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Building Spatial Databases – Theory / Vector data model

Learners guide

Summary

In this unit the principles of vector data model will be introduced, and the vector-based model of spatial data will be shown. The relationships of geometric primitives, the topology and basic spatial functions will be discussed, which are the basis of the spatial selections.

Requirement

To make the self-test successfully.

Vector data model

Vector data model represents geometrical objects with characteristic information like points position, which are (x, y) coordinates for two-dimensional data, and (x, y, z) coordinates for three-dimensional data. We should also know and store the projection system definition of coordinates. Supposedly, software programs responsible for storing geometrical data can process coordinate systems.

Every feature contains a set of point coordinates connected by rules (the simplest case is by incoming order). Objects are defined with graphs. Lines and polygons are built up by characteristic points like vertexes or nodes.

How can one decide which points are characteristic? In order to answer this question, let us take a closer look at an example of data input for vector-based data. Data source can be remote sensing imagery or aerial photography images. In order to vectorize input data, we must detect control objects like rivers, roads, buildings and their characteristic points (reference points of buildings, road junction points, river junction points, etc.). These points can be detected relatively easily. However, the substantial part is object detection, which can be done with human interaction's knowledge, experience and expertise. Without this, vectorization process cannot be delivered.

Another consideration aspect is based on the purpose of using the vectorized map. According to predefined purpose of usage, the list of important, less important and negligible objects are known before starting the vectorization process. For example, in the case of vectorizing administration maps based on scanned paper-based maps, every administrative boundary is important data; on the contrary, rivers are less important, although not negligible. Streams can be neglected, therefore they are not presented on the digitized map (even if they were present on the paper-based map).

You can open the (larger) image in new window.Fig.20. A model of reality represented by vector based model20_eletkep_vektor_full.jpgFig.20. A model of reality represented by vector based model

Figure 20. On the right hand side is the reality, which will be stored and represented in vector data model.

In vector-based representation as described in Figure 20, objects are projected perpendicularly to the surface in a coordinate system, which is scaled in North-South orientation. During the process of vectorization based on paper maps, human interaction is required with expertise in order to detect and select measure and characteristic points. At the end, our conclusion is that human interaction with vast background-knowledge is required in the process of vectorization.

Figure 21 (left hand side). Examples of one-dimensional objects a) line segment (section); b) linestring (polyline) with extreme points (end points) and vertices; c) non-intersected linestring; d) closed polyline; e) monotone polyline; f) non-monotone polyline;

Figure 21 (right hand side). Examples of two-dimensional objects aa) simple polygon; bb) complex-polygon (only exists as invalid object in geoinformatics); cc) convex-polygon; dd) monotone polygon; ee) polygon with inner structure (hollow polygon); ff) region with geometrically non-related objects [Rigaux et al]

As represented in Figure 20, the real objects are vectorized. For modelling real world objects, geometric elements are used, like 0-dimension points and 1-dimension lines. A special case for lines is a polyline, which is a sequence of connected lines (by connecting lines, a constraint has been stated on the vector data model by introducing topological relation between lines). The other geometrical object is a two-dimensional polygon built up by a sequence of points (Figure 21). A more accurate definition for a polygon is a sequence of connected segments, having identical start and end point; moreover, its topmost attribute is that it is a closed area. Connectivity and closeness are topological constraints on connected segments.

Figure 22. How complex features are built up from simple features (geometric primitives) 1 -- level of nodes; 2 -- level of lines and polygons; 3 -- level of features; 4 -- level of complex features.

As represented in Figure 22, only on base level, the nodes contain coordinate data. Other features higher than the node level, like linestring and polygons, contain only structural information. They describe information with related features on lower abstraction level, which means that storing geometrical data is not sufficient; therefore, creating relationship between hierarchy levels is also required. For example, features on lines and polygons level should contain corresponding data on the sequence of related points creating lines or polygons. The vector data model has various advantages, like

Figure 23 describes data stored in the database. Additional information and attributes can be added in the form of database tables, if business logic requires so.

Figure 23. Schematic diagram of the relationship between graphical and descriptive data. The relation between graphical objects and descriptive data is 1 : 1.

Figure 24. By creating feature groups yields adaptive data structures. Object-oriented systems name it a feature-class (attribute class), while the software developers based on classical CAD terminologies prefer calling it a layer. This is an example of a calculated feature class, the value of a real estate, which comes from the parcels, buildings and public utility classes.

For the ease of handling, vector data should be grouped logically depending on our purpose. Arbitrary grouping based on the declaration of the system designer or developer could be a grouping method, where the designer's job is to sort objects into groups (feature classes or layers); this job goes along with greater responsibility over the system. Data can be grouped by feature attributes. Grouping can be fixed with non-variable data or flexible with dynamic grouping conditions.

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