Radial variability in assessing shape compactness

Abstract The shape of an area is an important geographical concept that is largely defined by its degree of being compact. As a result, much attention and focus has been on the best approach(es) to measure compactness in order to assess the relative characteristics of an area. Geographers have made important contributions to the specification of measures and metrics associated with compactness. In fact, the radial deviation approach proposed by Boyce and Clark (Geogr Rev 54(4):561–572, 1964) remains particularly popular and broadly applied. This paper investigates this measure with respect to properties and theoretical relationships. A GIScience based generalization is possible that extends the radial sampling and approximation notion to a closed form exact approach. Empirical assessment explores the merits of this generalization with respect to implementation and application in GIS. The findings highlight that existing approaches do not accurately estimate average radial distance from a center to shape boundaries, creating bias and misleading compactness measurement. Further, the findings demonstrate that this can be overcome through the proposed generalization and extension relying on the actual average radial distance.