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/*
* GeoAPI - Java interfaces for OGC/ISO standards
* http://www.geoapi.org
*
* Copyright (C) 2004-2011 Open Geospatial Consortium, Inc.
* All Rights Reserved. http://www.opengeospatial.org/ogc/legal
*
* Permission to use, copy, and modify this software and its documentation, with
* or without modification, for any purpose and without fee or royalty is hereby
* granted, provided that you include the following on ALL copies of the software
* and documentation or portions thereof, including modifications, that you make:
*
* 1. The full text of this NOTICE in a location viewable to users of the
* redistributed or derivative work.
* 2. Notice of any changes or modifications to the OGC files, including the
* date changes were made.
*
* THIS SOFTWARE AND DOCUMENTATION IS PROVIDED "AS IS," AND COPYRIGHT HOLDERS MAKE
* NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
* TO, WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE OR THAT
* THE USE OF THE SOFTWARE OR DOCUMENTATION WILL NOT INFRINGE ANY THIRD PARTY
* PATENTS, COPYRIGHTS, TRADEMARKS OR OTHER RIGHTS.
*
* COPYRIGHT HOLDERS WILL NOT BE LIABLE FOR ANY DIRECT, INDIRECT, SPECIAL OR
* CONSEQUENTIAL DAMAGES ARISING OUT OF ANY USE OF THE SOFTWARE OR DOCUMENTATION.
*
* The name and trademarks of copyright holders may NOT be used in advertising or
* publicity pertaining to the software without specific, written prior permission.
* Title to copyright in this software and any associated documentation will at all
* times remain with copyright holders.
*/
/**
* {@linkplain org.opengis.referencing.cs.CoordinateSystem Coordinate systems} and their
* {@linkplain org.opengis.referencing.cs.CoordinateSystemAxis axis}. The following is adapted from
* {@linkplain org.opengis.annotation.Specification#ISO_19111 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 or Depth Cartesian Projected
* Easting or Westing,
* Northing or 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.
*
* @departure constraint
* ISO 19111 defines GeodeticCS, EngineeringCS and ImageCS
* unions for type safety, which ensures, for example, that a GeodeticCRS only be
* associated to a CartesianCS, an EllipsoidalCS or a SphericalCS.
* However the union construct found in some languages like C/C++ is not available
* in Java. In the particular case of ImageCS, the same type-safety objective can
* be obtained through a slight change in the interface hierarchy (see the departure documented
* in CartesianCS). For the other two unions (GeodeticCS and
* EngineeringCS), no workaround is proposed.
*
* @author Martin Desruisseaux (IRD)
* @version 3.0
* @since 1.0
*/
package org.opengis.referencing.cs;