An Algorithmic Definition of the Axial Map

Abstract

The fewest-line axial map, often simply referred to as the ‘axial map’, is one of the primary tools of space syntax. Its natural language definition has allowed researchers to draw consistent maps that present a concise description of architectural space; it has been established that graph measures obtained from the map are useful for the analysis of pedestrian movement patterns and activities related to such movement: for example, the location of services or of crime. However, the definition has proved difficult to translate into formal language by mathematicians and algorithmic implementers alike. This has meant that space syntax has been criticised for a lack of rigour in the definition of one of its fundamental representations. Here we clarify the original definition of the fewest-line axial map and show that it can be implemented algorithmically. We show that the original definition leads to maps similar to those currently drawn by hand, and we demonstrate that the differences between the two may be accounted for in terms of the detail of the algorithm used. We propose that the analytical power of the axial map in empirical studies derives from the efficient representation of key properties of the spatial configuration that it captures.

On space syntax as a configurational theory of architecture from a situated observer’s viewpoint

“…Hillier's "all lines map" includes all diagonals, e-lines and s-lines (Peponis et al, 1997), but does not provide any method to extract a more economic linear representation as did Peponis and his colleagues (1998a). Later, some of these ideas were applied to automate the generation of axial representations (Turner et al, 2005). Batty and Rana (2004), however, suggest a different method for solving the problem.…”

From Axial to Road-Centre Lines: A New Representation for Space Syntax and a New Model of Route Choice for Transport Network Analysis

“…Within the space syntax community, there has also been an interest in automation, in order to retrieve an algorithm for the generation of the axial map, a line-based representation of urban systems (e.g. Peponis et al, 1998;Batty and Rana, 2004;Turner et al, 2005).…”

Differentiating between Line and Point Maps Using Spatial Experience: Considering Richard Neutra’s Lovell House

“…The high degree of accuracy in the model allowed for both maps to be developed with a minimum of interpretation. The axial map of plans generated from this model was developed using a manual-intuitive method informed by research into developing automated generation methods [Peponis et al 1997;Turner et al 2005;Ostwald and Dawes 2011]. The definition of axial lines used in the map is that of unobstructed lines of sight and movement.…”

“…While this method is well known, there are a range of variations that produce different, but potentially equally valid maps for a single spatial configuration [Penn et al 1997;Peponis et al 1998;Peponis and Wineman 2002;Batty andCarvalho 2003, Penn 2003;Turner et al 2005;Yoon 2009]. …”