Measuring alignment with the grid: evaluating the earth mover's distance as a metric of alignment between orientations

How an origin and a destination align with the street network may, anecdotally, be used as a heuristic to infer the length and complexity of routes from the origin to the destination. However, no method of measuring alignment with a street network exists, and furthermore, it is unclear whether and under what circumstances it is useful as a heuristic. In this paper, we propose a novel method for measuring alignment using the Earth Mover's Distance (EMD) between orientation distributions. We evaluated this metric using a dataset of 77,293 origin and destination pairs from 100 cities with different street networks, in order to test the hypothesis that an increasing degree of misalignment is predictive of a longer and more complex route from origin to destination. Our evaluation shows that our method for measuring alignment becomes more useful as a heuristic, the more grid-like the street network surrounding the origin and destination is. To conclude, the results obtained indicate that alignment is an important factor for route properties, especially in grid-like street networks, a subclass of routes within an environment, where the configuration of the street network makes predicting the length and complexity easier.