Geometric probability and GIS: some applications for the statistics of intersections

This paper identifies analytical and empirical methods for determining the probability that lines and areas intersect tiles in a regular tessellation. Such intersections are common in geographical information systems (GIS) applications. Knowledge of intersection probabilities is valuable in many instances, including estimating complexity and time required to process a distance or viewshed operation, developing optimal tiling schemes for national georeferencing systems, precalculating the number of map sheets a spatial feature may occupy, and identifying appropriate cell resolutions for vector-to-raster conversions. Buffon's Needle-type solutions from the field of geometric probability provide the framework for deriving probabilities for lines. Probabilities for simple areas like rectangles and circles are derived using geometric techniques and illustrated using hypothetical examples. Employing such probabilities in spatial analysis may yield more rigorous and theoretically informed results from GIS analysis, leading to better decisions and greater insight into spatial phenomena.