A Survey-Based, Multi-Scale Framework for Geometric Characterization of Heritage Irregular Stone Masonry Facades: A Qing Dynasty Imperial-Garden Rockery as a Case Study

Rockeries in Qing-dynasty imperial gardens are irregular stone masonry structures combining aesthetic scene composition with engineering attributes. Existing geometric characterization methods, mostly oriented towards regular Western stone masonry walls and operating at a single scale, are inadequate for resolving the multi-tier composition rules on the primary viewing facade of rockeries. This study develops a multi-scale geometric quantification framework for the primary viewing facade of rockeries, extracting six categories of geometric factors at three scales: the overall layout, the single-stone hierarchy, and the individual stacked stone. The framework is validated on the Wanfang Anhe rockery in Yuanmingyuan. The results show that: (1) the overall layout exhibits a clear host-and-guest order, with the Main Rockery dominating in both area and count (area ratio 2.07:1.11:1.00); (2) at the single-stone hierarchy, the Rockery Side serves as the aggregation core (60.47% by area, 72.56% by count), while the Rockery Top forms an abrupt scale transition through a few large stones; (3) individual stones display slender, irregular shapes, a right-skewed size distribution (75% ≤0.12 m2) and near-random orientation (0.06°–179.90°). The proposed framework transforms qualitative rockery-stacking principles into quantifiable descriptions and may provide a methodological basis for stone-selection references in localized stacked-stone replacement and for the digital preservation of traditional construction principles.