Glossary¶

Coordinate system (CS)¶

A coordinate system (CS) defines how coordinates are expressed by specifying the coordinate axes, their order, orientation, and the units used to measure positions within the system. A coordinate system is an abstract mathematical construct and, by itself, is not physically anchored to the Earth or any other real-world object.

Datum¶

A datum defines the relationship of a coordinate system to the Earth by specifying the origin and orientation of the coordinate system relative to the Earth. This makes the resulting coordinates unambiguous and allows them to represent real-world positions.

CRS¶

A Coordinate Reference System (CRS) defines the meaning of a set of coordinates by combining a coordinate system, which specifies the axes, axis order, and units, with a datum that anchors the coordinate system to the Earth.

Conversion¶

A coordinate operation that stays on one datum: a map projection, a unit change, an axis swap. Exact, and applied without being named.

Coordinate operation¶

Any conversion or transformation between two CRSs.

Transformation¶

A coordinate operation that changes the datum. Multiple transformations may exist between the same source and target CRS, depending on the area of use, required accuracy, coordinate epoch, and available transformation parameters or grids.

Authority code¶

A unique identifier assigned to an object in an authoritative register, such as EPSG:4326. It consists of an authority name and a code, which together uniquely identify the object.

Bound CRS¶

A CRS that is explicitly linked to another CRS, known as the hub CRS, through a predefined coordinate transformation. Because the transformation is selected and included as part of the CRS definition, this is known as early binding. It helps users without specialised geodetic knowledge apply the intended transformation without having to choose between multiple available operations at runtime. The hub CRS is commonly WGS 84. A bound CRS is represented as BOUNDCRS in WKT2 and EBC in an OSDU payload. See Bound CRSs.

Concatenated operation¶

A published chain of operations applied in sequence, such as the datum transformation EPSG:8047 = EPSG:1147 + EPSG:1146.

Area of use¶

The region an operation is published as valid for, as a bounding box and a description. Reported on every OperationCandidate. Not enforced.

Accuracy of a transformation¶

The expected absolute difference, expressed in metres, between a transformed position and the position that would be obtained by directly determining the same physical point in the target CRS.

The calculation itself is exact, deterministic, and repeatable. The stated accuracy describes the limitations of the transformation model, not its arithmetic or numerical precision.

For example, a seven-parameter Helmert transformation applies a uniform translation, rotation, and scale to the entire reference frame. It cannot correct local distortions within a geodetic network, whereas a grid-based transformation such as NTv2 can model spatially varying corrections. The accuracy is generally a representative value without a formal confidence level and applies only within the transformation’s area of use. Differences between two transformations do not indicate their accuracy, since neither result is necessarily the reference value.

Early binding¶

Selecting a specific transformation in advance and including it as part of the CRS definition, as is done with a bound CRS. This ensures that the predefined transformation is used without requiring a transformation to be selected at runtime. The opposite of late binding.

Late binding¶

Selecting the most appropriate transformation at runtime, based on the source and target CRSs and the context of the operation. The selection may consider factors such as the area of use, required accuracy, coordinate epoch, and available transformation grids. Represented as LBC in an OSDU payload. The opposite of early binding.

Declared axis order¶

The order in which the coordinate axes are defined by a CRS, such as latitude followed by longitude in EPSG:4326. The declared axis order is an integrated part of the CRS definition.

Coordinate epoch¶

The time coordinates were observed at, as a decimal year. Required by operations that model motion over time.

Dynamic CRS¶

A CRS based on a dynamic datum or reference frame that accounts for changes in the Earth over time, including tectonic plate motion. Its datum has a frame reference epoch at which the reference frame is defined. This is distinct from the coordinate epoch, which specifies when an individual position applies.

For example, coordinates in an ITRF realisation change over time as the Eurasian tectonic plate moves, while ETRS89 moves with the stable part of the Eurasian plate so that coordinates remain approximately fixed relative to Europe. Consequently, coordinates for the same physical location expressed in ITRF and ETRS89 increasingly differ as time passes. Compare static CRS.

Static CRS¶

A CRS based on a static datum or reference frame that does not explicitly account for changes in the Earth over time. It can be understood as a snapshot of a dynamic reference frame at a specified epoch. Coordinates are treated as constant, even though the physical location may move because of tectonic plate motion, land uplift, or local deformation.

For example, ETRS89 was defined to coincide with ITRS at epoch 1989.0, approximately 1 January 1989, and was then fixed to the stable part of the Eurasian plate. ETRS89 coordinates therefore remain approximately constant relative to Europe, while coordinates in an ITRF realisation change over time as the tectonic plate moves. Consequently, ETRS89 and ITRF coordinates for the same physical location increasingly differ as time passes. Compare dynamic CRS.

Ballpark¶

PROJ’s fallback when it knows no transformation between two datums. It treats them as the same and states no accuracy. Errors can be hundreds of metres. Never returned by this package.

Grid¶

A file containing position-dependent correction values used by a coordinate operation. The correction applied at a given location is interpolated from the surrounding grid values. Grids may provide horizontal shifts, vertical corrections, deformation values, or velocities. Examples include NTv2 and NADCON grids for horizontal transformations and geoid models for converting between ellipsoidal and gravity-related heights.

Helmert transformation¶

A transformation between source and target geocentric CRSs using seven parameters:

three translations \((t_X, t_Y, t_Z)\)
three rotations \((r_X, r_Y, r_Z)\)
one scale difference \(dS\).

The transformation can be expressed as:

\[\begin{split}\begin{bmatrix} X_t \\ Y_t \\ Z_t \end{bmatrix} = (1 + dS) \begin{bmatrix} 1 & -r_Z & r_Y \\ r_Z & 1 & -r_X \\ -r_Y & r_X & 1 \end{bmatrix} \begin{bmatrix} X_s \\ Y_s \\ Z_s \end{bmatrix} + \begin{bmatrix} t_X \\ t_Y \\ t_Z \end{bmatrix}.\end{split}\]

Hub CRS¶

The intermediate CRS to which a bound CRS is linked through its predefined transformation. The hub CRS provides a common reference through which coordinates can be transformed to other CRSs. It is commonly WGS 84.

persistableReference¶

OSDU’s JSON envelope around ESRI WKT, stating a CRS, transformation or unit. See Persistable references (OSDU).

Pipeline¶

PROJ’s explicit, step-by-step description of a coordinate operation. Each step represents an individual operation, such as an axis swap, unit conversion, map projection, grid shift, or datum transformation, and the steps are applied sequentially. A pipeline records exactly how coordinates are transformed and can be reused with PROJ or pyproj to reproduce the operation.

Route¶

How the transformer that produced a result was arrived at. It is recorded on every result as OperationRoute and is one of:

transformer_group: the operation was selected from the candidates PROJ offers for the source and target CRS pair.
chained: the operation was built from the one requested, wrapped in conversions that stay on the same datum.
bound: the operation was taken from the transformation that a bound CRS carries in its own definition.
proj_default: no operation was requested, so PROJ chose one and the choice is recorded.

See Results and provenance.

Stated operation¶

A coordinate operation given in full, with its method and parameters, instead of being named by an authority code or a name. Examples are an OSDU persistableReference payload, an ESRI GEOGTRAN string and a pyproj CoordinateOperation.

A named operation is looked up in the database, so the parameters used are those the database holds under that code. A stated operation is applied exactly as stated, even when its code is also in the database with different parameters. It is applied alone and cannot be combined with other named operations in a list.

See A stated operation.

Value order¶

The order of the numbers you pass and receive. Always xy in this package: longitude before latitude, easting before northing, then height, wherever the CRS has such axes; a CRS without an east/north pair keeps its declared order.