In the field of documentation and preservation of cultural heritage, there is keen interest in 3D metric viewing and rendering of architecture for both formal appearance and color. On the other hand, operative steps of restoration interventions still require full-scale, 2D metric surface representations. The transition from 3D to 2D representation, with the related geometric transformations, has not yet been fully formalized for planar development of frescoed vaults. Methodologies proposed so far on this subject provide transitioning from point cloud models to ideal mathematical surfaces and projecting textures using software tools. The methodology used for geometry and texture development in the present work does not require any dedicated software. The different processing steps can be individually checked for any error introduced, which can be then quantified. A direct accuracy check of the planar development of the frescoed surface has been carried out by qualified restorers, yielding a result of 3 mm. The proposed methodology, although requiring further studies to improve automation of the different processing steps, allowed extracting 2D drafts fully usable by operators restoring the vault frescoes.

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.