The convex space as the 'atom' of urban analysis

Paul Osmond


The convex decomposition of a defined urban area provides a practical spatial framework to support a range of methods, which provide useful insights into aspects of urban ambience - the experienced physical and psychological qualities of the urban environment. This paper describes the integrated implementation of three such methods, convex, isovist and fractal analysis, to a densely built university campus. The convex space is employed as the fundamental unit of urban form; the starting point is the derivation of the convex map of the site. The centroids of the constituent convex spaces are taken as origin points to generate conventional two-dimensional isovists, and to photograph hemispherical images of the surrounding surfaces, representing a type of three-dimensional isovist. This latter construct opens a variety of analytical opportunities, only two of which are explored here - determination of skyline and surface fractal dimensions as indices of visual diversity. In addition to the standard convex and isovist metrics, two new measures are introduced: isovist fractal dimension, as an indicator of complexity; and isovist area divided by convex area, as an indicator of intervisibility. The outputs of this composite evaluation are redefined as a set of comparative indicators of several key ambience properties: physical and visual permeability, configurational and informational legibility, and visual diversity and stimulance, or exposure to new visual information. Multivariate statistics are applied to explore the relationships among the variables, and the similarities and differences between convex spaces in terms of the variable set. It is concluded that at neighbourhood scale these methods appear to identify real distinctions among convex spaces from the perspective of the occupant inhabiting and moving between them. Further, it is argued that convex decomposition offers a viable basis for comparative evaluation of a variety of significant urban ambience properties, with potential to inform design intervention.


Convex space; Urban ambience; Urban structural unit; Isovist; Fractal analysis

Full Text: JOSS_2011_p97-114.pdf