A Bi-Directional Procedural Model for Architectural Design

It is a challenge for shape grammars to incorporate spatial hierarchy and interior connectivity of buildings in early design stages. To resolve this difficulty, we developed a bi-directional procedural model: the forward process constructs the derivation tree with production rules, while the backward process realizes the tree with shapes in a stepwise manner (from leaves to the root). Each inverse-derivation step involves essential geometric-topological reasoning. With this bi-directional framework, design constraints and objectives are encoded in the grammar-shape translation. We conducted two applications. The first employs geometric primitives as terminals and the other uses previous designs as terminals. Both approaches lead to consistent interior connectivity and a rich spatial hierarchy. The results imply that bespoke geometric-topological processing helps shape grammar to create plausible, novel compositions. Our model is more productive than hand-coded shape grammars, while it is less computation-intensive than evolutionary treatment of shape grammars.