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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.
*
*
* CS CRS Permitted coordinate system axis names Cartesian Geocentric
* Geocentric X, Geocentric Y, Geocentric Z Spherical Geocentric
* Spherical Latitude, Spherical Longitude, Geocentric Radius Ellipsoidal Geographic
* Geodetic Latitude, Geodetic Longitude, Ellipsoidal height (if 3D) Vertical Vertical
* Gravity-related height Vertical Vertical
* Depth Cartesian Projected
* Easting, Northing Cartesian Projected
* Westing, 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;