6 Interpolation CRS . 53
17.2.7 Coordinate operation accuracy . 53
17.2.8 Other coordinate operation attributes . 53
17.3 Examples of WKT describing a coordinate operation . 54
18 WKT representation of CRS and coordinate operation couplets . 55
18.1 Bound CRS . 55
18.2 Bound CRS components . 56
18.2.1 Abridged coordinate transformation . 56
18.2.2 Coordinate operation method in abridged coordinate transformations . 56
18.2.3 Abridged coordinate transformation parameter . 57
18.2.4 Coordinate operation parameter file . 57
18.3 Examples of WKT describing a Bound CRS . 58
Annex A (normative) Abstract test suite . 59
A.1 Conformance of a WKT string describing a geodetic CRS . 59
A.2 Conformance of a WKT string describing a projected CRS . 59
A.3 Conformance of a WKT string describing a vertical CRS . 60
A.4 Conformance of a WKT string describing an engineering CRS . 60
A.5 Conformance of a WKT string describing an image CRS . 61
A.6 Conformance of a WKT string describing a parametric CRS . 61
A.7 Conformance of a WKT string describing a temporal CRS . 62
A.8 Conformance of a WKT string describing a derived CRS . 62
A.9 Conformance of a WKT string describing a compound CRS . 63
A.10 Conformance of a WKT string describing a coordinate operation . 63
A.11 Conformance of a WKT string describing a Bound CRS . 64
Annex B (informative) Recommended practice for implementation . 65
B.1 Introduction . 65
B.2 Keywords . 65
B.2.1 Keyword case sensitivity . 65
B.2.2 Alternative keywords . 65
B.2.3 Handling of unrecognised keywords . 65
B.3 Characters . 65
B.3.1 Handling of unrecognised characters . 65
B.3.2 String length . 65
B.4 White space . 66
B.4.1 Insertion of white space. 66
B.4.2 Parsing of white space outside of quoted text . 66
B.4.3 Parsing of white space within quoted text . 66
B.5 Identifiers . 66
B.5.1 Use of identifier . 66
B.5.2 Using names to interpret identity . 66
B.6 Numbers . 67
B.6.1 Precision . 67
B.6.2 Defining parameters for a sphere . 67
B.6.3 Implied units . 67
B.7 Attribute order . 67
B.8 Version of CRS WKT . 67
Annex C (informative) Mapping of concepts from previous versions of CRS WKT . 68
C.1 BNF . 68
C.2 Backward compatibility of CRS common attributes . 68
C.2.1 Name . 68
C.2.2 ID (Authority) .68
C.3 Backward compatibility of coordinate reference system components .69
C.3.1 Ellipsoid .69
C.3.2 Prime meridian .69
C.3.3 Datum .69
C.3.4 Map projection .70
C.3.5 Coordinate system .71
C.4 Backward compatibility of coordinate reference systems .72
C.4.1 Geodetic CRS .72
C.4.2 Projected CRS .73
C.4.3 Vertical CRS and engineering (local) CRS .73
C.4.4 Compound CRS .74
C.4.5 Fitted CS .74
C.5 Backward compatibility of coordinate operations .74
C.6 Mapping of tokens and keywords from previous versions of CRS WKT to this
International Standard .75
Annex D (informative) Triaxial ellipsoid .79
Annex E (informative) Identifiers for coordinate operation methods and parameters .80
E.1 Introduction .80
E.2 Map projection methods .81
E.3 Map projection parameters .81
E.4 Coordinate transformation methods .83
E.5 Coordinate transformation parameters .83
Bibliography .85

vi © ISO 2015 – 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
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.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of
ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2. www.iso.org/directives
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. Details of any patent
rights identified during the development of the document will be in the Introduction and/or on the ISO list of
patent declarations received. www.iso.org/patents
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment,
as well as information about ISO's adherence to the WTO principles in the Technical Barriers to Trade (TBT)
see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 211, jointly with the Open Geospatial Consortium
(OGC).
Introduction
Well-known Text (WKT) offers a compact machine- and human-readable representation of geometric objects.
WKT may also be used for succinctly describing the critical elements of coordinate reference system (CRS)
definitions.
WKT was described in the Open Geospatial Consortium implementation specifications 99-036 through 06-
103r4 and International Standard ISO 19125-1:2004, “Geographic information – Simple feature access – Part
1: Common architecture”. The WKT representation of coordinate reference systems was subsequently
extended in Open Geospatial Consortium implementation specification 01-009 "Coordinate Transformation
Services" and this extension was later adopted in the Open Geospatial Consortium GeoAPI 3.0
implementation standard 09-083r3 and GeoPackage 1.0 implementation standard 12-128r10. The WKT
representation of coordinate reference systems as defined in ISO 19125-1:2004 and OGC specification 01-
009 is inconsistent with the terminology and technical provisions of ISO 19111:2007 and OGC Abstract
Specification topic 2 (08-015r2), “Geographic information – Spatial referencing by coordinates”.
This International Standard provides an updated version of WKT representation of coordinate reference
systems that follows the provisions of ISO 19111:2007 and ISO 19111-2:2009. It extends earlier WKT to allow
for the description of coordinate operations. This International Standard defines the structure and content of
well-known text strings. It does not prescribe how implementations should read or write these strings.

viii © ISO 2015 – All rights reserved

INTERNATIONAL STANDARD ISO 19162:2015(E)

Geographic information — Well-known text representation of
coordinate reference systems
1 Scope
This International Standard defines the structure and content of a text string implementation of the abstract
model for coordinate reference systems described in ISO 19111:2007 and ISO 19111-2:2009. The string
defines frequently needed types of coordinate reference systems and coordinate operations in a self-
contained form that is easily readable by machines and by humans. The essence is its simplicity; as a
consequence there are some constraints upon the more open content allowed in ISO 19111:2007. To retain
simplicity in the well-known text (WKT) description of coordinate reference systems and coordinate operations,
the scope of this International Standard excludes parameter grouping and pass-through coordinate operations.
The text string provides a means for humans and machines to correctly and unambiguously interpret and
utilise a coordinate reference system definition with look-ups or cross references only to define coordinate
operation mathematics. Because it omits metadata about the source of the data and may omit metadata about
the applicability of the information, the WKT string is not suitable for the storage of definitions of coordinate
reference systems or coordinate operations.
2 Conformance requirements
This International Standard defines eleven classes of conformance (see Annex A) in three groups:
1) Any WKT string claiming conformance of coordinate reference system definition shall satisfy the
requirements in Annex A as shown in Table 1.
Table 1 — Conformance requirements for coordinate reference systems
Conformance
Coordinate reference system
requirements
type
given in
geodetic A.1
projected A.2
vertical A.3
engineering A.4
image A.5
parametric A.6
temporal A.7
derived geodetic
derived vertical
derived engineering A.8
derived parametric
derived temporal
compound A.9
2) Any WKT string claiming conformance of coordinate operation definition shall satisfy the
requirements given in A.10.
3) Any WKT string claiming conformance of coordinate transformation bound to a coordinate reference
system definition shall satisfy the requirements given in A.11.
Conformance is applicable to the WKT string. Recommended practices for implementations writing or reading
coordinate reference system WKT strings are given in Annex B.
3 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 8601:2004, Data elements and interchange formats — Information interchange — Representation of
dates and times
ISO/IEC 9075-1:2011, Information technology ― Database languages ― SQL ― Part 1: Framework
(SQL/Framework)
ISO/IEC 9075-2:2011, Information technology ― Database languages ― SQL ― Part 2: Foundation
(SQL/Foundation)
ISO/IEC 10646:2012, Information technology ― Universal Coded Character Set (UCS)
ISO 19111:2007, Geographic information ― Spatial referencing by coordinates
ISO 19111-2:2009, Geographic information ― Spatial referencing by coordinates ― Part 2: Extension for
parametric values
4 Definitions and abbreviations
4.1 Definitions
For the purposes of this document, the following terms and definitions apply.
4.1.1
affine coordinate system
coordinate system (4.1.8) in Euclidean space with straight axes that are not necessarily mutually
perpendicular
[SOURCE: ISO 19111:2007, 4.1]
4.1.2
bearing
horizontal angle at a point relative to a specified direction
Note 1 to entry: The direction is usually specified to be north. In some communities the term bearing refers specifically
to grid north and directions relative to true north are then termed ‘azimuth’; in other communities a bearing refers
specifically to true north. In this International Standard bearing is used for any specified reference direction. The angle
may be reckoned positive clockwise or positive counter-clockwise depending upon the application.
2 © ISO 2015 – All rights reserved

4.1.3
Cartesian coordinate system
coordinate system (4.1.8) which gives the position of points relative to n mutually perpendicular axes that each
has zero curvature
Note 1 to entry: n is 2 or 3 for the purposes of this International Standard.
4.1.4
compound coordinate reference system
coordinate reference system (4.1.7) using at least two independent coordinate reference systems
Note 1 to entry: Coordinate reference systems are independent of each other if coordinate values in one cannot be
converted or transformed into coordinate values in the other.
[SOURCE: ISO 19111:2007, 4.3]
4.1.5
coordinate conversion
coordinate operation (4.1.6) in which both coordinate reference systems (4.1.7) are based on the same datum
(4.1.11)
EXAMPLE Conversion from an ellipsoidal coordinate reference system based on the WGS 84 datum to a Cartesian
coordinate reference system also based on the WGS 84 datum, or change of units such as from radians to degrees or feet
to metres.
Note 1 to entry: A coordinate conversion uses parameters which have specified values that are not determined
empirically.
[SOURCE: ISO 19111:2007, 4.6]
4.1.6
coordinate operation
change of coordinates, based on a one-to-one relationship, from one coordinate reference system (4.1.7) to
another
Note 1 to entry: Supertype of coordinate transformation (4.1.9) and coordinate conversion (4.1.5).
[SOURCE: ISO 19111:2007, 4.7]
4.1.7
coordinate reference system
coordinate system (4.1.8) that is related to an object by a datum (4.1.11)
Note 1 to entry: For geodetic and vertical datums (4.1.19, 4.1.39), the object will be the Earth.
[SOURCE: ISO 19111:2007, 4.8]
4.1.8
coordinate system
set of mathematical rules for specifying how coordinates are to be assigned to points
[SOURCE: ISO 19111:2007, 4.10]
4.1.9
coordinate transformation
coordinate operation (4.1.6) in which the two coordinate reference systems (4.1.7) are based on different
datums (4.1.11)
Note 1 to entry: A coordinate transformation uses parameters which are derived empirically by a set of points with
known coordinates in both coordinate reference systems.
[SOURCE: ISO 19111:2007, 4.11]
4.1.10
cylindrical coordinate system
three-dimensional coordinate system (4.1.8) with two distance and one angular coordinates
[SOURCE: ISO 19111:2007, 4.13]
4.1.11
datum
parameter or set of parameters that define the position of the origin, the scale, and the orientation of a
coordinate system (4.1.8)
[SOURCE: ISO 19111:2007, 4.14]
4.1.12
ellipsoid
surface formed by the rotation of an ellipse about a main axis
Note 1 to entry: In this International Standard, ellipsoids are always oblate, meaning that the axis of rotation is always
the minor axis.
[SOURCE: ISO 19111:2007, 4.17]
4.1.13
ellipsoidal coordinate system
geodetic coordinate system
coordinate system (4.1.8) in which position is specified by geodetic latitude (4.1.20), geodetic longitude
(4.1.21) and (in the three-dimensional case) ellipsoidal height (4.1.14)
[SOURCE: ISO 19111:2007, 4.18]
4.1.14
ellipsoidal height
geodetic height
h
distance of a point from the ellipsoid (4.1.12) measured along the perpendicular from the ellipsoid to this point,
positive if upwards or outside of the ellipsoid
Note 1 to entry: Only used as part of a three-dimensional ellipsoidal coordinate system (4.1.13) and never on its own.
[SOURCE: ISO 19111:2007, 4.19]
4.1.15
engineering coordinate reference system
coordinate reference system (4.1.7) based on an engineering datum (4.1.16)
EXAMPLES Local engineering and architectural grids; coordinate reference system local to a ship or an orbiting
spacecraft.
[SOURCE: ISO 19111:2007, 4.20]
4.1.16
engineering datum
local datum
datum (4.1.11) describing the relationship of a coordinate system (4.1.8) to a local reference
4 © ISO 2015 – All rights reserved

Note 1 to entry: Engineering datum excludes both geodetic and vertical datums (4.1.19, 4.1.39).
EXAMPLE A system for identifying relative positions within a few kilometres of the reference point.
[SOURCE: ISO 19111:2007, 4.21]
4.1.17
flattening
f
ratio of the difference between the semi-major axis (a) (4.1.32) and semi-minor axis (b) (4.1.33) of an ellipsoid
(4.1.12) to the semi-major axis; f = (a – b)/a
Note 1 to entry: Sometimes inverse flattening 1/f = a/(a−b) is given instead; 1/f is also known as reciprocal flattening.
[SOURCE: ISO 19111:2007, 4.22, modified – The first occurrence of the words “semi-major” have been
expanded to “semi-major axis”.]
4.1.18
geodetic coordinate reference system
coordinate reference system (4.1.7) based on a geodetic datum (4.1.19)
[SOURCE: ISO 19111:2007, 4.23]
4.1.19
geodetic datum
datum (4.1.11) describing the relationship of a two- or three-dimensional coordinate system (4.1.8) to the
Earth
[SOURCE: ISO 19111:2007, 4.24]
4.1.20
geodetic latitude
ellipsoidal latitude

angle from the equatorial plane to the perpendicular to the ellipsoid (4.1.12) through a given point, northwards
treated as positive
[SOURCE: ISO 19111:2007, 4.25]
4.1.21
geodetic longitude
ellipsoidal longitude

angle from the prime meridian (4.1.30) plane to the meridian plane of a given point, eastward treated as
positive
[SOURCE: ISO 19111:2007, 4.26]
4.1.22
image coordinate reference system
coordinate reference system (4.1.7) based on an image datum (4.1.23)
[SOURCE: ISO 19111:2007, 4.30]
4.1.23
image datum
engineering datum (4.1.16) which defines the relationship of a coordinate system (4.1.8) to an image
[SOURCE: ISO 19111:2007, 4.31]
4.1.24
linear coordinate system
one-dimensional coordinate system (4.1.8) in which a linear feature forms the axis
EXAMPLES Distances along a pipeline; depths down a deviated oil well bore.
[SOURCE: ISO 19111:2007, 4.32]
4.1.25
map projection
coordinate conversion (4.1.4) from an ellipsoidal coordinate system (4.1.13) to a plane
[SOURCE: ISO 19111:2007, 4.33]
4.1.26
parametric coordinate reference system
coordinate reference system (4.1.7) based on a parametric datum (4.1.28)
[SOURCE: ISO 19111-2:2009, 4.2]
4.1.27
...