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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.

This paper presents preliminary findings from the ongoing Erasmus+ European project CoVHer, which focuses on the hypothetical virtual reconstructions of lost or unbuilt architecture. This contribution provides a critical assessment of the terminology specific to this field. A significant challenge lies in the absence of standardised terminology for many foundational aspects, which can lead to misconceptions and misunderstandings. The research begins with a comprehensive review of the relevant literature in the field, aiming to identify which terms are most widely accepted and appropriate to use and which are ambiguous or should be avoided. For concepts that lack a clear definition, new terminology is proposed. This paper analyses six key terms: reconstruction, uncertainty, raw model, informative model, digital representation methods, and 3D modelling techniques.

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.

This contribution to the literature presents an in-depth analysis of the scene drawn by Leonardo da Vinci in the preparatory drawing, Adoration of the Magi, dated 1481, that is now housed at the Département des Arts Graphiques du Musée du Louvre in Paris, France. This analysis focuses on the architectural elements and highlights how the drawing discloses three distinct vanishing points/centers of vision: one for the classical architecture to the left of the scene, one for the Nativity hut, and one for the structure with stairs. If we consider the structures as belonging to the same 2D projected space, at least two must be depicted out of square; conversely, if we consider them as straight, standard structures, they cannot belong to the same 2D projected space. Given this assumption, we propose, on the one hand, some variations of the scene where the structures are straightened and projected according to only one of the viewpoints at a time; on the other hand, a set of variants of the scene are presented, considering the out-of-square structures. The scenes are generated by applying inverse perspective projections. These results prompt a discussion on possible reasons why Leonardo made these conscious or unconscious “formal errors”.

Among many other themes, Leonardo da Vinci’s Manuscript B contains several drawings of centrally planned churches, some of which are represented using a plan view paired with a bird’s-eye view. The use of a bird’s-eye instead of an elevation represents an innovative depiction technique, which allows combining the immediacy of the perspective view with the measurability of the façades, and therefore to describe the three-dimensionality of the buildings. To understand the reasons behind the use of this original technique, the edifices’ shape and classify them, we decided to use 3D digital reconstruction techniques, for their ability to avoid misunderstandings in the reconstruction process and in the results. This article describes the method to create the digital models of sixteen churches. A Visual Programming Language (VPL) script was used as the 3D base for modelling the churches achieved from a classification code expressing the aggregative rules of the churches. Then, the geometric process for the construction of the plan and its relationship with the elevation measures were studied for each church. Finally, this information was used for the completion of the 3D models, distinguishing more output variants each time there was an inconsistency between plan and perspective view, a variability of one architectural element or an uncertainty.