Algorithms for the parametric analysis of metric, directional, and intersection reach

Abstract

By asking how much street length can be reached from a given origin within a specified distance limit, and by defining distance in different ways as a function of the physical or cognitive effort required to move in cities, the analysis of reach produces measures that effectively characterize street density, connectivity, and the associated urban potential. While the conceptual foundation for reach analysis has already been laid, the computational aspects have not been sufficiently addressed. We introduce the different graph representations and algorithms we developed to analyze metric reach, directional reach, and intersection reach—a new addition to the existing measures. The graph representation we developed for directional reach analysis also sets the foundation for more advanced graph-based street network analysis. We also provide formulae for computing the mean directional and intersection reach. Finally, we discuss common street network modeling issues that can be addressed by consistent mapping protocols.