Highlights: The article highlights the integration of advanced modelling software, showcasing their potential in reconstructing historical monuments with high accuracy and detail. The study uses modern techniques such as LiDAR, photogrammetry, and HBIM compared with historical documentation in digital 3D reconstruction. Reality-based parametric modelling and virtual anastylosis were employed to verify and visualise hypotheses about the original structure of the arch. The case study focuses on the virtual hypothetical 3D reconstruction of the Roman Three-bay Double Arch of Musti, Tunisia. This work, part of the AFRIPAL project, aims to enhance understanding of the Romanization and urban development of Musti between the 5th century BC and the 3rd century AD. It builds on research by Professor Naïdè Ferchiou, who provided a detailed reconstruction hypothesis based on measurements and documentation from the 1990s. Modern techniques such as LiDAR scanning, photogrammetry, Building Information Modeling (BIM), and parametric modeling were employed to visualize and verify this reconstruction. Scans of existing architectural fragments were used to create high and low-polygon models, enabling the testing of various hypotheses. The study highlights the use of tools like Reality Capture, Archicad, Rhino, and Grasshopper to reconstruct historical monuments, focusing on accuracy in modeling and detailed parametric representations. One of the main challenges was reconstructing the arch despite significant alterations due to centuries of redevelopment and later modifications. That challenge was addressed by cross-referencing historical documentation with modern scanning technologies and photogrammetry. Textured mesh and BREP modeling were incorporated with virtual anastylosis of elements to hypothesize the original structure. The study concludes by showcasing photorealistic visualizations of the reconstructed arch and discussing the potential for automating aspects of the reconstruction process using modern software. This work brings to life an ancient Roman monument and sets a workflow for future detailed virtual reconstructions of cultural architectural heritage.

The CoVHer Erasmus+ project addresses the long-standing lack of standardisation in hypothetical virtual 3D reconstruction and modelling in architectural heritage research. It aims to develop best practices for the 3D reconstruction of lost or never-built architectural heritage, enhancing research quality, transparency, and reusability. The collaborative effort includes contributions from five European universities and two private companies, focusing on architecture, archaeology, digital humanities, and art history. The presented workflow of documentation is the result of the joint effort in extensions of the approaches of the Scientific Reference Model (SRM) and Critical Digital Model (CDM), which strive for faithful reconstruction, documenting all decisions and inferences and advocate open licensing and use of non-proprietary formats to promote accessibility and reusability. The developed methodology aims to provide tools for the scientific evaluation of hypothetical reconstructions and support data exchange between researchers.

Digital technologies significantly influence architectural heritage perception, preservation, and presentation, particularly in reconstructing fragmented archaeological sites. This study explores innovative applications of algorithmic design, Heritage Building Information Modelling (HBIM), and interactive visualisation through the virtual reconstruction of the Roman Forum Transitorium in Musti, Tunisia—a complex historical site influenced by Numidian, Roman, and Byzantine cultures. The research integrates algorithmic modelling, digital surveying, and cloud-based collaboration, employing software tools such as Archicad, Rhino, Grasshopper, and Virtual Tour platforms. Central to this approach is a parametric, hypothesis-driven methodology, enabling the iterative exploration of multiple reconstruction scenarios informed by historical sources, architectural analyses, and scanned archaeological fragments. Immersive technologies enhance user engagement, allowing for the transparent exploration and interpretation of the site’s historical uncertainties. The results highlight the effectiveness of algorithmic methods in managing interpretative variability, offering flexible, academically rigorous, and publicly accessible virtual reconstructions. By emphasising the hypothetical nature of digital reconstructions and interactive visualisations, this research contributes meaningfully to digital archaeology, demonstrating how innovative algorithmic approaches can bridge academic scholarship and broader heritage preservation practices.