New advances in the automated architectural space plan layout problem

Over the past four decades several computer models have been developed to solve what has come to be known as the space planning problem in architectural design. Although, space planning cannot be defined as an independent problem in the whole architectural design process, the problem is important if considered within the context of the design process itself, i.e. exploring the topological options of the design and not as an optimization or form finding exercise. Given this pretext, the space planning problem in architectural design becomes one of exploring and perhaps enumerating the various spatial arrangements possible. This line of thinking has been considered in the earlier years of the research, where the problem was typically formulated using graph theoretical approaches. At the core of these efforts was trying to answer the question “Can you practically enumerate all the possible space arrangements given relationships between space and other geometric constraints”. However, this line of research has not received sufficient attention in the literature lately. Several findings related to graph theory have since been discovered in the last decade or so. This paper presents the new findings in graph theory that have direct implications on space layout and planning in architectural design. The paper presents the space planning problem from a graph theoretical approach with relevant definitions and posses questions related to the topology of the planar graphs that represent the spatial layout of any design. A refined definition of architectural floor plans as “simple, connected, labelled, planar graphs” is presented along with justification and discussions. Recent findings and algorithms related to enumerating rectangular dissections, and planar embeddings of planar graphs including area universal planar graphs are presented as well as the necessary and sufficient conditions for a graph to have a rectangular dual. The paper should be of interest to architectural professionals as well as researchers in the area.