GIS For Dummies

and convey some basic spatial relationships that humans express by using an English language construct called the prepositional phrase. (Don’t worry. You don’t have to diagram sentences.)

In everyday language, you use many prepositional phrases that describe the spatial relationships you encounter. For example, you may live “outside a town,” “next to your neighbor,” and “within the county.” You travel roads that go “through forests,” “along rail lines,” and “over hills.” The data models discussed in the section “Simple forms of vector representation,” earlier in this chapter, don’t have these relationships (known as topological relationships) explicitly coded. You need to incorporate the mathematics of these relationships — the topology — into the data model so that you don’t have to calculate these spatial relationships each time you want to analyze something.

Using the mathematics of neighborhood

When you look at a map, you can easily see where everything represented on the map is relative to everything else on that map. For example, when you look at a map of your own neighborhood, you get an instant view of that neighborhood. You can see shortcuts, recognize which places are close to your house and which are far from your school, determine what’s on each side of your street, and know which streets are connected to each other and which aren’t. To replicate this powerful property of the human brain inside the computer, computer scientists employ a branch of mathematics called

topology that studies the positions and relative locations of geometric figures. I like to call it the “mathematics of neighborhood” because it allows the computer to understand how a neighborhood works (including what features are located there, where they are relative to each other, and how to find them).

Because computers can’t reason or look around at their neighborhoods, you have to tell them everything. And so you explain

Each line you create is linked to other lines. If the computer understands these connections, you can move from one link to another, just like you’d drive your car from one street to another.

The classifications of nearby areas. Say that on the left side of a line (perhaps your street) is a polygon (a parcel of land) that’s agricultural, and on your right side is a single-family residential parcel.

The U.S. Bureau of the Census needed computers that understood the connections and classifications used in its work. This need led the bureau to develop two of the more well-known topological data models — the Dual Independent Map Encoding (DIME) and subsequent Topologically Integrated Geographical Encoding and Referencing (TIGER) models (discussed in the following section).

Figure 5-7 shows a generic topological vector model. All the others, including commercial ones, are based on this model, with minor variations. The left side of the figure shows several points, lines, and polygons, all of which are numbered:

Points: The numbers that have circles around them

Lines: The numbers that interrupt the lines

Polygons: The numbers inside the polygons

These numbers are essential because they allow the computer to know which part you’re referring to when you want to compare the relative locations of all the points, lines, and polygons.

The table at the top of Figure 5-7 contains information about the spatial relationships (the topology) of the points, lines (links), and polygons:

Link #: Lists all the links in the figure, numbered 1 through 11.

Right and left polygons: Tell you how the links are related to the polygons on either side of them. This is the contiguity property of topology, which identifies the polygon on either side of any given line. By default, it also tells you the direction of the line because it knows which polygon is on the left and which polygon is on the right of that line.

By default, polygon 0 is the outside polygon — the polygon that constitutes the area outside of the map.

Nodes 1 and 2: Show you which nodes (points at the end of each link) define the beginning and ending of each link. These nodes link links to other links (whew!). So, this information tells you another aspect of topology called connectivity — the order and sequence of links.

Because the nodes define the links, and the beginning and ending nodes of some links occur at the same place, these links create polygons. So, if you know the coordinates of all the nodes, you also know the third basic component of topology — area. Area, as one of the basic properties of this topological data model, simply means that the polygons are defined by identifiable links, the coordinates of which are stored in the computer. You have that necessary information in the bottom table in Figure 5-7, which shows all the X and Y coordinates of all the nodes for all the links.

Topology is a way of coding the geometry of spatial relationships inside the computer, and topology consists of three things:

Contiguity: The topological property that says links have a direction, as well as polygons on their left and right sides.

Connectivity: The topological property that says nodes connect links in a definable sequence.

Area: The topological property that says areas (polygons) are defined by identifiable links.

The coverage model supports the three major properties of topology: contiguity, connectivity, and area definition. The coverage model has been around for over two and a half decades, but most GIS software vendors still support it because of the large number of GIS users whose data were (or still are, in some cases) stored as coverages.

Working with object-oriented representations

Advances in computer languages and their associated data structures — the development of object-oriented programming (OOP) — brought about a useful adoption for GIS data models. OOP focuses on objects where an object is a set of computer code that can be copied from place to place in a computer program. In GIS, an object represents a type of geographic feature that you can move around and whose properties follow it (are inherited) no matter where you place it. Incorporating OOP languages resulted in wholesale rewriting of some GIS software and development of new software based entirely on this model.

Much of the power of OOP data models results from the objects’ shared properties, or the characteristics they have in common with other objects in their group. (I describe the sharing of properties briefly in the sidebar, “Sharing the property,” and talk more about object structure in Chapter 6.) Because of shared properties, an object always knows what it can and can’t do, and what it can and can’t support. So, you don’t have to worry about any surprises when you retrieve information from an object-oriented GIS. If you’re looking for information on a land parcel, you won’t pull data related to oceans because the ocean objects don’t share the properties of (and, so, aren’t grouped with) land parcel objects.

You can find several implementations of the object-oriented model available, including the ESRI Map Objects product and the GE Smallworld GIS product.

Taking on advanced geographic representations

Perhaps the most robust and advanced of the object-oriented models is the ESRI new geodatabase model. The geodatabase (not to be confused with a collection of geocoded data inside a GIS software package that’s sometimes referred to as a geodatabase) allows you to store a wide variety of data types (including raster, vector, CAD, and others) in the same system. Here’s a quick list of the types of data this model can incorporate:

Attribute tables from typical RDBMS (see Chapter 6).

Geographic features that you might find in land-use maps.

Satellite and other digital imagery such as the files you might get from the LANDSAT satellite.

Surface models you could obtain from the USGS Digital Elevation Models (DEMs).

Survey data from scientific vegetation samples, or telephone surveys, for example.

The geodatabase model, like the non-object-oriented coverage model, has tables of data that include objects (rows in the database table) and features (objects that have explicitly defined geometry). It’s a completely topological model, like its predecessors. What makes the geodatabase so powerful is that each of these objects can contain a wide array of rules and logic, which makes the objects more like real geographic objects. For example, if you have a geodatabase of electrical infrastructure, certain lines that represent a type of wiring don’t connect to non-compatible types of wiring because the database explicitly stores properties that prohibit such a dangerous connection. Or, if you have a road-network geodatabase, the rules might prohibit you from connecting a one-way street going east to another one-way street going west.

Although the geodatabase is new and quite different from its non-object-oriented cousins, it has a lot of tools that you can use to migrate your data to the geodatabase format. While GIS analysis becomes both more sophisticated and more realistic, the geodatabase and other object-oriented models like it will increase their capacity to represent rules and conditions that characterize real-world geographic features.

ESRI has made many industry-specific geodatabase models that contain complete logic available for use, so you don’t need to build them from scratch. If you’re looking for a GIS for a specific application, check to see whether ESRI has the model you need before reinventing the wheel.

Dealing with Surfaces

Surfaces of all kinds are very common in GIS, but because of their threedimensional nature, they place additional demands on the computer programmer who wants to represent them. Beyond having to represent the X and Y coordinate, and the associated attributes, you also have to worry

about how to effectively include the third dimension in such a way that the software can perform all the basic operations on surfaces that the other data types allow, such as storing, retrieving, editing, analyzing, comparing, and outputting.

Storing surface data in a raster model

The general raster model provides the easiest method of storing surface data. Each grid cell represents not just an area on the surface of the Earth, but also a single elevation value. So, a grid cell in column X and row Y would store a single value Z that represents the elevation for the entire grid cell (as shown in Figure 5-10).

This model does limit the accuracy of your elevation values, just like the raster model itself limits the locational accuracy and spatial representation of the actual geography (see “Making a quality difference with resolution,” earlier in the chapter). On the plus side, the model does allow for some very nice surface modeling with low computational overhead (far fewer calculations), and you can easily convert it to other forms of surface representation.

Figure 5-10:

A raster representation of surface data.