Algorithmic translation of Ying-tsao-fa-shih: A study on tou-kung Morphogenesis

This study focuses on parametric modelling of standardised tou-kung from the T’ang and Song dynasties, addressing the limitations of current digital methods in revealing assembly logic and algorithmic coherence. Constructing standardised tou-kung models is crucial for decoding assembly rules and advancing structural research in the digitisation of Chinese timber architecture. We propose a Grasshopper-based generative algorithm and derived through systematic analysis of the ts’ai-fen module system, component standards and assembly logic in Ying-tsao-fa-shih. This study elucidated the component morphologies and tectonic logic across various tou-kung typologies, enabling automated generation of individual components and self-organising assemblies. The methodology accurately constructed representative column, intermediate and corner tou-kung configurations spanning five to eight p’u-cho layers and enabled adaptive transformations in tou-kung structures, ranging from those without ang to those incorporating three angs. A key breakthrough lay in the dynamic control of the tilt angle of the ang through adjustments to the lower surface plane, which enabled controllable angular ranges. By optimising the spatial topological relationships of components through iterative algorithms, this approach overcame constraints of existing modelling methods, which depend on manual expertise and struggle to batch-produce diverse models. The results offer a parametric documentation strategy for digital heritage conservation independent of three-dimensional scanning while enhancing modelling precision and systematicity, providing new avenues for relic reconstruction and craft preservation. Future research will extend the algorithm to encompass tou-kung structures from other dynasties and incorporate the generation of shang-ang and other components, thereby establishing a comprehensive generative algorithm framework for traditional Chinese timber architectures.