The abstraction of the real world

The abstract process of geographical objects is generally considered to have nine levels [OGC],which are connected to them through eight interfaces between these nine levels, defining a transformation model from the real world to the world of geographic feature sets.These nine levels are Real World, Conceptual World, Geospatial World, Dimensional World, Project World, Points World, Geometry. Geometry World, Feature World, and Feature Collection World (Figure 2-8). The eight interfaces connecting them are Epistemic interface, GIS Discipline interface, Local Metric interface, Community interface, Spatial Reference interface, Geometric structure interface, Feature structure interface and project structure interface. The first five models are abstractions of the real world and are not implemented in computer software; the latter four models are mathematical and symbolic models of the real world that will be implemented in software.


Nine model of OpenGIS

Real world

The real world is a collection of all things, whether people know them or not. According to the nature of things, people can understand and understand things in the real world. Figure 2-9 shows the real world in which human beings live. Cloud-like texture structure occupies the vast majority of the graphics, representing things that people do not understand, and they create a chaotic state of the universe. People only know some familiar facts, some of which are drawn in the graph.


Real world

conceptual world

The conceptual world is the world of human natural language. Human beings understand and recognize the things they name. Therefore, these things constitute the “world of language”. In the conceptual world of Figure 2-10, clouds representing the chaotic state of the universe do not exist because they are usually invisible in natural language content. The sketch shows easily identifiable things: doors, roads, bricks, roofs, houses, etc. In this way, we can return to the real world and abstract the essence of a fact, called the essence (Pith). The interaction between the real world and the conceptual world is called Epistemic Interface because it can give the names of the known things and feel the essence of the same known things.


Conceptual world

For GIS, the conceptual world of natural language is not sufficiently abstract. In GIS, only a simplified subset of the conceptual world is of interest. This subset is called the geospatial world, and the way people interact with the conceptual world is called choice.

In Figure 2-11, there are three entity types. Each is represented by a rectangle, and each is represented by its upper name. The lines between rectangles represent the connections between entities, and each line has a function name at the end to explain the connections. The diamond represents Aggregation. For example, the existence of the conceptual world depends on the existence of the real world. Solid circles mean that there is a set (not a single object) at the end of the connection. For example, each conceptual world is embedded in a series of different geospatial worlds.


Links between the Real World and the Geospatial World

Geospatial World

Technicians engaged in GIS are accustomed to seeing the world as an abstract, almost cartoon-like world. This is because the world at the conceptual level is full of complex shapes, styles and details. These complexities are eliminated in the geospatial world and replaced with simple and shallow abstractions,that are usually static in both time and space. Through the abstraction of the geospatial world, rivers are regarded as lines, terrain as simplification of contour polygons, and forests are treated as polygons.

The conceptual world described above is redrawn in a cartoon manner on the geospatial world level in Figure 2-12. Figure 2-12 is drawn in perspective, but the geospatial world is usually viewed from a “vertex”, that is,viewed vertically from top to bottom. Note that in the figure, some features have disappeared and others have been greatly simplified. For example, some windows, walls and roofs of buildings have disappeared. This is because they are not interested in the perspective of the GIS world. They have become invisible in the consciousness of GIS. Of course, there is no universal definition - exactly what features are of interest to a GIS technician, and maybe sometimes a roof might be of interest. Cartoons only show that the geospatial world is a subset and a simplification of the conceptual world. The language spoken in the geospatial world is the subject language of GIS. In the figure, the foundation of the house remains, although in the conceptual world, part of the foundation is hidden behind other elements. From the point of view of GIS, all foundations of a building are visible - although some are invisible. Each GIS implementation has specific rules that specify what features are recognized in the geospatial world and how they are simplified from the conceptual world. For example, a rule can simplify a brick house into a three-dimensional polyhedron; however, a house with another surface material is simplified into its foundation polygon. Simply put, things that are invisible in the conceptual world become visible in the geospatial world because they are of special interest in GIS. The interaction between conceptual world and geospatial world is called GIS subject interface, and the interaction method from conceptual space is called selection. In order to transform this interaction from geospatial to conceptual world, people can adopt Embed method, which places the content of interest in GIS in the appropriate context of the conceptual world.

The elements that are recognized in the geospatial world usually have a natural dimension: 0, 1, 2 or 3, depending on whether they are regarded as points, lines, surfaces and bodies. In addition, according to binary topological relationships (such as inclusion, adjacency or separation), they also have additional measures. The next level of abstraction identifies the inherent dimensionality and Metrics characteristics of elements, so it is called the dimension world, which can be measured by tools in Euclidean space.


Geospatial World

Dimensional World

The Dimensional world is an abstraction of geospatial world, including some measuring tools, such as tape measure and compass. The facts recognized at this level include the Unary relation (such as the length of an arc) and the Binary relation (such as the distance between two points), which are themselves abstractions of various elements.

The interface between the dimensional world and the geospatial world is called Fit. The distance between the two telephone line poles belongs to the world of dimension. This length line is suitable for the length span seen in the geospatial world, and some of the abstractions represented in the dimension space are included in Figure 2-13.

Dimensional world is the last abstraction of the real world. The next abstraction is called a project world, which only occurs in a specific implementation, each of which is aimed at a particular GIS discipline or sub-discipline. In each actual implementation, only one subset of the dimension world is identified. Usually this subset is determined by the scope of the study area and the specific phenomena to be measured.

At the level of project world, the concept of the Spatial Reference System was introduced. The most common reference system is the coordinate system (longitude and latitude) built around the earth’s surface. In addition, there are other indirect reference systems, such as linear reference system, which can identify a point on a line (such as a highway) with a parameter. No matter which coordinate reference system is adopted, the coordinates of each “corner point” of the elements in the dimension world can be determined. The interface between the dimension world and the project world is called the information group interface, and the method of calling the interface from the dimension world is called codify. The result is that the coordinates of each “corner point” are represented by a set of numerical values. On the contrary, the method invoked from the project world is called positioning, which determines the relative relationship between each element and other elements.


Dimensional World

Project World

There are two commonly used methods to model geospatial elements. The first model defines the spatial range of an element of points, lines and polygons, as well as a set of known primitive geometric elements, in which the element is called “Features with Geometry”.

The second type is called Coverage. Image is a special example of this model. Geometric elements and coverage are closely related, but they are quite different in concept.

Feature models are used to model real-world objects in the real world, such as roads, cities and so on, while coverlay models are used to model phenomena, including temperature, soil distribution and so on. A element has many attributes, such as spatial location attributes, spatial relationship attributes, description attributes, time attributes and so on. Coverage can also be regarded as an attribute of a feature.

GIS is not just a discipline, It is also a language for the representation of geospatial information. The information comes from many disciplines related to geography, such as forest management, soil mapping, transportation model, cadastral management, etc. Each of these disciplines has many sub-disciplines, and a GIS project can contain any combination of these disciplines.

It is the diversity of project world languages that leads to the most complex problem of interaction between GIS information storage. This is the reason why the geospatial world is artificially divided. However, if the language structure is fully unified,that this situation can be managed.

Geographic information organizations refer to users who share data. They belong to different professional fields. They can be data users or data providers. The geographic information community regards a special subset of the whole geospatial world as an abstraction. In three different applications, the above examples are abstracted into three different project world models. They are shown in Figure 2-14, reflecting the project world from the perspective of a cartographer, a Cadastral manager and a road manager, respectively.


Project World


* Because the four levels behind the nine-tier model are related to software implementation and involve specific data structures, this chapter does not introduce them. We can refer to the contents of the two chapters of “Spatial Data Model” and “Spatial Data Management”. This chapter only introduces the first five models - abstracting the real world and getting digitized models that can be managed by GIS.