Knowledge of location also allows the analyst to determine the distance and direction between objects. Distance between points is easily calculated using formulas for straight-line distance on the plane or on the curved surface of the Earth, and with a little more effort it is possible to determine the actual distance that would be travelled through the road or street network, and even to predict the time that it would take to make the journey. Distance and direction between lines or areas are often calculated by using representative points, but this can be misleading (as noted in Section 2.2.3). They can also be calculated using the nearest pair of points in the two objects, or as the average distance and direction between all pairs of points (note the difficulties of averaging direction, however, as mentioned in Section 2.2.2).

Many types of spatial analysis require the calculation of a table or matrix expressing the relative proximity of pairs of places, often denoted by W (a spatial weights matrix). Proximity can be a powerful explanatory factor in accounting for variation in a host of phenomena, including flows of migrants, intensity of social interaction, or the speed of diffusion of an epidemic. Software packages will commonly provide several alternative ways of determining the elements of W, including:

·         1 if the places share a common boundary, else 0

·         the length of any common boundary between the places, else 0

·         a decreasing function of the distance between the places, or between their representative points

In such analyses it will be W that captures the spatial aspects of the problem, and the actual coordinates become irrelevant once the matrix is calculated. Note that W will be invariant with respect to displacement, rotation, and mirror imaging.