A Digital Restoration Method Driven by Mathematical Composition Rules and Their Application: A Case Study of Ming Dynasty Pavilion-Style Stone Pagodas in Fuzhou and the Restoration of the Luoxing Pagoda’s Finial

In the practice of historic building conservation and restoration, the authentic restoration of damaged components often faces challenges due to the lack of definitive design evidence. To address this issue, this paper proposes a restoration derivation method that integrates digital survey technologies, such as UAV oblique photogrammetry and 3D laser scanning, with the analysis of historical mathematical composition rules. Taking five Ming Dynasty pavilion-style stone pagodas in Fuzhou as subjects, this study first employed digital surveying and cross-verification with ancient texts to reveal their shared, precise proportional system: the eave–column ratio of the Ruiyun Pagoda approaches √2 (≈1.414), while the other four pagodas approach the golden ratio of 1.618. Furthermore, the pagoda silhouettes are governed by a √2 hierarchical system and a √3/2 visual correction mechanism. Based on these mathematical rules, a triple logical chain of “historical evidence verification–functional constraints–traditional adaptation” was constructed and applied to the quantitative restoration design of the damaged finial of the Luoxing Pagoda. This process ultimately derived the relationship between its total height and the first-story width as (L/2 + √2/2), with the finial height being 1/7 of the pagoda body’s total height. This case study validates the effectiveness of the proposed method in transforming profound historical wisdom into clear engineering parameters, offering a replicable and verifiable technical pathway for the digital conservation and scientific restoration of similar architectural heritage.