Parameterizing the Curvilinear Roofs of Traditional Chinese Architecture

The curvilinear roofs of ancient Chinese wooden architecture feature unique functional, hierarchical, and aesthetic elements. However, the digitalization of these roofs has yet to be explored because of the lack of accurate mathematical models for these roof geometries. This research aims to parameterize the design and construction rules for these roofs as stipulated in the Yingzao fashi. We first illustrate the major features of curvilinear roofs, followed by a comprehensive investigation on the raising and bending rules via the original texts and drawing samples provided in the Yingzao fashi and the Annotated yingzao fashi by Sicheng Liang. Then, the mathematical models are developed. The main contribution of this research is the transformation of the design and building rules for complex curvilinear roofs into mathematical models, enabling designers to generate such roof architecture and adding new insights to existing mathematical methods in studying ancient architecture.