A shared commitment to standardising the process of hypothetically reconstructing lost buildings from the past has characterised academic research in recent years and can manifest at various stages of the reconstructive process and with different perspectives. This research specifically aims to establish a user-independent and traceable procedure that can be applied at the end of the reconstructive process to quantify the average level of uncertainty of 3D digital architectural models. The procedure consists of applying a set of mathematical formulas based on numerical values retrievable from a given scale of uncertainty and developed to simplify reuse and improve transparency in reconstructive 3D models. This effort to assess uncertainty in the most user-independent way possible will contribute to producing 3D models that are more comparable to each other and more transparent for academic researchers, professionals, and laypersons who wish to reuse them. Being able to calculate a univocal numerical value that gives information on the global average uncertainty of a certain reconstructive model is an additional synthetic way, together with the more visual false-colour scale of uncertainty, to help disseminate the work in a clear and transmissible way. However, since the hypothetical reconstructive process is a process based on personal interpretation, which inevitably requires a certain level of subjectivity, it is crucial to define a methodology to assess and communicate this subjectivity in a user-independent and reproducible way.

For the hypothetical reconstruction of architectural heritage, there are still no scientific standards of reference concerning their sharing and documentation. Recent international initiatives established the basis to address this problem; however, still, much work needs to be done in order to systematise good practices for the process of reconstruction and its dissemination. This contribution aims to take a step forward in the analysis and visualisation of uncertainty. Some authors have suggested various approaches to visualise uncertainty for single buildings; however, case studies at the urban scale are rarely investigated. This research proposes an improved source-based multi-feature approach aimed at analysing and visualising (through false-colour shading) the uncertainty of hypothetical 3D digital models of urban areas. The assessment of uncertainty is also quantified qualitatively by using newly defined formulas which calculate the average uncertainty weighted on the volume of the 3D model. This methodology aims to improve the objectiveness, unambiguity, transparency, reusability, and readability of hypothetical reconstructive 3D models, and its use is exemplified in the case study of the hypothetical reconstruction of Piazza delle Erbe in Verona, a project presented in the form of a docufilm at EXPO 2015 in Milan.

The sixteenth-century Fountain of Neptune is one of Bologna’s most renowned landmarks. During the recent restoration activities of the monumental sculpture group, consisting in precious marbles and highly refined bronzes with water jets, a photographic campaign has been carried out exclusively for documentation purposes of the current state of preservation of the complex. Nevertheless, the highquality imagery was used for a different use, namely to create a 3D digital model accurate in shape and color by means of automated photogrammetric techniques and a robust customized pipeline. This 3D model was used as basic tool to support many and different activities of the restoration site. The paper describes the 3D model construction technique used and the most important applications in which it was used as support tool for restoration: (i) reliable documentation of the actual state; (ii) surface cleaning analysis; (iii) new water system and jets; (iv) new lighting design simulation; (v) support for preliminary analysis and projectual studies related to hardly accessible areas; (vi) structural analysis; (vii) base for filling gaps or missing elements through 3D printing; (viii) high-quality visualization and rendering and (ix) support for data modelling and semantic-based diagrams.

Two case studies of hypothetical reconstruction are presented according to the principles of the Critical Digital Model [Apollonio et al. 2019]. One of the case studies is an architecture that was designed but never realized, and the other is the reconstruction of a historical art exhibition hosted into an architecture still existing today. This study is part of a wider research which is being currently carried out in the international Erasmus + project CoVHer. The main objective of the CoVHer project is to identify shared standards for the construction, evaluation and sharing of 3D hypothetical reconstructions. This research exploits the diversities of the two case studies to classify and re-define the methods of digital representation, which deal with the geometrical/mathematical nature of the models themselves and tries to define good practices to produce scientifically valid, sharable, and reusable 3D reconstructions.

Among the many cases concerning the process of digital hypothetical 3D reconstruction a particular case is constituted by never realized projects and plans. They constitute projects designed and remained on paper that, albeit documented by technical drawings, they pose the typical problems that are common to all other cases. From 3D reconstructions of transformed architectures, to destroyed/lost buildings and part of towns.This case studies start from original old drawings which has to be implemented by different kind of documentary sources, able to provide - by means evidence, induction, deduction, analogy - information characterized by different level of uncertainty and related to different level of accuracy.All methods adopted in a digital hypothetical 3D reconstruction process show us that the goal of all researchers is to be able to make explicit, or at least intelligible, through a graphical system a synthetic/communicative level representative or the value of the reconstructive process that is behind a particular result.The result of a reconstructive process acts in the definition of three areas intimately related one each other which concur to define the digital consistency of the artifact object of study: Shape (geometry, size, spatial position); Appearance (surface features); Constitutive elements (physical form, stratification of building/manufacturing systems)The paper, within a general framework aimed to use 3D models as a means to document and communicate the shape and appearance of never built architecture, as well as to depict temporal correspondence and allow the traceability of uncertainty and accuracy that characterizes each reconstructed element.