The Mathematics of Spatial Configuration: Revisiting, Revising and Critiquing Justified Plan Graph Theory

Abstract

Abstract. The justified plan graph (JPG) was the first practical analytical method developed as part of the theory of Space Syntax, which purported to provide a graphical, mathematical and associated theoretical model for analysing the spatial configuration of buildings. In spite of early interest, in recent years relatively little research using this method has been published, perhaps because the JPG method is rarely explained in its totality and when it is, the descriptions are often inconsistent or unclear. Although it is now embedded in several software programs and its use may be more widespread, it is no better understood and after processing there is a marked lack of consistency in how the results are interpreted. This paper provides a historical background for the development of the JPG and a discussion of its conceptual or theoretical origins, followed by a "worked example" of the mathematics of the JPG. In combination with the results for two further cases, the paper identifies some important interpretative limits in the method and uses the examples to explain its potential use in design analysis. Finally, the paper discusses how the consistent application of this method to sets of related buildings is likely to produce a more valuable, and statistically viable, basis for future work.

Viraph: exploring the potentials of visibility graphs and their analysis

“…It is possible to use a genuine space syntax convex mapping (whether drawn manually or automatically like the medial axial skeleton algorithm used by Miranda Carranza and Koch 2013). In this way, it will be possible to combine the usefulness of VGA and convex mapping to analyze programmatic configuration of the built environment (Ostwald 2011). Another main limitation of Viraph is for analyzing spatially and geometrically fluid spaces which may lead to an intensive E-line graph.…”

“…One of the most elaborate approaches of the space syntax theory is Visibility Graph Analysis (VGA). This approach features a quantitative analysis of visual properties in the built environment, offering modelling and understanding of how the space may be used and perceived by its occupants (Ostwald 2011). Like other techniques of space syntax, VGA is based on a graph representation of the gross geometry of built environment.…”

Integrating clinic process flow, space syntax and space adjacency analysis: Formalization of computational method in building programming

“…JPG is a graph form that has been applied in architecture as part of Space Syntax theory. This theory is interested in the correlation of space configuration with social or organizational aspects (Ostwald, 2011), which has not been the focus of the other graph theories. The basic method is to transform spaces and their access to other spaces in a floor plan layout into topological graphs as nodes and lines; abstracting out any geometrical aspects of a floor plan such as length, width, and distance.…”

“…(Figure 5d). From the JPG, some configurational plan quality can be observed such as relative depth/shallowness, control/permeability, and symmetry/asymmetry (Ostwald, 2011). Example from Figure 5d displays the building configuration from the entrance is five steps depths.…”

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

“…2). In this way, the method is effectively quantifying the properties or importance of functional spaces in a plan [Ostwald 2011]. In contrast, the Axial Line approach identifies lines or paths through space as nodes and each intersection between them as edges ( fig.…”