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Symbols, terms and definitions
Symbols and abbreviated terms
a semi-major axis b semi-minor axis CC Change Coordinates (package abbreviation in UML model) CD Coordinate datum (package abbreviation in UML model) CCRS Compound coordinate reference system CI Citation CRS Coordinate reference system CS Coordinate system (also package abbreviation in UML model) DQ Data quality (package abbreviation in UML model) E Easting f flattening h ellipsoidal height H gravity-related height ISO International Organization for Standardization N Northing OGC Open GIS Consortium RS Reference System (package abbreviation in UML model) SC Spatial referencing by Coordinates (package abbreviation in UML model) SI Le Système International d'Unités UML Unified Modeling Language XML eXtensible Markup Language 1D One Dimensional 2D Two Dimensional 3D Three Dimensional λ geodetic longitude φ geodetic latitude X, Y, Z
Cartesian coordinates in a geocentric coordinate reference system i, j, k
Cartesian coordinates in an engineering coordinate reference system, (integer or real)
Terms and definitions
Cartesian coordinate system
Coordinate system which gives the position of points
relative to N mutually-perpendicular straight axes. In the
context of geospatial coordinates the maximum value of N
is three.
Compound coordinate reference system
Coordinate system describing the position of points
through two or more independent coordinate reference systems. For example,
one coordinate reference system can be a two-dimensional horizontal
coordinate system, and the other coordinate reference system can be a
vertical gravity-related height system.
Concatenated transformation
Sequential application of multiple transformations.
Coordinate
One of a sequence of N numbers designating the
position of a point in N-dimensional space. In a coordinate
reference system, the coordinate numbers must be qualified by units.
Coordinate conversion
Change of coordinates, based on a one-to-one relationship,
from one coordinate reference system to another based on the same datum.
For example between geodetic and Cartesian coordinate systems or between
geodetic coordinates and projected coordinates, or change of units such as
from radians to degrees or feet to metres. A conversion uses parameters
which have specified values, not empirically determined values.
Coordinate reference system
Coordinate system which is related to the real world by
a datum. NOTE For geodetic and vertical datums, it will be related to the
Earth.
Coordinate system
Set of (mathematical) rules for specifying how coordinates
are to be assigned to points. One coordinate system may be used in many
coordinate reference systems. The geometric properties of a coordinate space
determine how distances and angles between points are calculated from the
coordinates. For example, in an ellipsoidal (2D) space distances are defined
as curves on the surface of the ellipsoid, whereas in a Euclidean plane as
used for projected CRS distance is the length of a straight line between two
points. The mathematical rules that determine distances and angles are
calculated from coordinates and vice versa are comprised in the concept of
coordinate system.
Coordinate transformation
Computational process of converting a position given in
one coordinate reference system into the corresponding position in another
coordinate reference system. A coordinate transformation can require and use
the parameters of the ellipsoids associated with the source and target
coordinate reference systems, in addition to the parameters explicitly
associated with the transformation. The term "transformation" is used only
when the parameter values associated with the transformation have been
determined empirically from a measurement / calculation process. This is
typically the case when a change of datum is involved.
Covariance matrix
Matrix of elements (or cells) that contain the expected
average values of the product of the error in the matrix row coordinate
times the simultaneous error in the matrix column coordinate. A covariance
matrix is a form of detailed error estimate data. Covariance matrices are
sometimes called variance-covariance matrices. All complete covariance
matrices are symmetrical, meaning that the same element values appear on
both sides of the diagonal elements. Covariance matrices contain information
about the absolute and/or relative accuracy of the data elements (e.g.
coordinates). The absolute accuracy information is contained in the diagonal
matrix elements. Relative accuracy is a function of multiple diagonal and
off-diagonal elements. A complete covariance matrix for N specific
points in 3D space would contain 3N rows by 3N columns.
For example, for three coordinates, a covariance matrix is a 3 by 3 matrix,
with the matrix rows and columns each corresponding to the three coordinates.
For just two horizontal coordinates, a covariance matrix is a 2 by 2 matrix,
with the matrix rows and columns each corresponding to the two horizontal
coordinates. Similarly, for two image coordinates, a covariance matrix is a
2 by 2 matrix, with the matrix rows and columns each corresponding to the two
image coordinates.
Cylindrical coordinates
3-dimensional coordinates with two distance and one
angular coordinate.
Datum
Parameter or set of parameters that determine the location
of the origin, the orientation and the scale of a coordinate reference system.
Depth
Distance of a point below a chosen reference surface usually
measured along the local vertical (gravity vector). Depth is sometimes measured
along a line that does not follow the vector of gravity locally. An example is
depth in an oil or gas well. These are generally measured along the wellbore
path, which may vary significantly from the local vertical. Some sections of
a wellbore path may even run horizontally or slope upwards. Nevertheless the
distance along the wellbore path is referred to as "depth". See elevation,
ellipsoidal height, and gravity-related height.
Dimension
Number of ordinates needed to describe a position in a
coordinate system.
Elevation
Distance of a point from a chosen reference surface along
the direction of the gravity vector from the point to that surface. See
ellipsoidal height and gravity-related height. It should be noted that
ellipsoidal height is defined w.r.t. an ellipsoidal model of the shape
of the earth. Ellipsoidal height is measured from the point along the line
perpendicular to the ellipsoid's surface. Height of a point outside the
surface treated as positive; negative height is also named as depth.
Ellipsoid
Surface formed by the rotation of an ellipse about an axis
In this document the axis of rotation is always the minor axis. Sometimes the
alternative word "spheroid" is used in geodetic or survey practice to express
the same concept. Although mathematically speaking incorrect the more common
term in geodetic or survey practice is "ellipsoid". An alternative term used
in geodetic practice is "reference ellipsoid".
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, associated with one or more geographic coordinate reference
systems.
Ellipsoidal height
Geodetic height
Distance of a point from the ellipsoid
measured along the perpendicular from the ellipsoid to this point, positive
if upwards or outside of the ellipsoid. Only used as part of a three-dimensional
geodetic coordinate system and never on its own.
Engineering coordinate reference system
A coordinate reference system that is defined for and
usually used in a contextually local sense, which may be an area, significantly
less than the complete surface of the earth or a moving platform and its
vicinity. For example local engineering and architectural coordinates, grids,
and drawings; also: vessel navigation systems and CRSs associated with orbiting
spacecraft. A transformation of engineering coordinates to geodetic coordinates
may or may not be possible depending on whether such operation parameters have
been determined (or defined). An Engineering CRS may be defined to describe
geometry that is local to the context of a moving platform, such as a car,
a ship, an aircraft or a spacecraft. Transformation of such engineering
coordinates to geodetic coordinates involves time dependent operation parameters
and, when repeated at (regular) time-intervals, will result in a record of
the "track" of the moving platform. Additionally such a transformation may
be used for real-time navigation of the platform. The term "vicinity of the
moving platform" may constitute an area varying from the immediate surroundings
of the platform to the entire earth, the latter being the case in a number of
space applications.
Flattening
Ratio of the difference between the semi-major (a)
and semi-minor axis (b) of an ellipsoid to the semi-major axis;
f = (a-b)/a.
Sometimes inverse flattening
1/f = a/(a-b)
is given instead of flattening; 1/f is also known as
reciprocal flattening.
Geocentric coordinate reference system
3-dimensional coordinate reference system with its origin
at the (approximate) centre of the Earth.
Geodetic coordinates
Coordinates defined in a geocentric, geographic (2D or 3D)
or projected coordinate reference system.
Geodetic datum
Datum describing the relationship of a 3D or 2D coordinate
system to the Earth. In most cases, the geodetic datum includes an ellipsoid
definition.
Geographic coordinate reference system
Coordinate reference system using an ellipsoidal coordinate
system and based on an ellipsoid that approximates the shape of the Earth. A
geographic coordinate system can be 2D or 3D. In a 3D geographic coordinate
system, the third dimension is height above the ellipsoid surface.
Geographic dataset
Dataset with a spatial content.
Geoid
Level surface which best fits mean sea level either locally
or globally. "Level surface" means an equipotential surface of the Earth's
gravity field that is everywhere perpendicular to the direction of gravity.
Gravity-related height
Height dependent on the Earth's gravity field. In particular,
orthometric height or normal height, which are both approximations of the
distance of a point above the geoid.
Gregorian calendar
Calendar in general use first introduced in 1582 to correct
an error in the Julian calendar. In the Gregorian calendar, common years have
365 days and leap years 366 days divided into 12 sequential months.
Greenwich meridian
Prime meridian passing through Greenwich, United Kingdom.
Most geodetic datums use the Greenwich meridian as the prime meridian.
Ground coordinates
Earth referenced coordinates
Terrestrial coordinates
Coordinates of points expressed in a non-image, earth-fixed
coordinate reference system. The term ground coordinates is used herein to
distinguish such coordinates from image coordinates. Even when an image is
collected by a near vertical camera, image coordinates are different from
ground coordinates.
Image
Record of the likeness of any features, objects, and activities.
An image can be acquired through the sensing of visual or any other segment of the
electromagnetic spectrum by sensors, such as thermal infrared, and high resolution
radar.
Image coordinates
Definition of position within an image, expressed in image
row and column coordinates.
Image geometry model
Mathematical model that specifies the mapping (or projection)
from 3D ground position coordinates to the corresponding 2D image position
coordinates. An image geometry model is alternately called an image sensor model,
sensor model, imaging model, or image mathematical model. The term "sensor" is
often used when the image is generated by a digital camera and is thus originally
digital. The word "camera" is usually used when the image is recorded in analogue
form, normally on film. Of course, film images can be later scanned or digitised
and are then "digital". An image geometry model can also be used to determine the
correct ground position for an image position, if used with additional data. When
a single (or monoscopic) image is used, this additional data normally defines the
shape and position of the visible ground (or object) surface. For example, this
additional data is often a single elevation or is grid elevation data, sometimes
called a Digital Terrain Model (DTM). Alternately, two stereoscopic images or
multiple overlapping images can be used, that show the same ground point viewed
from different directions. In this case, the two (or more) image geometry mathematical
models can also be used, with the point coordinates in each individual image, to
determine the corresponding 3D ground position.
Image version
New image produced by sub-setting and/or re-sampling the
pixels in an original image.
Interface
Named set of operations that characterise the behaviour of
an element. An interface standard specifies the services in terms of the functional
characteristics and behaviour observed at the interface. The standard is a contract
in the sense that it documents a mutual obligation between the service user and
provider and assures stable definition of that obligation.
Latitude
Geodetic latitude
Ellipsoidal latitude
Angle from the equatorial plane to the perpendicular to the
ellipsoid through a given point, northwards treated as positive.
Local datum
Engineering datum
Datum with a local reference, used as a basis for an
engineering coordinate reference system. Engineering datum excludes both
geodetic and vertical datums.
Longitude
Geodetic longitude
Ellipsoidal longitude
Angle from the prime meridian plane to the meridian plane
of the given point, eastward treated as positive.
Map projection
Conversion from a geodetic coordinate system to a planar
surface.
Mean sea level
Average level of the surface of the sea over all stages
of tide. Mean sea level in a local context normally means mean sea level for
the region as measured by tide gauge measurements at one or more points over
a given period of time. Mean sea level in a global context differs from a global
geoid by not more than 2 metres.
Meridian
Intersection of an ellipsoid by a plane containing the minor
axis of the ellipsoid. This term is often used for the pole-to-pole arc rather
than the complete closed figure.
Oblique Cartesian coordinate system
Coordinate system with straight axes that are not necessarily
mutually perpendicular.
Pixel
Two-dimensional picture element that is the smallest
non-divisible element of a digital image. In image processing, the smallest
element of a digital image that can be assigned a grey level. This term
originated as a contraction for "picture element".
Polar coordinates
2-dimensional coordinates in which position is specified
by distance to the origin and the direction angle. NOTE ISO/DIS 19111 does
not specify the number of dimensions and therefore implicitly permits a
3-dimensional polar coordinate system to exist. The equivalent of the latter
is termed "spherical coordinate system" in this document.
Position
Spatial reference of a point or an object.
Prime meridian
Zero meridian
Meridian from which the longitudes of other meridians are
quantified.
Projected coordinate reference system
Two-dimensional coordinate system resulting from a map
projection. A projected coordinate reference system is derived from a 2D
geographic coordinate reference system by applying a parameterised coordinate
transformation known as a "map projection". A projected coordinate reference
system commonly uses a Cartesian coordinate system.
Reference ellipsoid
Ellipsoid used as the best local or global approximation
of the surface of the geoid.
Semi-major axis
Semi-diameter of the longest axis of a reference ellipsoid.
This equates to the semi-diameter of the reference ellipsoid measured in its
equatorial plane.
Semi-minor axis
Semi-diameter of the shortest axis of a reference ellipsoid.
The shortest axis coincides with the rotation axis of the reference ellipsoid
and therefore contains both poles.
Spherical coordinate system.
3-dimensional coordinate system with one distance, measured
from the origin and two angular coordinates, commonly associated with a geocentric
coordinate reference system. Not to be confused with an ellipsoidal coordinate
system based on an ellipsoid "degenerated" into a sphere.
Temporal coordinate
Distance from the origin of the interval time scale used
as the basis for a temporal reference system.
Temporal coordinate reference system
Reference system against which time is measured.
Transformation
Change of coordinates from one coordinate reference system
to another coordinate reference system based on a different datum through a
one-to-one relationship. A transformation uses parameter values which may
have to be derived empirically by a set of points common to both coordinate
reference systems. See coordinate conversion and coordinate transformation.
Unit
Unit of measure
Defined quantity in which dimensioned parameters are
expressed. In this document, the subtypes of units are length units, angular
units, time units, scale units and pixel spacing units.
UTC
Coordinated Universal Time
Time scale maintained by the Bureau International
des Poids et Mesures (International Bureau of Weights and Measures)
and the International Earth Rotation Service (IERS) that forms the basis
of a coordinated dissemination of standard frequencies and time signals.
Vertical coordinate system
1-dimensional coordinate reference system used for
elevation, height, or depth measurements.
Vertical datum
Datum describing the relation of gravity-related heights
to the Earth. In most cases the vertical datum will be related to sea level.
Ellipsoidal heights are treated as related to a three-dimensional ellipsoidal
coordinate system referenced to a geodetic datum. Vertical datums include
sounding datums (used for hydrographic purposes), in which case the heights
may be negative heights or depths.