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/*
 *    GeoTools - The Open Source Java GIS Toolkit
 *    http://geotools.org
 *
 *    (C) 2011, Open Source Geospatial Foundation (OSGeo)
 *    (C) 2004-2005, Open Geospatial Consortium Inc.
 *
 *    All Rights Reserved. http://www.opengis.org/legal/
 */

/**
 * {@linkplain org.opengis.referencing.cs.CoordinateSystem Coordinate systems} and their {@linkplain
 * org.opengis.referencing.cs.CoordinateSystemAxis axis}. The following is adapted from OpenGIS® Spatial Referencing
 * by Coordinates (Topic 2) specification.
 *
 * 

Coordinate system

* *

The coordinates of points are recorded in a coordinate system. A coordinate * system is the set of coordinate system axes that spans the coordinate space. This concept implies * the set of mathematical rules that determine how coordinates are associated with invariant * quantities such as angles and distances. In other words, a coordinate system implies how * coordinates are calculated from geometric elements such as distances and angles and vice versa. * The calculus required to derive angles and distances from point coordinates and vice versa in a * map plane is simple Euclidean 2D arithmetic. To do the same on the surface of an ellipsoid * (curved 2D space) involves more complex ellipsoidal calculus. These rules cannot be specified in * detail, but are implied in the geometric properties of the coordinate space. * *

* *

NOTE: The word "distances" is used loosely in * the above description. Strictly speaking distances are not invariant quantities, as they are * expressed in the unit of measure defined for the coordinate system; ratios of distances are * invariant. * *

* *

One {@linkplain org.opengis.referencing.cs.CoordinateSystem coordinate system} * may be used by multiple {@linkplain org.opengis.referencing.crs.CoordinateReferenceSystem * coordinate reference systems}. A coordinate system is composed of an ordered set of coordinate * system axes, the number of axes being equal to the dimension of the space of which it describes * the geometry. Its axes can be spatial, temporal, or mixed. Coordinates in coordinate tuples shall * be supplied in the same order as the coordinate axes are defined. * *

The dimension of the coordinate space, the names, the units of measure, the * directions and sequence of the axes are all part of the Coordinate System definition. The number * of coordinates in a tuple and consequently the number of coordinate axes in a coordinate system * shall be equal to the number of coordinate axes in the coordinate system. It is therefore not * permitted to supply a coordinate tuple with two heights of different definition in the same * coordinate tuple. * *

Coordinate systems are divided into subtypes by the geometric properties of * the coordinate space spanned and the geometric properties of the axes themselves (straight or * curved; perpendicular or not). Certain subtypes of coordinate system can only be used with * specific subtypes of coordinate reference system.
* *

Coordinate system axis

* *

A coordinate system is composed of an ordered set of coordinate system axes. * Each of its axes is completely characterised by a unique combination of axis name, axis * abbreviation, axis direction and axis unit of measure. * *

The concept of coordinate axis requires some clarification. Consider an * arbitrary x, y, z coordinate system. The x-axis may * be defined as the locus of points with y = z = 0. This * is easily enough understood if the x, y, z coordinate system is * a Cartesian system and the space it describes is Euclidean. It becomes a bit more difficult to * understand in the case of a strongly curved space, such as the surface of an ellipsoid, its * geometry described by an ellipsoidal coordinate system (2D or 3D). Applying the same definition * by analogy to the curvilinear latitude and longitude coordinates the latitude axis would be the * equator and the longitude axis would be the prime meridian, which is not a satisfactory * definition. * *

Bearing in mind that the order of the coordinates in a coordinate tuple must * be the same as the defined order of the coordinate axes, the "i-th" coordinate axis of * a coordinate system is defined as the locus of points for which all coordinates with sequence * number not equal to "i", have a constant value locally (whereby i = * 1...n, and n is the dimension of the coordinate space). * *

It will be evident that the addition of the word "locally" in this definition * apparently adds an element of ambiguity and this is intentional. However, the definition of the * coordinate parameter associated with any axis must be unique. The coordinate axis itself should * not be interpreted as a unique mathematical object, the associated coordinate parameter should. * For example, geodetic latitude is defined as the "Angle from the equatorial plane to the * perpendicular to the ellipsoid through a given point, northwards usually treated as positive". * However, when used in an ellipsoidal coordinate system the geodetic latitude axis will be * described as pointing "north". In two different points on the ellipsoid the direction "north" * will be a spatially different direction, but the concept of latitude is the same. * *

Furthermore the specified direction of the coordinate axes is often only * approximate; two geographic coordinate reference systems will make use of the same ellipsoidal * coordinate system. These coordinate systems are associated with the earth through two different * geodetic datums, which may lead to the two systems being slightly rotated w.r.t. each other. * *

Usage of coordinate system axis names is constrained by * geodetic custom in a number of cases, depending mainly on the coordinate reference system * type. These constraints are shown in the table below. This constraint works in two * directions; for example the names "geodetic latitude" and "geodetic longitude" shall be used to * designate the coordinate axis names associated with a geographic coordinate reference system. * Conversely, these names shall not be used in any other context. * *

* * * * * * * * * * * * * * * *
CSCRSPermitted coordinate system axis names
CartesianGeocentricGeocentric X, Geocentric Y, Geocentric Z
SphericalGeocentricSpherical Latitude, Spherical Longitude, Geocentric Radius
EllipsoidalGeographicGeodetic Latitude, Geodetic Longitude, Ellipsoidal height (if 3D)
VerticalVerticalGravity-related height
VerticalVerticalDepth
CartesianProjectedEasting, Northing
CartesianProjectedWesting, Southing
* *

Image and engineering coordinate reference systems may make use of names * specific to the local context or custom and are therefore not included as constraints in the * above list. * * @version Abstract * specification 2.0 * @since GeoAPI 1.0 */ package org.opengis.referencing.cs;





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