A Methodology for Planar Representation of Frescoed Oval Domes: Formulation and Testing on Pisa Cathedral

This paper presents an original methodology for planar development of a frescoed dome with an oval plan. Input data include a rigorous geometric survey, performed with a laser scanner, and a photogrammetry campaign, which associates a high-quality photographic texture to the 3D model. Therefore, the main topics include the development of geometry and, contextually, of the associated textures. In order to overcome the inability to directly develop the surface, an orthographic azimuthal projection is used. Starting from a prerequisite study of building methodology, the dome is divided into sectors and bands, each linked with the maximum acceptable deformations and the actual geometric discontinuities detectable by the analysis of Gaussian curvature. Upon definition of the development model, a custom automation script has been devised for geometry projection. This effectively generates a (u,v) map, associated to the model, which is used for model texturing and provides the planar development of the fresco