How are spatial relations measured and analysed?

A set of syntactic methods are applied to measure interior layout of a building, with regards to spatial configuration.

1. Convex map or J-graph analysis
One of the basic tools for analysing building layout  is convex map analysis. Below is an example of how to create or undertake the analysis.

a. Construct graph
Convert a building layout into a graph (A) in which each node indicates a room and the links between them indicate doorways.

b. Step depth
Step depth measures from the root space, the number of steps required to reach all the other rooms in the building. A Justified or J-graph is a representation of step depth from a particular room. For example, the J-graph of Room 5 (B) is shallower than Room 10.

c. Integration measure
Integration values can be then calculated according to the number of steps required to reach every other room in the system. The higher the integration, the fewer the steps required to traverse every room in the building.

d. Integration thematic (C)
Colour up the layout according to integration values of the nodes, where red denotes more integrated rooms, and blue indicates more segregated rooms. This enables us to capture relationships between each room to all others.