The Borromini's helicoidal staircase in Barberini Palace: scan laser survey and parametric modeling.

Abstract

The paper concerns the study of the shape and geometry of the helicoidal staircase in Barberini Palace. Integrated models of representation (graphic and 3D) have been produced starting from the digital data acquired by a laser scanner, processed and subsequently managed through procedures for optimizing the cloud-points.

The realization of the helicoidal staircase in the Barberini Palace has an important rule in the architectural history because  it is a wonderful example of the constructive development of a complex geometric shape which is a helix oval. This stair should be read and interpreted as evidence of a particular period,the Roman Baroque, rich of intertwining and overlapping of ecclesiastical and noble commissions, of alternations in the yards of the greatest artists and architects of the era, often working simultaneously. Borromini proposes a modification to the first design of Maderno, which included a helicoidal staircase to the right of the large porch entrance to the palace, imagining a new oval stair  with a set of six twin columns for each revolution, very similar to the staircase that had been built a few years earlier, in 1585, at the Quirinale Palace by the Mascherino. Borromini had worked a few years earlier, under the direction of Maderno, in the Quirinal Palace, having a possibility to carefully study the Mascherino’s oval stair .

Following the death of Maderno (1629) the yard of the Barberini Palace takes over the Bernini. Borromini will initiate a collaboration destined to end soon. The scale will be built in 1633 when now Borromini had already left the yard.

The article wants above all to highlight the correlations between form and geometry when designing a campaign of digital acquisition using a laser scanner. Indeed, there are important implications to choice the positioning points of the instrument, with important fallout on the relationship between quality and quantity of a points cloud. The points cloud is a 3D model, first of all measurable, but also able to disclosing shapes and geometries otherwise hardly perceptible, selecting parts or showing details.

A first reading level of the models, obtained according to consolidated  procedures of the points-cloud management, has highlighted the formal matrix of the oval with the identification of the centers of the polycentric line, the resulting three-dimensional development of the various helices belonging to cylindrical surface portions adjacent to each other and different radius, the relationship with the slope. Within this formal matrix of the first level it enters the formal matrix of the architectural order into the rhythm of the six pairs of alternate columns and of the balustrades, and in the entablature that develops as a tape into the central space illuminated by a skylight.

The modular structure of the scale has also suggested a experimentation by means of parametric modeling techniques to try to trace the ideal model of the Borromini’s helical staircase. The digital parametric model tested here is a new mode of representation than the models already consolidated, either analog or digital. Through a critical selection of some remarkable points belonging to the geometries present, through a statistical and normalized observation of the recurring measures, we have identified a generative algorithm able to be representative of the design intentions of the author. The entire search path followed to reach the definition of parametric generative model – from analysis of the real model to the design of the virtual parametric model; from the development of the algorithm generative until to his check made by comparing the generated model and the model survey - it was found to be a constraint rigorous methodological for a more complete and appropriate knowledge of the work.