i.          Keywords

The following are keywords to be used by search engines and document catalogues.

Ogcdoc, OGC document, Topic 2, Spatial Referencing, Referencing by coordinates

ii.          Preface

This document is consistent with the third edition (2019) of ISO 19111, Geographic Information - Referencing by coordinates. ISO 19111:2019 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics, in close collaboration with the Open Geospatial Consortium (OGC). It replaces the second edition, ISO 19111:2007 and also ISO 19111-2:2009, OGC documents 08-015r2 and 10-020. This OGC document, 18-005r5, incorporates three editorial corrections made in ISO 19111:2019 amendment 1 of 2021.

 

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. The Open Geospatial Consortium shall not be held responsible for identifying any or all such patent rights.

Recipients of this document are requested to submit, with their comments, notification of any relevant patent claims or other intellectual property rights of which they may be aware that might be infringed by any implementation of the standard set forth in this document, and to provide supporting documentation.

iii.          Submitting organizations

The following organizations submitted this Document to the Open Geospatial Consortium (OGC):

Name Affiliation

Roger Lott (editor)

IOGP

Keith Ryden

ESRI

Martin Desruisseaux

Geomatys

Mark Hedley

UK Met Office

Charles Heazel

WiSC Enterprises

All questions regarding this submission should be directed to the editor or the submitters:

iv.          Revision history

Date Release Author Paragraph modified Description

2018-03-01

1.0.0

Roger Lott

 

Initial draft

2018-04-04

1.0.1

Roger Lott

(iii) Submitting organisations

Additional submitters added

2018-08-23

1.0.2

Roger Lott

Minir revisions throughout to address comments made in ISO DIS ballot and OGC RFC

As submitted to ISO for publication as IS.

2018-09-13

1.03

Roger Lott

Figures 5, 9, 13 and 214 replaced, tables 2, 9, 50 and 64 updated.

Correction of UML errors.

2019-01-17

1.04

Roger Lott

 

Minor editorial corrections.

2021-02-22

5.0.1

Roger Lott

3.18, 7.4 figure 5 and table 2.

Corridenda.


 

 

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.

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 (see 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 (see 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 voluntary nature of standards, the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO’s adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) (see the following URL: www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 211 Geographic information/Geomatics, in close collaboration with the Open Geospatial Consortium (OGC).

This third edition cancels and replaces the second edition (ISO 19111:2007), which has been technically revised. This document also incorporates the provisions of ISO 19111-2:2009, which is cancelled.

The changes in this edition compared to the previous edition are:

Further details are given in Annex G.

In accordance with the ISO/IEC Directives, Part 2, 2018, Rules for the structure and drafting of International Standards, in International Standards the decimal sign is a comma on the line. However the General Conference on Weights and Measures (Conférence Générale des Poids et Mesures) at its meeting in 2003 passed unanimously the following resolution:

                  “The decimal marker shall be either a point on the line or a comma on the line.”

In practice, the choice between these alternatives depends on customary use in the language concerned. In the technical areas of geodesy and geographic information it is customary for the decimal point always to be used, for all languages. That practice is used throughout this document.

 

Introduction

Geographic information is inherently four-dimensional and includes time. The spatial component relates the features represented in geographic data to positions in the real world. Spatial references fall into two categories:

Spatial referencing by geographic identifiers is defined in ISO 19112[5]. This document describes the data elements, relationships and associated metadata required for spatial referencing by coordinates, expanded from a strictly spatial context to include time. The temporal element is restricted to temporal coordinate systems having a continuous axis. The temporal element excludes calendars and ordinal reference systems due to their complexities in definition and in transformation. The context is shown in Figure 1.

Context of referencing by coordinates
Figure : Context of referencing by coordinates

Certain scientific communities use three-dimensional systems where horizontal position is combined with a non-spatial parameter. In these communities, the parameter is considered to be a third, vertical, axis. The parameter, although varying monotonically with height or depth, does not necessarily vary in a simple manner. Thus conversion from the parameter to height or depth is non-trivial. The parameters concerned are normally absolute measurements and the datum is taken with reference to a direct physical measurement of the parameter. These non-spatial parameters and parametric coordinate reference system modelling constructs were previously described in ISO 19111-2:2009 but have been incorporated into this revision because the modelling constructs are identical to the other coordinate reference system types included in this document.

This document describes the elements that are necessary to fully define various types of coordinate reference systems applicable to geographic information. The subset of elements required is partially dependent upon the type of coordinates. This document also includes optional fields to allow for the inclusion of metadata about the coordinate reference systems. The elements are intended to be both machine and human readable.

In addition to describing a coordinate reference system, this document provides for the description of a coordinate operation between two different coordinate reference systems or a coordinate operation to account for crustal motion over time. With such information, spatial data referenced to different coordinate reference systems can be referenced to one specified coordinate reference system at one specified time. This facilitates spatial data integration. Alternatively, an audit trail of coordinate manipulations can be maintained.

 


1      Scope

This document defines the conceptual schema for the description of referencing by coordinates. It describes the minimum data required to define coordinate reference systems. This document supports the definition of:

  • spatial coordinate reference systems where coordinate values do not change with time. The system may:
  • be geodetic and apply on a national or regional basis, or
  • apply locally such as for a building or construction site, or
  • apply locally to an image or image sensor;
  • be referenced to a moving platform such as a car, a ship, an aircraft or a spacecraft. Such a coordinate reference system may be related to a second coordinate reference system which is referenced to the Earth through a transformation that includes a time element;
  • spatial coordinate reference systems in which coordinate values of points on or near the surface of the earth change with time due to tectonic plate motion or other crustal deformation. Such dynamic systems include time evolution, however they remain spatial in nature;
  • parametric coordinate reference systems which use a non-spatial parameter that varies monotonically with height or depth;
  • temporal coordinate reference systems which use dateTime, temporal count or temporal measure quantities that vary monotonically with time;
  • mixed spatial, parametric or temporal coordinate reference systems.

The definition of a coordinate reference system does not change with time, although in some cases some of the defining parameters may include a rate of change of the parameter. The coordinate values within a dynamic and in a temporal coordinate reference system may change with time.

This document also describes the conceptual schema for defining the information required to describe operations that change coordinate values.

In addition to the minimum data required for the definition of the coordinate reference system or coordinate operation, the conceptual schema allows additional descriptive information - coordinate reference system metadata - to be provided.

This document is applicable to producers and users of geographic information. Although it is applicable to digital geographic data, the principles described in this document can be extended to many other forms of spatial data such as maps, charts and text documents.

2      Normative references

The following documents are referred to in the text in such a way that some or all of their content constitutes requirements 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 8601, Data elements and interchange formats — Information interchange — Representation of dates and times

ISO 19103, Geographic information — Conceptual schema language

ISO 19115-1:2014, Geographic information — Metadata Part 1: Fundamentals

 

3      Terms, definitions, symbols and abbreviated terms

3.1     Terms and definitions

For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

—     IEC Electropedia: available at http://www.electropedia.org/

—     ISO Online browsing platform: available at https://www.iso.org/obp

3.1.1

affine coordinate system

coordinate system in Euclidean space with straight axes that are not necessarily mutually perpendicular

3.1.2

Cartesian coordinate system

coordinate system in Euclidean space which gives the position of points relative to n mutually perpendicular straight axes all having the same unit of measure

Note 1 to entry: n is 2 or 3 for the purposes of this document.

Note 2 to entry: A Cartesian coordinate system is a specialisation of an affine coordinate system.

3.1.3

compound coordinate reference system

coordinate reference system 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.

3.1.4

concatenated operation

coordinate operation consisting of the sequential application of multiple coordinate operations

3.1.5

coordinate

one of a sequence of numbers designating the position of a point

Note 1 to entry: In a spatial coordinate reference system, the coordinate numbers are qualified by units.

3.1.6

coordinate conversion

coordinate operation that changes coordinates in a source coordinate reference system to coordinates in a target coordinate reference system in which both coordinate reference systems are based on the same datum

Note 1 to entry: A coordinate conversion uses parameters which have specified values.

EXAMPLE 1           A mapping of ellipsoidal coordinates to Cartesian coordinates using a map projection.

EXAMPLE 2           Change of units such as from radians to degrees or from feet to metres.

3.1.7

coordinate epoch

epoch to which coordinates in a dynamic coordinate reference system are referenced

3.1.8

coordinate operation

process using a mathematical model, based on a one-to-one relationship, that changes coordinates in a source coordinate reference system to coordinates in a target coordinate reference system, or that changes coordinates at a source coordinate epoch to coordinates at a target coordinate epoch within the same coordinate reference system

Note 1 to entry: Generalization of coordinate conversion, coordinate transformation and point motion operation.

3.1.9

coordinate reference system

coordinate system that is related to an object by a datum

Note 1 to entry: Geodetic and vertical datums are referred to as reference frames.

Note 2 to entry: For geodetic and vertical reference frames, the object will be the Earth. In planetary applications, geodetic and vertical reference frames may be applied to other celestial bodies.

3.1.10

coordinate set

collection of coordinate tuples referenced to the same coordinate reference system and if that coordinate reference system is dynamic also to the same coordinate epoch

3.1.11

coordinate system

set of mathematical rules for specifying how coordinates are to be assigned to points

3.1.12

coordinate transformation

coordinate operation that changes coordinates in a source coordinate reference system to coordinates in a target coordinate reference system in which the source and target coordinate reference systems are based on different datums

Note 1 to entry: A coordinate transformation uses parameters which are derived empirically. Any error in those coordinates will be embedded in the coordinate transformation and when the coordinate transformation is applied the embedded errors are transmitted to output coordinates.

Note 2 to entry: A coordinate transformation is colloquially sometimes referred to as a ‘datum transformation’. This is erroneous. A coordinate transformation changes coordinate values. It does not change the definition of the datum. In this document coordinates are referenced to a coordinate reference system. A coordinate transformation operates between two coordinate reference systems, not between two datums.

3.1.13

coordinate tuple

tuple composed of coordinates

Note 1 to entry: The number of coordinates in the coordinate tuple equals the dimension of the coordinate system; the order of coordinates in the coordinate tuple is identical to the order of the axes of the coordinate system.

3.1.14

cylindrical coordinate system

three-dimensional coordinate system in Euclidean space in which position is specified by two linear coordinates and one angular coordinate

3.1.15

datum

reference frame

parameter or set of parameters that realize the position of the origin, the scale, and the orientation of a coordinate system

3.1.16

datum ensemble

group of multiple realizations of the same terrestrial or vertical reference system that, for approximate spatial referencing purposes, are not significantly different

Note 1 to entry: Datasets referenced to the different realizations within a datum ensemble may be merged without coordinate transformation.

Note 2 to entry:   ‘Approximate’ is for users to define but typically is in the order of under 1 decimetre but may be up to 2 metres.

EXAMPLE               “WGS 84” as an undifferentiated group of realizations including WGS 84 (TRANSIT), WGS 84 (G730), WGS 84 (G873), WGS 84 (G1150), WGS 84 (G1674) and WGS 84 (G1762). At the surface of the Earth these have changed on average by 0.7m between the TRANSIT and G730 realizations, a further 0.2m between G730 and G873, 0.06m between G873 and G1150, 0.2m between G1150 and G1674 and 0.02m between G1674 and G1762).

3.1.17

depth

distance of a point from a chosen vertical reference surface downward along a line that is perpendicular to that surface

Note 1 to entry: The line direction may be straight, or be dependent on the Earth’s gravity field or other physical phenomena.

Note 2 to entry: A depth above the vertical reference surface will have a negative value.

3.1.18

derived coordinate reference system

coordinate reference system that is defined through the application of a specified coordinate conversion to the coordinates within a previously established coordinate reference system

Note 1 to entry: The previously established coordinate reference system is referred to as the base coordinate reference system.

Note 2 to entry: A derived coordinate reference system inherits its datum or reference frame from its base coordinate reference system.

Note 3 to entry: The coordinate conversion between the base and derived coordinate reference system is implemented using the parameters and formula(s) specified in the definition of the coordinate conversion.

3.1.19

dynamic coordinate reference system

coordinate reference system that has a dynamic reference frame

Note 1 to entry:   Coordinates of points on or near the crust of the Earth that are referenced to a dynamic coordinate reference system may change with time, usually due to crustal deformations such as tectonic motion and glacial isostatic adjustment.

Note 2 to entry: Metadata for a dataset referenced to a dynamic coordinate reference system should include coordinate epoch information.

3.1.20

dynamic reference frame

dynamic datum

reference frame in which the defining parameters include time evolution

Note 1 to entry: The defining parameters that have time evolution are usually a coordinate set.

3.1.21

easting

E

distance in a coordinate system, eastwards (positive) or westwards (negative) from a north-south reference line

3.1.22

ellipsoid

reference ellipsoid

<geodesy> geometric reference surface embedded in 3D Euclidean space formed by an ellipse that is rotated about a main axis

Note 1 to entry: For the Earth the ellipsoid is bi-axial with rotation about the polar axis. This results in an oblate ellipsoid with the midpoint of the foci located at the nominal centre of the Earth.

3.1.23

ellipsoidal coordinate system
geodetic coordinate system

coordinate system in which position is specified by geodetic latitude, geodetic longitude and (in the three-dimensional case) ellipsoidal height

3.1.24

ellipsoidal height

geodetic height

h

distance of a point from the reference ellipsoid along the perpendicular from the reference ellipsoid to this point, positive if upwards or outside of the reference ellipsoid

Note 1 to entry: Only used as part of a three-dimensional ellipsoidal coordinate system or as part of a three-dimensional Cartesian coordinate system in a three-dimensional projected coordinate reference system, but never on its own.

3.1.25

engineering coordinate reference system

coordinate reference system based on an engineering datum

EXAMPLE 1           System for identifying relative positions within a few kilometres of the reference point, such as a building or construction site.

EXAMPLE 2           Coordinate reference system local to a moving object such as a ship or an orbiting spacecraft.

EXAMPLE 3           Internal coordinate reference system for an image. This has continuous axes. It may be the foundation for a grid.

3.1.26

engineering datum

local datum

datum describing the relationship of a coordinate system to a local reference

Note 1 to entry: Engineering datum excludes both geodetic and vertical reference frames.

3.1.27

epoch

<geodesy> point in time

Note 1 to entry: In this document an epoch is expressed in the Gregorian calendar as a decimal year.

EXAMPLE   2017-03-25 in the Gregorian calendar is epoch 2017.23.

3.1.28

flattening

f

ratio of the difference between the semi-major axis (a) and semi-minor axis (b) of an ellipsoid to the semi-major axis: f=(ab)/a

Note 1 to entry: Sometimes inverse flattening 1/f  = a/(- b) is given instead; 1/f is also known as reciprocal flattening.

3.1.29

frame reference epoch

epoch of coordinates that define a dynamic reference frame

3.1.30

geocentric latitude

angle from the equatorial plane to the direction from the centre of an ellipsoid through a given point, northwards treated as positive

3.1.31

geodetic coordinate reference system

three-dimensional coordinate reference system based on a geodetic reference frame and having either a three-dimensional Cartesian or a spherical coordinate system

Note 1 to entry: In this document a coordinate reference system based on a geodetic reference frame and having an ellipsoidal coordinate system is geographic.

3.1.32

geodetic latitude

ellipsoidal latitude

j

angle from the equatorial plane to the perpendicular to the ellipsoid through a given point, northwards treated as positive

3.1.33

geodetic longitude

ellipsoidal longitude

l

angle from the prime meridian plane to the meridian plane of a given point, eastward treated as positive

3.1.34

geodetic reference frame

reference frame or datum describing the relationship of a two- or three-dimensional coordinate system to the Earth

Note 1 to entry: In the data model described in this document, the UML class GeodeticReferenceFrame includes both modern terrestrial reference frames and classical geodetic datums.   

3.1.35

geographic coordinate reference system

coordinate reference system that has a geodetic reference frame and an ellipsoidal coordinate system

3.1.36

geoid

equipotential surface of the Earth’s gravity field which is perpendicular to the direction of gravity and which best fits mean sea level either locally, regionally or globally

3.1.37

gravity-related height

H

height that is dependent on the Earth’s gravity field

Note 1 to entry: This refers to, amongst others, orthometric height and Normal height, which are both approximations of the distance of a point above the mean sea level, but also may include Normal-orthometric heights, dynamic heights or geopotential numbers.

Note 2 to entry: The distance from the reference surface may follow a curved line, not necessarily straight, as it is influenced by the direction of gravity.

3.1.38

height

distance of a point from a chosen reference surface positive upward along a line perpendicular to that surface

Note 1 to entry: A height below the reference surface will have a negative value.

Note 2 to entry: Generalisation of ellipsoidal height (h) and gravity-related height (H).

3.1.39

linear coordinate system

one-dimensional coordinate system in which a linear feature forms the axis

EXAMPLE 1           Distances along a pipeline.

EXAMPLE 2           Depths down a deviated oil well bore.

3.1.40

map projection

coordinate conversion from an ellipsoidal coordinate system to a plane

3.1.41

mean sea level

MSL

<geodesy> average level of the surface of the sea over all stages of tide and seasonal variations

Note 1 to entry: 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. To meet IHO standards that period should be one full lunar cycle of 19 years. Mean sea level in a global context differs from a global geoid by not more than 2 m.

3.1.42

meridian

intersection of an ellipsoid by a plane containing the shortest axis of the ellipsoid

Note 1 to entry: This term is generally used to describe the pole-to-pole arc rather than the complete closed figure.

3.1.43

northing

N

distance in a coordinate system, northwards (positive) or southwards (negative) from an east-west reference line

3.1.44

parameter reference epoch

epoch at which the parameter values of a time-dependent coordinate transformation are valid

Note 1 to entry: The transformation parameter values first need to be propagated to the epoch of the coordinates before the coordinate transformation can be applied.

3.1.45

parametric coordinate reference system

coordinate reference system based on a parametric datum

3.1.46

parametric coordinate system

one-dimensional coordinate system where the axis units are parameter values which are not inherently spatial

3.1.47

parametric datum

datum describing the relationship of a parametric coordinate system to an object

Note 1 to entry: The object is normally the Earth.

3.1.48

point motion operation

coordinate operation that changes coordinates within one coordinate reference system due to the motion of the point

Note 1 to entry: The change of coordinates is from those at an initial epoch to those at another epoch.

Note 2 to entry: In this document the point motion is due to tectonic motion or crustal deformation.

3.1.49

polar coordinate system

two-dimensional coordinate system in Euclidean space in which position is specified by one distance coordinate and one angular coordinate

Note 1 to entry: For the three-dimensional case, see spherical coordinate system.

3.1.50

prime meridian

meridian from which the longitudes of other meridians are quantified

3.1.51

projected coordinate reference system

coordinate reference system derived from a geographic coordinate reference system by applying a map projection

Note 1 to entry: May be two- or three-dimensional, the dimension being equal to that of the geographic coordinate reference system from which it is derived.

Note 2 to entry: In the three-dimensional case the horizontal coordinates (geodetic latitude and geodetic longitude coordinates) are projected to northing and easting and the ellipsoidal height is unchanged.

3.1.52

reference frame

datum

parameter or set of parameters that realize the position of the origin, the scale, and the orientation of a coordinate system

3.1.53

semi-major axis

a

semi-diameter of the longest axis of an ellipsoid

3.1.54

semi-minor axis

b

semi-diameter of the shortest axis of an ellipsoid

3.1.55

sequence

finite, ordered collection of related items (objects or values) that may be repeated

3.1.56

spatial reference

description of position in the real world

Note 1 to entry: This may take the form of a label, code or coordinate tuple.

3.1.57

spatio-parametric coordinate reference system

compound coordinate reference system in which one constituent coordinate reference system is a spatial coordinate reference system and one is a parametric coordinate reference system

Note 1 to entry: Normally the spatial component is “horizontal” and the parametric component is “vertical”.

3.1.58

spatio-parametric-temporal coordinate reference system

compound coordinate reference system comprised of spatial, parametric and temporal coordinate reference systems

3.1.59

spatio-temporal coordinate reference system

compound coordinate reference system in which one constituent coordinate reference system is a spatial coordinate reference system and one is a temporal coordinate reference system

3.1.60

spherical coordinate system

three-dimensional coordinate system in Euclidean space in which position is specified by one distance coordinate and two angular coordinates

Note 1 to entry: Not to be confused with an ellipsoidal coordinate system based on an ellipsoid ‘degenerated’ into a sphere.

3.1.61

static coordinate reference system

coordinate reference system that has a static reference frame

Note 1 to entry: Coordinates of points on or near the crust of the Earth that are referenced to a static coordinate reference system do not change with time.

Note 2 to entry: Metadata for a dataset referenced to a static coordinate reference system does not require coordinate epoch information.

3.1.62

static reference frame

static datum

reference frame in which the defining parameters exclude time evolution

3.1.63

temporal coordinate reference system

coordinate reference system based on a temporal datum

3.1.64

temporal coordinate system

<geodesy> one-dimensionalcoordinate system where the axis is time

3.1.65

temporal datum

datum describing the relationship of a temporal coordinate system to an object

Note 1 to entry: The object is normally time on the Earth.

3.1.66

terrestrial reference system

TRS

set of conventions defining the origin, scale, orientation and time evolution of a spatial reference system co-rotating with the Earth in its diurnal motion in space

Note 1 to entry: The abstract concept of a TRS is realised through a terrestrial reference frame that usually consists of a set of physical points with precisely determined coordinates and optionally their rates of change. In this document terrestrial reference frame is included within the geodetic reference frame element of the data model.

3.1.67

transformation reference epoch

epoch at which the parameter values of a time-specific coordinate transformation are valid

Note 1 to entry: Coordinates first need to be propagated to this epoch before the coordinate transformation is applied. This is in contrast to a parameter reference epoch where the transformation parameter values first need to be propagated to the epoch of the coordinates before the coordinate transformation is applied.

3.1.68

tuple

ordered list of values

[SOURCE: ISO 19136:2007, 4.1.63]

3.1.69

unit

defined quantity in which dimensioned parameters are expressed

Note 1 to entry: In this document, the subtypes of units are length units, angular units, scale units, parametric quantities and time quantities.

3.1.70

vertical coordinate reference system

one-dimensional coordinate reference system based on a vertical reference frame

3.1.71

vertical coordinate system

one-dimensional coordinate system used for gravity-related height or depth measurements

3.1.72

vertical reference frame

vertical datum

reference frame describing the relation of gravity-related heights or depths to the Earth

Note 1 to entry: In most cases, the vertical reference frame will be related to mean sea level. Vertical datums include sounding datums (used for hydrographic purposes), in which case the heights may be negative heights or depths.

Note 2 to entry: Ellipsoidal heights are related to a three-dimensional ellipsoidal coordinate system referenced to a geodetic reference frame.

3.1.73

vertical reference system

VRS

set of conventions defining the origin, scale, orientation and time evolution that describes the relationship of gravity-related heights or depths to the Earth

Note 1 to entry: The abstract concept of a VRS is realised through a vertical reference frame.

3.2          Symbols

a                          semi-major axis of ellipsoid

b                          semi-minor axis of bi-axial ellipsoid

E                          easting

f                           flattening

H                         gravity-related height

h                          ellipsoidal height

N                         northing

l                          geodetic longitude

j                         geodetic latitude

E, N, [h]           Cartesian coordinates in a projected coordinate reference system

X, Y, Z               Cartesian coordinates in a geodetic coordinate reference system

i, j, [k]               Cartesian coordinates in an engineering coordinate reference system

r, q                     polar coordinates in a 2D engineering coordinate reference system

r, W, q               spherical coordinates in a 3D engineering coordinate reference system

                             Note: In this document W is the polar (zenith) angle and q is the azimuthal angle.

j,l, [h]           ellipsoidal coordinates in a geographic coordinate reference system

 

3.3          Abbreviated terms

CC                       coordinate conversion

CCRS                compound coordinate reference system

CRS                   coordinate reference system

CT                      coordinate transformation

MSL                   mean sea level

pixel                 a contraction of “picture element”, the smallest element of a digital image to which attributes are assigned

PMO                  point motion operation

SI                        le Système International d’unités (International System of Units)

UML                  Unified Modeling Language

URI                    Uniform Resource Identifier

1D                      one-dimensional

2D                      two-dimensional

3D                      three-dimensional

 

4              Conformance requirements

This document defines

—     two classes of conformance for relating coordinates to coordinate metadata; and

—     twenty six classes of conformance for the definition of a coordinate reference system (CRS) or of a coordinate operation.

These are differentiated by type, as shown in Table 1. Implementations should indicate which conformance classes they comply with. Any implementations claiming conformance shall satisfy the requirements in Annex A.

Table : Conformance classes
Conformance class Description Conformance requirements given in

Conformance for relating coordinates to coordinate metadata

A.2

1

2

CRS with static reference frame

CRS with dynamic reference frame

 

Conformance of a CRS definition

A.3

 

3

4

5

Geodetic CRS

with static reference frame

with dynamic reference frame

derived geodetic CRS

 

 

6

7

8

Geographic CRS

with static reference frame

with dynamic reference frame

derived geographic CRS

 

9

10

Projected CRS

derived projected CRS

 

 

11

12

13

Vertical CRS

with static reference frame

with dynamic reference frame

derived vertical CRS

 

14

15

Parametric CRS

derived parametric CRS

 

16

17

Engineering CRS

derived engineering CRS

 

 

18

19

20

21

Temporal CRS

dateTime

temporal count

temporal measure

derived temporal CRS

 

22

CRS with datum ensemble

 

23

Compound CRS

A.3

Conformance of a coordinate operation definition

A.4

24

25

26

27

28

Coordinate conversion

Coordinate transformation

Point motion operation

Concatenated operation

Pass-through operation

 

 

The requirements classes for the definition of a coordinate reference system or a coordinate operation are described in this document through tables grouped by UML package. The requirements are then brought together in the conformance classes in Annex A. This retains the package-based layout for describing requirements used in previous versions of this document.

 

5      Conventions

5.1          Unified Modeling Language notation

In this document, the conceptual schema for describing coordinate reference systems and coordinate operations are presented in the Unified Modeling Language (UML). ISO 19103 Conceptual schema languagepresents the specific profile of UML used in this document.

In the UML diagrams in this document, a grey background surround to boxes indicates classes from other standards.

5.2          Attribute and association status

In this document the conceptual schema is described in Clauses 6 to 12 through tables. In these tables:

·       attributes and associations are given an obligation status:

Obligation Definition Meaning

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 tables indicates the maximum number of occurrences of attribute values that are permissible, with N indicating no upper limit.

·       non-navigable associations are not included in the UML diagrams or tables.

In the event of any discrepancies between the UML diagrams and text, the UML shall prevail.

6      Referencing by coordinates - Data model overview

The specification for referencing by coordinates is described in this document in the form of a UML model with supplementary text. The UML model contains six UML packages, as shown in Figure 2. Each box represents a package, and contains the package name. Each arrowed line shows the dependency of one package upon another package (at the head of the arrow).

UML model packages and dependencies
Figure : UML model packages and dependencies

Coordinates require metadata that fully specifies the coordinate reference system to which they are referenced; without this CRS reference the description of position is ambiguous. The UML package for coordinates and their metadata is described in Clause 7. This includes aspects of coordinate operations required to change coordinate values when the coordinate reference system is changed.

A coordinate reference system is usually comprised of two components, one coordinate system and one datum. In modern geodetic terminology the datum is referred to as a reference frame. Some geodetic concepts underpinning spatial referencing by coordinates are given in Annex B. The information required to fully specify a coordinate reference system is described in Clauses 9 to 11, with attributes common to all three packages described in Clause 8.

Some coordinate reference systems have a third component, a defining coordinate conversion from another pre-existing CRS. In this document a CRS having this third component is a derived CRS. The specification for describing coordinate operations, including a defining coordinate conversion, is described in Clause 12.

Further context for the requirements of Clauses 8 to 12 is given in Annexes C and D. Examples illustrating how the specifications of this document can be applied when defining a coordinate reference system or a coordinate operation are given in Annex E. Recommendations for referencing to classes defined in this document are given in Annex F. Changes between this document and the previous version ISO 19111:2007 are described in Annex G.

7      Coordinates package

7.1          Relationship between coordinates and coordinate reference system

In this document, a coordinate is one of n scalar values that define the position of a single point. In other contexts, the term ordinate is used for a single value and coordinate for multiple ordinates. Such usage is not part of this document.

A coordinate tuple is an ordered list of coordinates that define the position of a single point. The coordinates within a coordinate tuple are mutually independent. The number of coordinates in a tuple is equal to the dimension of the coordinate space.

A coordinate set is a collection of coordinate tuples referenced to the same coordinate reference system. For a coordinate set, one CRS identification or definition may be associated with the coordinate set and then all coordinate tuples in that coordinate set inherit that association. If only one point is being described, the association between coordinate tuple and coordinate reference system is direct.

The concepts of dynamic and static coordinate reference systems are outlined in B.3. If the coordinate reference system is dynamic, operations on the geometry of the tuples within the coordinate set are valid only if all tuples are referenced to the same coordinate epoch. In this document all coordinate tuples in a spatial coordinate set are referenced to one specified coordinate epoch.

Together the coordinate reference system and the coordinate epoch are the coordinate metadata.

Coordinate sets referenced to one CRS may be referenced to another CRS through the application of a coordinate operation. A coordinate operation operates on coordinates, not on coordinate reference systems. A coordinate operation may be single or concatenated: refer to Clause 12. The high level conceptual model for changing coordinates is shown in Figure 3.

Conceptual model for coordinate operations to produce a merged coordinate set
Figure : Conceptual model for coordinate operations to produce a merged coordinate set

Coordinate sets referenced to a dynamic CRS at a given coordinate epoch t1 may be converted to another coordinate epoch t2 through a point motion coordinate operation that includes time evolution, often described using velocities, as shown schematically in Figure 4.

Conceptual model for a coordinate operation to change coordinate epoch
Figure : Conceptual model for a coordinate operation to change coordinate epoch

It is also possible to change coordinates from being referenced to one dynamic CRS at one coordinate epoch to being referenced to another dynamic CRS at another coordinate epoch, or to change coordinates between a dynamic CRS and a static CRS or vice-versa. Further information is in C.1 and C.5.

The description of quality of coordinates is covered by the provisions of ISO 19157[8].

7.2          Coordinate reference system identification

The elements required for the definition of coordinate reference systems and coordinate operations are described in Clauses 8 to 12.

CRS or coordinate operation identification may be through:

a)    a full description, as defined in this document; or

b)    reference to a full description in a register of geodetic parameters (the reference is made to the register and to the identifier of the object description within that register); or

c)     both a full description and a reference to a full description in a register. If there is a conflict between the two, the object full description should prevail over the reference to a register.

a) and b) are alternative means of providing a full description. b) is recommended for simplicity, but if it is not available from a register the description is required to be given explicitly and in full. In both methods, the order of coordinates in each coordinate tuple is required to be as given in the coordinate reference system’s coordinate system description.

When using method b), reference to a register, applications that are required only to confirm the identification of a CRS or coordinate operation can do so through the register citation and the identifier from that register. They do not need to retrieve the elements that constitute the full description from the register unless there is a need to quote these or to perform a coordinate operation on the coordinate set.

7.3     Requirements for coordinate metadata

7.3.1      Requirements class: static CRS coordinate metadata

Requirement 1: All coordinate tuples in a coordinate set shall be referenced to the same coordinate reference system.

7.3.2      Requirements class: dynamic CRS coordinate metadata

CRS is described in Clause 9 and datum or reference frame in Clause 11. The following subtypes of CRS may have a dynamic reference frame and therefore may be dynamic CRSs: geodetic, geographic, vertical, projected and derived variants of these subtypes. Implementers are warned that CRSs of these subtypes are not necessarily dynamic; their reference frame attributes need to be examined to clarify this.

Requirement 2: When the coordinate reference system to which a coordinate set is referenced is dynamic, all coordinate tuples in the coordinate set shall be referenced to the same coordinate epoch.

7.4          UML schema for the Coordinates package

Figure 5 shows the UML class diagram for coordinate metadata. The definition of the classes in the package are provided in Tables 2 to 4.