Enumerating architectural arrangements by generating their underlying graphs

Abstract

One mathematical correspondence to the partitioning of the plane is a weighted plane graph (WPG). This paper first focuses on the systematic generation of WPGs, in a fashion similar to crystal growth. During this process, the WPGs are represented by adjacency matrices. We, thus, present a method for embedding the WPG in the plane, given its adjacency matrix. These graphs can, then, be mapped into floor plans. The common practice here is the use of the 'geometric dual' of a WPG. We propose, instead, the use of the 'pseudogeometric dual' of a WPG directly to translate (part of) a design brief into alternative spatial layouts. Also discussed is the ability to create courtyards and/or circulation spaces given a specific WPG, without increasing the size of the problem.