Computation of the distance between a polygon and a point in spatial analysis

Distance is one of the most important concepts in geography and spatial analysis. Since distance calculation is straightforward for points, measuring distances for non-point objects often involves abstracting them into their representative points. For example, a polygon is often abstracted into its centroid, and the distance from/to the polygon is then measured using the centroid. Despite the wide use of representative points to measure distances of non-point objects, a recent study has shown that such a practice might be problematic and lead to biased coefficient estimates in regression analysis. The study proposed a new polygon-to-point distance metric, along with two computation algorithms. However, the efficiency of these distance calculation algorithms is low. This research provides three new methods, including the random point-based method, polygon partitioning method, and axis-aligned minimum areal bounding box-based (MABB-based) method, to compute the new distance metric. Tests are provided to compare the accuracy and computational efficiency of the new algorithms. The test results show that each of the three new methods has its advantages: the random point-based method is easy to implement, the polygon partitioning method is most accurate, and the MABB-based method is computationally efficient.