The definition and selection of boundaries is often a difficult, but nevertheless essential element in many areas of spatial analysis. One group of problems where this is especially important is in the analysis of point patterns — sets of points in the plane representing cases of a particular disease, or the location of ancient artefacts, or a particular species of plant. If the density of points (frequency of occurrence per unit area) is required then the total area under examination needs to be defined. Definition of this area, A, requires identification of a boundary, although there is now a variety of special procedures (known as kernel density methods) available for computation of densities without pre-defined fixed boundaries (see further, Section 4.3.4).
A further problem relates to the process of modelling the real world with abstracted linear forms (i.e. polylines and polygons). There are a variety of ways of modelling linear forms — mathematical, statistical, fractal, zonal — and each of these models will have implications for analysis. Data recorded in a GIS database, either as vector or grid elements, have already been modelled and to some extent the kinds of analyses that may be carried out are pre-determined. For example, most GIS packages do not provide facilities for analysing the complexity or “texture” of modelled lines and surfaces, although some, such as Idrisi and Fragstats do support such analyses by examining grid datasets at various scales and/or using variable sized windows. The ArcGIS add-in, Hawth’s Tools, provides a line metrics tool for generating measures of estimated fractal dimension and sinuosity of stored polylines. For fractal dimension this software computes, for each polyline:
where n is the number of line segments that make up the polyline, d is the distance between the start and end points of the polyline, and L is the total length of the polyline, i.e. the cumulative length of all polyline segments. Sinuosity is computed as a simple ratio: d/L, for each polyline. In both cases the results are added as new fields to the feature attribute table.
