UCL Discovery

Abstract

We explore ways of introducing Euclidean distances associated with street systemsrepresented by axial lines into the two connectivity graphs based on points (or streetjunctions), and on lines (or streets), the so-called dual and primal representations ofthe space syntax problem. As the axial line is embedded in the connectivity graphbetween the points, for the dual problem the specification of Euclidean distancebetween points is relatively trivial but for the original syntax problem, this isproblematic in that it requires us to find a unique point representation for each line.The key is to find the centroids of the lines (of sight or unobstructed movement)between the points on each axial line, and then to use these to form a weightedcentroid of centroids. The distances between axial lines which form paths through theconnectivity graph between streets, are then computed using these centroids asstarting points for each line and routing distance through the street junctions.There are many issues involving interpretation of these measures. It might be thoughtthat the longer an axial line, the more important it is. But by giving an axial linedistance, this suggests that this is a deterrence to interaction, as in spatial interactiontheory, with longer axial lines being individually less important, notwithstanding theprobability that they are better connected within the overall street system. Clearly inmany finer-scale morphologies, this assumption might not be tenable but the measuresdeveloped here can be easily adapted to various circumstances. What this focus ondistance enables us to do is to treat a ?mixed syntax? problem where we are able toembed truly planar graphs into the axial map. This extends the technique to deal withsystems not only comprising streets down which we can see, but also fixed rail lines,subway systems, footpaths and so on which currently are hard to handle in thetraditional theory. We illustrate the extended theory for a pure syntax problem, theFrench village of Gassin, and a mixed syntax problem based on the grid of streets andunderground railways in central Melbourne. In conclusion, we introduce the notionthat proximity or adjacency at different orders might form more appropriate measuresof syntax distance, the proximity of nodes to nodes and lines to lines in the dual andthe primal being illustrated for both Gassin and central Melbourne.

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