Drawings are communicators of ideas that need to be considered not only very carefully and precisely, but also in the context of their purpose and audience. In the specific case of Francesco Borromini's plans for the church of Sant'Ivo alla Sapienza (1638-1667), additional information on the earliest designs is extracted from the famous "bee" plan through its comparison with a new, accurate survey of the constructed building, another newly identified plan fragment, and contemporary historic documents. While a straightforward chronological comparison is sufficient to "read" the earliest drawings, from before 1640, the drawings of the 1660 period, when arranged only by date, do not at first reveal a coherent order. The complete chronology and typological comparison of the early and late plans, including analysis of variations in plan sizes and geometric construction, strongly suggest that the church's form originated from a hexagon, but the building itself and Borromini's depictions of it were later changed in response to pressures from structural problems and changes in patronage to emphasize tripartite and triangular conditions in spatial form and iconography. In the late period, Borromini deliberately falsified certain specific drawings, both because he wanted to obscure certain conditions and also to portray the building in idealized terms that would enhance his reputation.

The unusual complexities of the oval plan of Bernini's S. Andrea al Quirinale result from a series of variations founded in traditional Renaissance geometric method. Through the comparative analysis of new measured drawings of the church and existing archival evidence, the development of the design is traced from its initial Serlian beginnings to its final innovative resolution. Analysis of the drawings in conjunction with historical documents confirms Bernini's use of conservative geometric procedures and reveals the reasons for his subsequent departure from strictest practice. The manipulation of geometry, proportion, and dimension arose not only out of Bernini's concern for conceptual clarity and theoretical orthodoxy, but also from a desire to use geometry in the support of spatial organization. The geometry of the final design illuminates and underlines the essential simplicity of the interior and gives us a better understanding of Bernini's intentions for the viewer's visual experience.