Geometric Analysis of Architectural Domes and Vaults Using Descriptive Geometry Methods

Domes and vaults represent foundational arcuated structural systems in architectural history, spanning vast interior volumes through complex double-curvature surfaces and stereotomic masonry assemblies. However, teaching the geometric construction of barrel vaults, groin vaults, cloister vaults, and spherical domes over square bays (via squinches and pendentives) poses severe pedagogical challenges due to the high cognitive load of 3D mental rotation. This study evaluates the effectiveness of Gaspard Monge’s double orthographic projection method integrated with physical stereotomic models and 3D digital verification (N = 120 architecture students). Over a 14-week empirical intervention, spatial visualization growth was quantitatively assessed using the Revised Purdue Spatial Visualization Test (PSVT:R) and stereotomic error-identification rubrics. Results demonstrate that the hybrid descriptive geometry approach improved spatial visualization scores by +61.6% compared to a 2D drafting control group (+12.4%) and elevated geometric error detection accuracy to 89.6%.