The aip function

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Overall

The aip function calculates the total area of non-overlap for the zones of influence for a given point pattern. This additional level of point pattern secondary description is useful in situations where the overlap/non-overlap of zones of influence (associated with each point in the observed point pattern) is of interest.

In the plot below, the purple line denotes the aip function for a regular point pattern, the green, for a clustered point pattern, and the dark orange for a point pattern with points which are completely randomly distributed.

The grey lines represents the aip function for 100 point patterns with points which are completely spatial random.

Each point pattern contains 25 points in a 10x10 square.

This aip function takes in a point pattern (spatstat object, http://spatstat.org/about.html) and calculates the total area of non-overlap for the zones of influence associated with said point pattern. The calculation is performed for a range of interaction radii, \(r_{i:n}\), and the results are depicted graphically. This secondary point pattern characterization provides an indication of how the points in the point pattern are distributed in relation to each other; different curves would be expected for points which are clustered for example, in relation to those randomly distributed.