On Shapes and Topologies
Graph theoretic representations of shapes and shape computations
Shape grammars are an established method in the field of design computation. Since their initial formulation in the 70s the underlying theory has been developed intensively. Applications have mostly
been restricted to showcase grammars remodelling existing bodies of work. Difficulties in automating shape grammars have restricted their extramural impact.
This thesis attempts to remedy the situation in two ways. First, additional applications of grammars in the field of architecture are shown. Notably a method to generate, enumerate and denominate topologies of a specific typology. Second, it is shown how to map the problem of shape grammars onto graph grammars. Graph grammars are more widely used and have further developed implementations. Structurally they resemble shape grammars and they are well suited to carry out the underlying computations. Additionally by abstracting shapes to graphs a novel solution to implementing parametric shape grammars is developed.
Chapter 2 “Sort Machines” examines possible topologies for the U.S. federal courthouse typology. Here it is shown how to use graph grammars to generate possible courthouse topologies. The examination is then extended by enumerating these possibilities. Finally, the structure introduced by the grammar is used to develop a nomenclature for the topologies, giving each an informative name for discussion and comparison.
Chapter 3 “Transformational Palladians” describes an implementation of a specific grammar. The existing shape rules are transcribed into graph rules. Due to an appropriate mapping all operations can be carried out on the graph. The result is then transformed back to shapes.
This all culminates in Chapter 4 “From Topologies to Shapes” where a general solution for mapping parametric labelled shape grammar to graph grammars is presented. The novelty lies in the flexible description of shapes by constrained topologies. The presented method recognises emergent shapes and can be extended with arbitrary weights.