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Most GIS's provide the capability to build complex models by combining primitive analytical functions. Systems vary as to the complexity provided for spatial modelling, and the specific functions that are available. However, most systems provide a standard set of primitive analytical functions that are accessible to the user in some logical manner. Aronoff identifies four categories of GIS analysis functions. These are:

Retrieval, Reclassification, and Generalization;
Topological Overlay Techniques;
Neighbourhood Operations; and
Connectivity Functions.

The range of analysis techniques in these categories is very large. Accordingly, this section of the book focuses on providing an overview of the fundamental primitive functions that are most often utilized in spatial analyses.

Retrieval, Reclassification and Generalization

Perhaps the initial GIS analysis that any user undertakes is the retrieval and/or reclassification of data. Retrieval operations occur on both spatial and attribute data. Often data is selected by an attribute subset and viewed graphically. Retrieval involves the selective search, manipulation, and output of data without the requirement to modify the geographic location of the features involved.

Reclassification involves the selection and presentation of a selected layer of data based on the classes or values of a specific attribute, e.g. cover group. It involves looking at an attribute, or a series of attributes, for a single data layer and classifying the data layer based on the range of values of the attribute. Accordingly, features adjacent to one another that have a common value, e.g. cover group, but differ in other characteristics, e.g. tree height, species, will be treated and appear as one class. In raster based GIS software, numerical values are often used to indicate classes. Reclassification is an attribute generalization technique. Typically this function makes use of polygon patterning techniques such as crosshatching and/or color shading for graphic representation.

In a vector based GIS, boundaries between polygons of common reclassed values should be dissolved to create a cleaner map of homogeneous continuity. Raster reclassification intrinsically involves boundary dissolving. The dissolving of map boundaries based on a specific attribute value often results in a new data layer being created. This is often done for visual clarity in the creation of derived maps. Almost all GIS software provides the capability to easily dissolve boundaries based on the results of a reclassification. Some systems allow the user to create a new data layer for the reclassification while others simply dissolve the boundaries during data output.

One can see how the querying capability of the DBMS is a necessity in the reclassification process. The ability and process for displaying the results of reclassification, a map or report, will vary depending on the GIS. In some systems the querying process is independent from data display functions, while in others they are integrated and querying is done in a graphics mode. The exact process for undertaking a reclassification varies greatly from GIS to GIS. Some will store results of the query in query sets independent from the DBMS, while others store the results in a newly created attribute column in the DBMS. The approach varies drastically depending on the architecture of the GIS software.

Topological Overlay

The capability to overlay multiple data layers in a vertical fashion is the most required and common technique in geographic data processing. In fact, the use of a topological data structure can be traced back to the need for overlaying vector data layers. With the advent of the concepts of mathematical topology polygon overlay has become the most popular geoprocessing tool, and the basis of any functional GIS software package.

Topological overlay is predominantly concerned with overlaying polygon data with polygon data, e.g. soils and forest cover. However, there are requirements for overlaying point, linear, and polygon data in selected combinations, e.g. point in polygon, line in polygon, and polygon on polygon are the most common. Vector and raster based software differ considerably in their approach to topological overlay.

Raster based software is oriented towards arithmetic overlay operations, e.g. the addition, subtraction, division, multiplication of data layers. The nature of the one attribute map approach, typical of the raster data model, usually provides a more flexible and efficient overlay capability. The raster data model affords a strong numerically modelling (quantitative analysis) modelling capability. Most sophisticated spatial modelling is undertaken within the raster domain.

In vector based systems topological overlay is achieved by the creation of a new topological network from two or more existing networks. This requires the rebuilding of topological tables, e.g. arc, node, polygon, and therefore can be time consuming and CPU intensive. The result of a topological overlay in the vector domain is a new topological network that will contain attributes of the original input data layers. In this way selected queries can then be undertaken of the original layer, e.g. soils and forest cover, to determine where specific situations occur, e.g. deciduous forest cover where drainage is poor.

Most GIS software makes use of a consistent logic for the overlay of multiple data layers. The rules of Boolean logic are used to operate on the attributes and spatial properties of geographic features. Boolean algebra uses the operators AND, OR, XOR, NOT to see whether a particular condition is true or false. Boolean logic represents all possible combinations of spatial interaction between different features. The implementation of Boolean operators is often transparent to the user.

To date the primary analysis technique used in GIS applications, vector and raster, is the topological overlay of selected data layers.

Generally, GIS software implements the overlay of different vector data layers by combining the spatial and attribute data files of the layers to create a new data layer. Again, different GIS software utilize varying approaches for the display and reporting of overlay results. Some systems require that topological overlay occur on only two data layers at a time, creating a third layer.

This pairwise approach requires the nesting of multiple overlays to generate a final overlay product, if more than two data layers are involved. This can result in numerous intermediate or temporary data layers. Some systems create a complete topological structure at the data verification stage, and the user merely submits a query string for the combined topological data. Other systems allow the user to overlay multiple data layers at one time. Each approach has its drawbacks depending on the application and the nature of the implementation. Determining the most appropriate method is based on the type of application, practical considerations such as data volumes and CPU power, and other considerations such personnel and time requirements. Overall, the flexibility provided to the operator and the level of performance varies widely among GIS software offerings.

The following diagram illustrates a typical overlay requirements where several different layers are spatially joined to created a new topological layer. By combining multiple layers in a topological fashion complex queries can be answered concerning attributes of any layer.