Coordinate system Topic 2 - Spatial referencing by coordinates

28 Copyright © 2010 Open Geospatial Consortium, Inc. In this Abstract Specification, coordinate systems shall be 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 shall be used only with specific subtypes of coordinate reference system as shown in the UML class diagram in Figure 8 and Table 15. For derived CRSs, the constraints on CS association shall be by derived CRS subtype and follow the constraints for the equivalent subtype of principle CRS. A description of coordinate system subtypes is included in Table 15. This Abstract Specification additionally allows for user-defined coordinate systems. Each of these shall be used with one of the coordinate reference system subtypes described in Clause 8. Table 15 — Subtypes of coordinate system and constraints in its relationship with coordinate reference system CS subtype Description Used with CRS types affine two- or three-dimensional coordinate system with straight axes that are not necessarily orthogonal. Engineering Image Cartesian two- or three-dimensional coordinate system which gives the position of points relative to orthogonal straight axes. All axes shall have the same unit of measure. Geodetic Projected Engineering Image cylindrical three-dimensional coordinate system consisting of a polar coordinate system extended by a straight coordinate axis perpendicular to the plane spanned by the polar coordinate system. Engineering ellipsoidal two- or three-dimensional coordinate system in which position is specified by geodetic latitude, geodetic longitude and in the three-dimensional case ellipsoidal height. Geodetic linear one-dimensional coordinate system that consists of the points that lie on the single axis described. Example: usage of the line feature representing a pipeline to describe points on or along that pipeline. This Abstract Specification only lends itself to be used for simple =continuous linear systems. For a more extensive treatment of the subject, particularly as applied to the transportation industry, refer to ISO 19133 [7]. Engineering polar two-dimensional coordinate system in which position is specified by distance from the origin and the angle between the line from origin to point and a reference direction. Engineering spherical three-dimensional coordinate system with one distance, measured from the origin, and two angular coordinates. Not to be confused with an ellipsoidal coordinate system based on an ellipsoid ‘degenerated’ into a sphere. Geodetic Engineering vertical one-dimensional coordinate system used to record the heights or depths of points dependent on the Earth’s gravity field. An exact definition is deliberately not provided as the complexities of the subject fall outside the scope of this specification. Vertical Coordinate systems are described further in B.2.1.

9.3 Coordinate system axis

A coordinate system shall be composed of a non-repeating sequence of coordinate system axes. Each of its axes shall be completely characterized by a unique combination of axis name, axis abbreviation, axis direction and axis unit. Aliases for these attributes may be used as described in Clause 7. Copyright © 2010 Open Geospatial Consortium, Inc. 29 EXAMPLE 1 The combination {Latitude, Lat, north, degree} would lead to one instance of the object class “coordinate system axis”; the combination {Latitude, j, north, degree} to another instance, the axis abbreviation being different. In this Abstract Specification, usage of coordinate system axis names shall be constrained by geodetic custom, depending on the coordinate reference system type. These constraints are shown in Table 16. This constraint shall work in two directions. EXAMPLE 2 As “geodetic latitude“ and “geodetic longitude” are used as names for coordinate axes forming a geodetic coordinate reference system, these terms cannot also be used in another context. Aliases for these constrained names shall be permitted. Table 16 — Naming constraints for coordinate system axis CS type When used in CRS type Permitted coordinate system axis names Cartesian geodetic geocentric X, geocentric Y, geocentric Z Cartesian projected northing or southing, easting or westing ellipsoidal geodetic geodetic latitude, geodetic longitude, [ellipsoidal height if 3D] spherical geodetic spherical latitude, spherical longitude, geocentric radius vertical vertical depth or gravity-related height Image and engineering coordinate reference systems may make use of names specific to the local context or custom. Coordinate system axes are described further in B.2.2.

9.4 UML schema for the Coordinate System package

Figure 7 shows the UML class diagram of the CS_CoordinateSystem package. The associations between Coordinate Reference System subtypes and Coordinate System subtypes are shown in the UML class diagram in Figure 8. The definitions of the object classes of the CS_CoordinateSystem package are provided in Tables 17 through 32.