A Bi‐Directional Procedural Model for Architectural Design

Abstract

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.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.