acre The Dimensional World

Euclidean metric space that is assumed to exist at least locally throughout the Geospatial World.

2.6. The Dimensional World

The Dimensional World is an abstraction of the Geospatial World where we become equipped with measuring tools such as tape measure, theodolites, GPS, andor compass. The facts that are recognized at this level of abstraction include unary relations such as length of an arc, and bearing of a horizontal line and binary relations such as distance between two points, buffer zone, and the “contains” relation that are abstractions of the features themselves. Other examples include North, overlap, touch, dimensionality, intersect, and so forth. abstraction localize Discipline IF Discipl ine Metric Dime nsional World fit instrument abstraction Local Metric IF 1600 sq. ft . 100 ft. 32 o E as t of N or th Ν codify

0.16 acre

Figure 2-8: The Dimensional World The method by which the Dimensional World interfaces to the Geospatial World is called fit. A distance between two telephone poles is a fact that belongs to the Dimensional World. A wire of this length fits the span between them as seen in the Geospatial World. We include in Figure 2-8 some of the abstractions that are present in the Dimensional World. The Dimensional World is the last of the “generic geospatial” abstractions of the Real World. The next abstraction is called a Domain World some authors use the term “World View” with a similar meaning that occurs only in the context of an actual domain implementation. Each implementation is specific to a particular discipline or sub- discipline or a combination of a few of them. In each actual implementation, only a subset of the Dimensional World is recognized. Often, the subset is determined by map neat lines and by the particular phenomena that have been instrumented. In addition to the elimination of all but the features of specific interest to the particular domain discipline or disciplines, there is another abstraction at the Project World level: we introduce the notion of a project-wide Coordinate Reference System CRS. The most common CRS establish a coordinate structure around the abstraction we call the Earth’s surface, but there are other indirect reference methods, such as the use of a linear reference technique to identify points with a single parameter e.g., highway mileposts. Whatever the method, we shall insist that all the coordinates that define the geometry of the features abstracted into the Project World carry an abstraction that can be defined by the Coordinate Reference System abide by the coordinate system framework. Hence, coordinates are defined to be a collection of points sufficient for the geometric construction of the geospatial extent of any feature of interest. For the purposes of this document, he term “coordinate” is meant to be generic; it includes “poles” for spline The OpenGIS ® Abstract Specification Page 9 Volume 5: Topic 5: Features construction, “knots” for NURB construction, “center” for circle construction, and so forth. The interface between the Dimensional World and the Project World is called the Community Interface. The method for invoking the Community Interface from a feature in the Dimensional World is called codify, and results in a coordinate system being invoked in terms of which all the features’ corners can be abstracted as an n-tuple n is usually 2 or 3 or into an equivalent abstraction. Conversely, a feature with known coordinates in the Project World can invoke the localize interface to result in the feature’s proper placement relative to other features in the Dimensional World, and with appropriate measurements.

2.7. The Project World or The “World View”