A new approach based on plane and circular fitting to survey the axial shape and assess the inclination of ancient Chinese pagodas

This paper presents a practical new approach for determining the geometric shape of an ancient pagoda structure and its axial shape along its height. Because of ancient Chinese pagodas’ unique characteristics (multiple eaves, Dougong, and vague edges), it is difficult to select appropriate measurement points. Moreover, the plane size of most ancient Chinese pagodas decreases from the bottom to the top floor. Considering these characteristics, we employed an electronic total station to monitor more than three measurement points of each wall façade of each pagoda floor, fitted plane equations using 3-D coordinates of the monitored measurement points and the least square method, calculated the corner points coordinates of each floor or cross section selected, fitted a circumscribed circle of each floor using the corner point coordinates and spatial axial equations based on the central coordinates, and performed an inclination evaluation of the ancient Chinese pagoda. This approach is practical and can be widely used in other high-rise polygonal buildings that have different plane sizes for each floor.