ISO 19111:2019 Coordinate Operations

two- or three-dimensional coordinate system in Euclidean space with straight axes that are not necessarily orthogonalNote: The number of associations shall equal the dimension of the coordinate system.

coordinate reference system which is usually single but may be compound

two- or three-dimensional coordinate system in Euclidean space with straight axes that are not necessarily orthogonalNote: The number of associations shall equal the dimension of the coordinate system.

coordinate reference system describing the position of points through two or more independent single coordinate reference systemsNote: two coordinate reference systems are independent of each other if coordinate values in one cannot be converted or transformed into coordinate values in the other.

ordered sequence of two or more single coordinate operationsNote: The sequence of coordinate operations is constrained by the requirement that the source coordinate reference system of step (n + 1) shall be the same as the target coordinate reference system of step (n). The source coordinate reference system of the first step and the target coordinate reference system of the last step are the source and target coordinate reference system associated with the concatenated coordinate operation. For a concatenated coordinate operation sequence of n coordinate operations: source CRS (concatenated coordinate operation) .eq. source CRS (coordinate operation step 1) target CRS (coordinate operation step i) .eq. source CRS (coordinate operation step i + 1); i .eq. 1 ...(n - 1) target CRS (concatenated coordinate operation) .eq. target CRS (coordinate operation step n) Instead of a forward coordinate operation, an inverse coordinate operation may be used for one or more of the coordinate operation steps mentioned above, if the inverse coordinate operation is uniquely defined by the forward coordinate operation method.

mathematical operation on coordinates in which the parameter values are defined rather than empirically derived; application of the coordinate conversion introduces no error into output coordinatesNote: The best-known example of a coordinate conversion is a map projection. For coordinate conversions the output coordinates are referenced to the same datum as are the input coordinates.Coordinate conversions forming a component of a derived CRS have a source CRS and a target CRS that are NOT specified through the source and target associations, but through associations from DerivedCRS to SingleCRS.

metadata required to reference coordinates

mathematical operation (a) on coordinates that transforms or converts them from one coordinate reference system to another coordinate reference system, or (b) that decribes the change of coordinate values within one coordinate reference system due to the motion of the point between one coordinate epoch and another coordinate epochNote: Many but not all coordinate operations (from CRS A to CRS B) also uniquely define the inverse coordinate operation (from CRS B to CRS A). In some cases, the coordinate operation method algorithm for the inverse coordinate operation is the same as for the forward algorithm, but the signs of some coordinate operation parameter values have to be reversed. In other cases, different algorithms are required for the forward and inverse coordinate operations, but the same coordinate operation parameter values are used. If (some) entirely different parameter values are needed, a different coordinate operation shall be defined.

description of the coordinate tuples in a coordinate set Note: A single coordinate tuple is treated as a special case of coordinate set containing only one member.

non-repeating sequence of coordinate system axes that spans a given coordinate spaceNote: A coordinate system is derived from a set of mathematical rules for specifying how coordinates in a given space are to be assigned to points. The coordinate values in a coordinate tuple shall be recorded in the order in which the coordinate system axes associations are recorded.

definition of a coordinate system axis

three-dimensional coordinate system in Euclidean space consisting of a polar coordinate system extended by a straight coordinate axis perpendicular to the plane spanned by the polar coordinate systemNote: A CylindricalCS shall have three axis associations.

time attribute of a coordinate set that is referenced to a dynamic CRS

one-dimensional coordinate system used to record time in dateTime representation as defined in ISO 8601.Note: A DateTimeTemporalCS shall have one axis association. It does not use axisUnitID; the temporal quantities are defined through the ISO 8601 representation.

specification of the relationship of a coordinate system to an object, thus creating a coordinate reference systemNote: For geodetic and vertical coordinate reference systems, it relates a coordinate system to the Earth. With other types of coordinate reference systems, the datum may relate the coordinate system to another physical or virtual object. A datum uses a parameter or set of parameters that determine the location of the origin of the coordinate reference system. Each datum subtype can be associated with only specific types of coordinate reference systems.

A collection of two or more datums (or if geodetic or vertical, a collection of two or more reference frames) that are realizations of one Conventional Reference System and which for all but the highest accuracy requirements may be considered to be insignificantly different from each other.Note: Within the datum ensemble every frame or datum is constrained to be a realization of the same reference system.

parameter value, an ordered sequence of values, or a reference to a file of parameter values that define a paramtric datum

single coordinate reference system that is defined through the application of a specified coordinate conversion to the definition of a previously established single coordinate reference system referred to as the base CRSNote: A derived coordinate reference system inherits its datum (or datum ensemble) from its base CRS. 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.

derived coordinate reference system which has an engineering coordinate reference system as its base CRS, thereby inheriting an engineering datum, and is associated with one of the coordinate system types within the engineeringCS class

derived coordinate reference system which has either a geodetic or a geographic coordinate reference system as its base CRS, thereby inheriting a geodetic reference frame, and associated with a 3D Cartesian or spherical coordinate system

derived coordinate reference system which has either a geodetic or a geographic coordinate reference system as its base CRS, thereby inheriting a geodetic reference frame, and an ellipsoidal coordinate systemNote: A derived geographic CRS can be based on a geodetic CRS only if that geodetic CRS definition includes an ellipsoid.

derived coordinate reference system which has a parametric coordinate reference system as its base CRS, thereby inheriting a parametric datum, and a parametric coordinate system

derived coordinate reference system which has a projected coordinate reference system as its base CRS, thereby inheriting a geodetic reference frame, but also inheriting the distortion characteristics of the base projected CRS

coordinate system used by a DerivedProjected CRS, one of an affine coordinate system, a Cartesian coordinate system, a cylindrical coordinate system, an ordinal coordinate system, a polar coordinate system or a spherical coordinate system

derived coordinate reference system which has a temporal coordinate reference system as its base CRS, thereby inheriting a temporal datum, and is associated with a temporal coordinate system

derived coordinate reference system which has a vertical coordinate reference system as its base CRS, thereby inheriting a vertical reference frame, and a vertical coordinate system

geodetic reference frame in which some of the parameters describe time evolution of defining station coordinatesExample: defining station coordinates having linear velocities to account for crustal motion.

vertical reference frame in which some of the defining parameters have time dependencyExample: Defining station heights have velocity to account for post-glacial isostatic rebound motion.

geometric reference surface embedded in 3D Euclidean space formed by an ellipse that is rotated about a main axisNote: 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.

two- or three-dimensional coordinate system in which position is specified by geodetic latitude, geodetic longitude, and (in the three-dimensional case) ellipsoidal heightNote: An EllipsoidalCS shall have two or three associations; the number of associations shall equal the dimension of the coordinate system.

contextually local coordinate reference system associated with an engineering datum and which is applied either to activities on or near the surface of the Earth without geodetic corrections, or on moving platforms such as road vehicles, vessels, aircraft or spacecraft, or as the internal CRS of an image

coordinate system used by an engineering coordinate reference system, one of an affine coordinate system, a Cartesian coordinate system, a cylindrical coordinate system, a linear coordinate sytem, an ordinal coordinate system, a polar coordinate system or a spherical coordinate system

definition of the origin and orientation of an engineering coordinate reference systemNote: The origin can be fixed with respect to the Earth (such as a defined point at a construction site), or be a defined point on a moving vehicle (such as on a ship or satellite), or a defined point of an image.

specification of the coordinate operation method formula

definition of a parameter or group of parameters used by a coordinate operation method

parameter value or group of parameter values

coordinate reference system associated with a geodetic reference frame and a three-dimensional Cartesian or spherical coordinate systemNote: If the geodetic reference frame is dynamic then the geodetic CRS is dynamic, else it is static.

coordinate system used by a Geodetic CRS, one of a Cartesian coordinate system or a spherical coordinate system

definition of the position, scale and orientation of a geocentric Cartesian 3D coordinate system relative to the EarthNote 1: It may also identify a defined ellipsoid (or sphere) that approximates the shape of the Earth and which is centred on and aligned to this geocentric coordinate system. Older geodetic datums define the location and orientation of a defined ellipsoid (or sphere) that approximates the shape of the earth.Note 2: In 19111:2007 this class was called GeodeticDatum.

coordinate reference system associated with a geodetic reference frame and a two- or three-dimensional ellipsoidal coordinate system Note: If the geodetic reference frame is dynamic then the geographic CRS is dynamic, else it is static.

identification of an object used as a parameter in a coordinate transformation, point motion operation or coordinate conversion

identifications of a CRS-related object

one-dimensional coordinate system that consists of the points that lie on the single axis describedNote: The associated coordinate is the distance – with or without offset – from the origin point, specified through the datum definition, to the point along the axis. Example: usage of the line feature representing a pipeline to describe points on or along that pipeline. A LinearCS shall have one axis association.

scope and validity of a CRS-related object

usage of a CRS-related object

method (algorithm or procedure) used to perform the coordinate operation

definition of a parameter used by a coordinate operation methodNote: Most parameter values are numeric, but other types of parameter values are possible.

definition of a group of related parameters used by a coordinate operation method

parameter value, ordered sequence of values, or reference to a file of parameter values

n-dimensional coordinate system in which every axis uses integersNote: The number of associations shall be equal the dimension of the coordinate system.

value of the coordinate operation parameter

group of related parameter valuesNote: The same group can be repeated more than once in a coordinate operation or higher level ParameterValueGroup, if those instances contain different values of one or more ParameterValues which suitably distinguish among those groups.

coordinate reference system having a parametric datum and a one-dimensional parametric coordinate system which uses parameter values or functions

one-dimensional coordinate reference system which uses parameter values or functions that may vary monotonically with heightNote: A ParametricCS shall have one axis association.

textual description and.sl.or a set of parameters identifying a particular reference surface used as the origin of a parametric coordinate system, including its position with respect to the Earth

specification of a subset of coordinate tuples that is subject to a coordinate operation

mathematical operation that decribes the change of coordinate values within one coordinate reference system due to the motion of the point between one coordinate epoch and another coordinate epoch Note: In this document the motion is due to tectonic plate movement or deformation.

two-dimensional coordinate system in Euclidean space in which position is specified by the distance from the origin and the angle between the line from the origin to a point and a reference directionNote: A PolarCS shall have two axis associations.

origin meridian from which longitude values are determined Note: The default value for prime meridian name is “Greenwich”. When the default applies, the value for the greenwichLongitude shall be 0 (degrees).

derived coordinate reference system which has a geodetic (usually geographic) coordinate reference system as its base CRS, thereby inheriting a geodetic reference frame, is converted using a map projection, and has a Cartesian coordinate system, usually two-dimensional but may be three-dimensionalNote: In the 3D case the base geographic CRSs ellipsoidal height is passed through unchanged and forms the vertical axis of the projected CRS's Cartesian coordinate system.

operations supported in the Coordinate Operations package

A rdf-enabled registry for SRS definitions

definition of the second parameter that defines the shape of a biaxial ellipsoid, or the third parameter that defines a triaxial ellipsoidNote: A biaxial ellipsoid requires two defining parameters: a semi-major axis and inverse flattening or a semi-major axis and a semi-minor axis. When the reference body is a sphere rather than an ellipsoid, only a single defining parameter is required, namely the radius of the sphere; in that case, the semi-major axis “degenerates” into the radius of the sphere.

coordinate reference system consisting of one coordinate system and either one datum or one datum ensemble

single (not concatenated) coordinate operation

a grid that divides space with precise positions relative to a datum and acts as a spatial index

System for identifying position in the real world

three-dimensional coordinate system in Euclidean space with one distance measured from the origin and two angular coordinatesNote: Not to be confused with an ellipsoidal coordinate system based on an ellipsoid .gu.degenerated.gu. into a sphere. A SphericalCS shall have three axis associations.

coordinate reference system associated with a temporal datum and a one-dimensional temporal coordinate system

one-dimensional coordinate system used to record time Note: A TemporalCS shall have one axis association.

one-dimensional coordinate system used to record time as an integer countNote: A TemporalCountCS shall have one axis association.

definition of the relationship of a temporal coordinate system to an objectNote: The object is normally time on the Earth.

one-dimensional coordinate system used to record a time as a real numberNote: A TemporalMeasureCS shall have one axis association.

mathematical operation on coordinates in which parameters are empirically derived from data containing the coordinates of a series of points in both coordinate reference systemsNote: This computational process is usually “over-determined”, allowing derivation of error (or accuracy) estimates for the coordinate transformation. Also, the stochastic nature of the parameters may result in multiple (different) versions of the same coordinate transformations between the same source and target CRSs. Any single coordinate operation in which the input and output coordinates are referenced to different datums (reference frames) will be a coordinate transformation.

A spatial reference system which definition is not known

coordinate reference system having a vertical reference frame and a one-dimensional vertical coordinate system used for recording gravity-related heights or depths; vertical CRSs make use of the direction of gravity to define the concept of height or depth, but the relationship with gravity may not be straightforward. Note 1: If the vertical reference frame is dynamic then the vertical CRS is dynamic, else it is static. Note 2: Ellipsoidal heights cannot be captured in a vertical coordinate reference system. They exist only as an inseparable part of a 3D coordinate tuple defined in a geographic 3D coordinate reference system.

one-dimensional coordinate system used to record the heights or depths of points, usually dependent on the Earth's gravity fieldNote: An exact definition is deliberately not provided as the complexities of the subject fall outside the scope of this document. A VerticalCS shall have one axis association.

textual description and.sl.or a set of parameters identifying a particular reference level surface used as a zero-height or zero-depth surface, including its position with respect to the EarthNote: In 19111:2007 this class was called VerticalDatum.

two- or three-dimensional coordinate system in Euclidean space with straight axes that are not necessarily orthogonal. The number of associations shall equal the dimension of the CS.

boolean value of a coordinate operation parameterNote: A Boolean value does not have an associated unit.

two- or three-dimensional coordinate system in Euclidean space with orthogonal straight axes. All axes shall have the same length unit. A CartesianCS shall have two or three axis associations; the number of associations shall equal the dimension of the CS.

three-dimensional coordinate system in Euclidean space consisting of a polar coordinate system extended by a straight coordinate axis perpendicular to the plane spanned by the polar coordinate system. A CylindricalCS shall have three axis associations.

two- or three-dimensional coordinate system in which position is specified by geodetic latitude, geodetic longitude, and (in the three-dimensional case) ellipsoidal height. An EllipsoidalCS shall have two or three associations; the number of associations shall equal the dimension of the CS.

formula(s) or procedure used by the coordinate operation method

reference to a publication giving the formula(s) or procedure used by the coordinate operation method

identifier of a geographic feature of which the coordinates are used as operation parameters

positive integer value of a coordinate operation parameter, usually used for a countNote: An integer value does not have an associated unit.

ordered collection, i.e. sequence, of two or more integer values of a coordinate operation parameter list, usually used for countsNote: These integer values do not have an associated unit.

inverse flattening value of the ellipsoid

ellipsoid is degenerate and is actually a sphereNote: The sphere is completely defined by the semi-major axis, which is the radius of the sphere. This attribute has the value “true” if the figure is a sphere.

one-dimensional coordinate system that consists of the points that lie on the single axis described. The associated coordinate is the distance – with or without offset – from the origin point, specified through the datum definition, to the point along the axis. Example: usage of the line feature representing a pipeline to describe points on or along that pipeline. A LinearCS shall have one axis association.

n-dimensional coordinate system in which every axis uses integers. The number of associations shall be equal the dimension of the CS.

two-dimensional coordinate system in Euclidean space in which position is specified by the distance from the origin and the angle between the line from the origin to a point and a reference direction. A PolarCS shall have two axis associations.

length of the semi-minor axis of the ellipsoid

three-dimensional coordinate system in Euclidean space with one distance measured from the origin and two angular coordinates. Not to be confused with an ellipsoidal coordinate system based on an ellipsoid .gu.degenerated.gu. into a sphere. A SphericalCS shall have three axis associations.

string value of a coordinate operation parameterNote: A string value does not have an associated unit.

numeric value of the coordinate operation parameter with its associated unit

reference to a file or an identified part of a file containing one or more parameter values.gu. and note changed to .gu.Note: The referenced file or part of a file can reference another part of the same or different files, as allowed in XML documents

citation for a reference to a file or an identified part of a file containing one or more parameter valuesNote: The referenced file or part of a file can reference another part of the same or different files, as allowed in XML documents

ordered collection, i.e. sequence, of two or more numeric values of a coordinate operation parameter list, where each value has the same associated unit