The parametric modeling of a barrel vault in Grasshopper begins with the construction of an arc profile, governed by parameters such as span and rise. This profile is subdivided into segments corresponding to individual voussoirs, whose widths are also parametrically controlled. Each segment is extruded along the longitudinal axis to generate a sequence of base surfaces, which are then further extruded along their respective surface normals to define the volumetric geometry of the voussoirs. The resulting elements are systematically arrayed to form the complete vaulted system. The use of parameter sliders enables real-time manipulation of geometric and constructive variables, facilitating iterative design and formal exploration.

Given its geometric clarity and structural logic, the barrel vault constitutes an exemplary case study for investigating the potential of parametric modeling in architecture, and more specifically in stereotomy. Its modular nature lends itself to applications in digital fabrication and structural analysis.

Interactive model at: https://www.shapediver.com/app/builder/v1/main/latest/?slug=vaultrectangularshdi&redirect=0