Generating the Underlying Graphs for Architectural Arrangements

Abstract

The mathematical correspondence to a floorplan is a Metric Planar Graph. Several methods for systematic direct generation of metric planar graphs have been developed including polyominoes, March and Matela and shape grammars. Another approach has been to develop a spatial composition in two separate steps. The first step involves discrete variables, and consists of enumerating a defined set of non-metric planar graphs. The second step involves spatial dimensions, e.g. continuous variables, and maps the graphs onto the Euclidean plane, from which a satisfactory or optimal one is selected. This paper focusses on the latter 2-step process. It presents a general method of solving the first step, that is the exhaustive enumeration of a set of planar graphs. The paper consists of three sections: The first section is an introduction to graph theory. The second section presents the generation of maximal planar graphs. The last section summarizes the presentation and comments on the appropriateness of the metho