The three types of GI representation refer to concepts used by most GIS to represent things and events. Each representation type uses specific storage
Examples for each type of geographic information.
and indexing formats for recording the GI representation with information- processing technology. This section introduces each representation type, dis- cusses how it used to represent things and events, and explains how, in very general terms, it is stored in a GIS. This section also introduces topology, a foundation for vector GIS.
Position-Based Geographic Representation
Most GI is recorded using a position-based representation as points, lines, or areas (also known as polygons). This type of GI representation corresponds to the geometric primitives used to draw two-dimensional map elements. It is a handy and convenient way to create GI based on existing maps and for people used to working with maps. It is also very useful for many types of analysis (see Chapters 13–15). Of course, it can be transformed to other GI representation types.
Positional GI representations are usually two-dimensional and static.
Events can only be shown in terms of positions and characteristics at a cer- tain point in time. Measured properties are (1) either recorded as attributes of a spatial object, (2) are defined by the extent of the property, or (3) are associated with the measured properties of a predefined area (raster). Rela- tionships are either defined by associations between attributes or relation- ships that can be established and analyzed by transformations. The two most common storage techniques for this type of representation are vector and raster (see Chapter 2).
Animation can be used to show events with position-based GI represen- tations, but it is always based on a series of static geographic representations.
Animations that show a series of images, just as frames in a comic, are rela- tively easy to create and show. However, they may be based on the interpola- tion of specific changes rather than measurements, which lessen their accu- racy.
Vector GI is stored in a variety of ways. The most common format has been what people refer to as the “georelational model.” This model is being
Examples of raster and vector geographic information representation types.
increasingly replaced by proprietary database storage formats. Although the use of databases is expensive and usually requires specialized organization of the GI and work, they are much quicker than the georelational model stor- age. However, because of its additional complexity, the traditional georela- tional model should remain a commonplace fixture of GIS for some time.
The georelational model relies on topology. Topology not only provides a way to reduce the storage requirements for GI, it also provides a means to speed up many processes and check for errors (see Chapter 7).
The georelational model consists of three main components connected topologically. All three components are present and are linked to each other. The first component is a table with a list of polygons (or areas). It records the internal number of a polygon and the chains in the order that make up the polygon’s boundary. The second component is the table with a list of chains (also called “lines” or “arcs”). Each chain entry consists of infor- mation about the polygons to either side of the chain and the start and end node of the chain. The start and end node define the direction of the chain and which polygons are left and right. The third component of the georelational model is a table of nodes. This table consists of the node identi- fier and the x and y coordinates of each node.
Additions to the three components of the georelational model can be made to improve the geographic representation and the cartographic repre- sentation, especially the addition of additional points used to define the pre- cise shape of a chain and indexes to speed up queries and the drawing time.
Raster GI representation relies on various types of encoding to reduce the amount of storage required by a computer. If each raster or pixel cell is
Key components of the georelational model.
stored individually, the files become very large. A simple way to reduce the required storage (and one of the oldest) is to process each row of the raster data set from left to right, recording only when the attribute value changes and the number of cells following the change to the right. For example, if a row is 100 cells long and cell 1–20 has the value 156, cells 21–78 have the attribute value 123, and cells 79–100 have the attribute value 156 again, the run-length encoded (RLE) raster storage would only store 156:20; 123:59;
and 156:21. Other systems are more complicated, but even more efficient.
One of the most interesting storage formats is the quad-tree format which works like the RLE approach, but puts areas into a hierarchy of cell value.
For example, an agricultural raster data set representing types of crops could distinguish crops at the highest level by the genus, at the next level down in the quad-tree hierarchy it could show the Linnean classification family, and at the third level of the quad-tree it could show individual species. The quad- tree is very efficient and very fast, but changes to the hierarchy can be very complicated and require a great amount of processing.
Network-Based Geographic Representation
The network geographic representation type is usually considered to be a subtype of the position-based geographic information type, but is distinct because of its special properties for representing topological relationships.
The network geographic representation type uses nodes and links, which correspond to nodes and chains in the vector position-based geo- graphic representation type. The distinction is that nodes in the network store information about possible connections (e.g., possible turns at an inter- section) and links store the information about how nodes are topologically connected (e.g., Chicago is connected to St. Louis by Interstate 55). Topolog- ical information is extremely helpful for vector-based network GI.
Nodes can be added with coordinates from a coordinate system and with additional points with coordinates to define the shape of the networks, for example, situating Chicago and St. Lous on the map in a geographically correct arrangement. However, many networks are represented without this location information, allowing the map to be very simple and easily read (e.g., public transportation maps). (See Plate 6, the London Underground Map.)
Field-Based Geographic Representation
For the representation of nondiscrete, mainly environmental, properties including soil moisture, soil pH, or the distribution of airborne particles and substances including ozone, dust, or pollen, fields are the ideal GI represen- tation type.
Conceptually, fields are nondiscrete, meaning no precise and accurate boundaries can be made between soil pH 6.7 and 6.8, and the properties of a field can be modeled using geostatistical techniques that take these relation-
ships into account, but the storage of the GI representation type usually uses raster data structures. This should always be considered when working with field data. It is easy, but wrong, to interpret raster cell boundaries as the sharp boundaries between different attribute values, when, in fact, the geo- graphic things and events represented by a field are nondiscrete.
A triangular irregular network (TIN) is a specific format for the repre- sentation of fields that relies on a network of lines connecting sampled points with known values. The connections form a Delauney triangulation, which means that each point is connected to only two other points to create triangular faces. This type of GI representation is most commonly used for the visualization of elevation data, but can be used for any data that is col- lected using irregular samples in an area. Dynamic versions of TIN make it possible to rapidly change the TIN. The changes can be so rapid that dynamic TIN holds potential to help train people for complex navigation sit- uations.
Transformations
Even if GI is represented as a field, it may not originate with data collected for every point in the area of the field. Since this detailed data collection would be practically impossible, most field data is usually the result of trans- forming position-based GI observations and measurements. For instance, a property of soil, pH, shown as a nondiscrete field for an area, may be based on an interpolation of soil samples collected at various points. The soil pH data could be transformed back into a position-based GI representation as contours that show where soil pH changes (e.g., a contour for every 0.5 change in soil pH). Transformations can be applied to any representation of GI. GI can be transformed to different types—for example, positions to fields, or networks to positions, or from one position-based GI representa- tion to another (e.g., points to lines).
Two examples of field GI. On the left a DEM, on the right GIRAS land use.
The transformation concept goes back to Tobler’s development and application of the mathematical transformation concept to cartography. For Tobler, the map is more than a representation; it is a device for storing infor- mation. Tobler worked on mathematical techniques and analytical methods to transform maps into forms of information that can be changed further.
Thanks to Tobler’s conceptual work, we regard GI not just as data, but as data with meaning, which can be transformed and combined with other GI to create new forms of GI. With the transformation concept comes an understanding of GI as sets of associations with particular representations that can be converted to create other sets of associations.
WHAT ARE TRANSFORMATIONS?
Transformations are operations on GI that change the information content by geometrically manipulating GI and changing it into other GI representa- tion types. For example, a buffer operation can transform a point that repre- sents a well into a polygon that represents the zone around the well. This zone can be represented as positional or field GI, depending on the opera- tion chosen. The zone can be transformed into the other GI representation types. Transformations of GI can also change attributes. An example of an attribute change is converting temperature recorded in degrees Celsius to degrees Fahrenheit. In both cases, the key change involves transforming the GI representation. What information is measured for a point, such as a well, Example of a TIN data structure. Each triangle is a facet of a hill slope representing a change in elevation, orientation, or the relationship between these two characteristics.
is only of limited validity for an area, such as a theoretical plume extent. A transformation can produce new GI based on calculations that show a rela- tion, as in the example of a buffer.
Examples
The two most fundamental GIS operations, buffers and overlays, are exam- ples of GI representation transformations. Buffers transform position-based GI into other types of position-based GI or fields. Overlays transform two position-based GI data sets into one. What these operations involve and how they transform demonstrates the key role of transformations for GI and its much greater usefulness compared to maps.
BUFFER TRANSFORMATIONS
A buffer transformation is the simplest transformation to grasp, but its operation can actually be quite complex. Practically, based on the position of one or more GI objects, it determines the zone around the objects using one or more distances. Figure 9.6 (left) shows a simple 100-foot buffer around a well. But what do the 100 feet (about 30 m) represent? They may simply be the regulatory zone where no animal waste disposal is allowed.
But it could be based on more complex geographical relationships. Maybe the 100 feet corresponds to the well recharge zone calculated using a hydro- logical model that considers both the soil type and geology. The areas of buffers usually are used to show a geographical relationship. Based on an understanding of the relationship, distances are used to show the extent of the relationship. This technique is used to indicate area affected by vehicle or airplane traffic. Complex models may only use buffers to represent the results of calculations that work with fields and model things and events in
A 100-foot buffer around a point representing a well produces a vector area or field (left); Buffered zone of land use around the Cincinnati/Northern Kentucky Airport (right).
terms of relationship vectors. This simple operation is a very powerful trans- formation. In all cases, obviously the accuracy and quality of a buffer de- pend on the underlying model and explicit (or implicit) assumptions.
OVERLAY TRANSFORMATIONS
GIS overlay is, depending on who you speak with, the first or second most important operation for GIS. Either way, it is without doubt one of the most significant operations. It is also one of the primary transformations, but the transformations performed by an overlay depend on the type of GI represen- tation.
Positional GI combines the geometries (points, lines, or areas) of two data sets based on a common coordinate system. The geometrical transfor- mation is only the geometric process of determining the intersections between objects from each data set and the assembly of new objects that cor- respond to the original objects. Attributes from the original objects are assigned to the new objects based on the location of the original objects. The
Overlay transforms by combining two (or more) data sets based on the location of features in a coordinate system.
attribute transformation begins only here. Various operations, logical and mathematical, are used to transform attributes and relate them—for exam- ple, evaluating soil type and soil moisture to determine crop suitability. Ras- ter GI performs these attribute transformation as the overlay transforma- tion, assuming both raster data sets use the same raster size and origin point (otherwise some complex geometric transformations must first take place).
Chapter 14 covers these issues and the overlay operation in more detail.
Summary
This chapter examined GI representation types and transformations. GI rep- resentation types are the formats available for GI: positions, networks, and fields. Positions and networks rely on vector data formats; fields rely on ras- ter data formats. Positional GI is stored in a GIS as points, lines, or areas (also known as polygons), most often following the georelational model that uses topology. Networks also use these data formats, but areas are of very limited use in a network. Points, called nodes in networks, are much more important.
Transformations are operations on GI representation types that change the information content. A buffer transforms a point through a distance measure into an impacted area.