Glossary

Term

3D Modelling

Definition

In computer graphics, 3D modelling is the process of creating a three-dimensional representation of an object or scene using specialized software. 3D modelling can be classified according to the 3D digital representation method that the software uses for the creation of shapes, or according to the practical 3D modelling technique used by the operator (refer to Figure 1). In the context of virtual hypothetical 3D reconstruction, 3D models can also be classified according to their level of interpretation (Raw Model, Informative Model).

Figure 1: Taxonomic scheme of 3D digital modelling techniques compared with 3D digital
representation methods

Term

3D Modelling Technique

Definition

Term

Definition

Copyright is a legal concept that regulates intellectual property. In simpler terms, Copyright protects the right of not being copied by someone else and gives the owners of the rights the exclusivity to copy, distribute, sell, perform, adapt, modify, display, and exhibit, their creative work.

This means that anyone that wants to use a specific creative product must ask for permission from the original author first (or another legitimate right holder). In different fields, Copyright is regulated differently, but more importantly, it varies between countries. All over the world Copyright protect the creative products between 20 to 100 years from the creation/publication of the product or the death of the author. The differences depend on the country’s regulations and on the type of work. Since the differences are so impactful it is important to study the Copyright legislation in the country of application before using any authorial creative work.

In Europe, Copyright protection is granted automatically upon the creation (with proved authorship) of the creative product, and lasts up to 70 years after the death of the author. Thus, most of the historical sources (e.g., drawings, paintings, sculptures, medals, texts) that are usually used in 3D hypothetical virtual reconstructions of architecture should lie in the public domain. However, the identification of the right holder might have some exceptions based on the single case or the specific European country.

Let’s take the example of a historic blueprint or a painting of an old building, even if the original author of the work died more than 70 years ago, the digital image of the work, for German legislation, is considered a duplication (Vervielfältigung) of the original work and the author of said acquisition (in this case the operator/institution that digitised the original) holds its Copyrights. However, this practice is highly criticized within scientific communities.

Another example concerns modern measurement campaigns (e.g., SFM, laser-scanning, photogrammetry) and their derivates used for digital 3D reconstructions. Even if these types of works are still in a grey legal area, it is always preferable to not only ask for permission before proceeding with the acquisition, but it is suggested to sign a mutual contract to prove said permission in advance, in order to avoid legal issues later on. The legal contract should also concern future uses of the acquired data and the allowed forms of publication.

If photographs are considered most of the times creative original works, there is a debate on whether 3D digitisations (e.g., point clouds, photogrammetric models) fulfil, in the same way, all requirements of producing an original, with all related Copyrights and properties or if it is to be considered as a mere copy like a scan of a document, and therefore creating only non-original works, without such rights.

In mathematics, the word discretisation refers to the process of transforming a continuous/smooth function into its non-continuous (discrete) counterpart. In 3D modelling, for example, the discretisation of a model can refer to the process that converts a NURBS continuous/smooth curved surface into a discretised/faceted polygonal mesh. Thus, in the context of 3D modelling, discrete representation refers to those 3D models that describe the shapes with a set of discontinuous entities (e.g., point clouds, voxels, triangular faces) as opposed to continuous representation (e.g., a NURBS surface).

Term

Dissemination

Definition

There are many output possibilities to disseminate cultural heritage with 3D models apart from the basic interaction through a 3D viewer. Once the model is ready, it can be converted to various formats (e.g., an image, a video), it can be 3D printed, animated, included in a videogame, or XR experience, or it can be used for dynamic storytelling through a web interface, etc. The list below shows the most popular methodologies and technologies to disseminate a 3D model (with a focus on the optimization required and the most used exchange formats in the various contexts):

Renders: a rendered image (or simply a render) can be done in applications like Blender, Maya, or Cinema 4D. If the image has only visualization purposes, it is often not necessary to dedicate much effort to the optimisation of the model other than the one needed to improve render times without loss of quality. All the most popular render engines nowadays can only work with polygonal geometries, so in order to import the models in the render engine of choice, it is preferable to use mesh-based exchange formats that possibly support also the texture parametrization (e.g., OBJ, FBX, GLB, glTF).

VR and videogames: Virtual Reality and videogames are popular options for dissemination, as they enable the user to interact with the model in a more free way. Depending on the device and the game engine used, severe optimisation (concerning geometry and textures) might be needed before uploading the model in the 3D environment as the experience must be rendered in real-time, and it has to offer good performance on many devices (modern game engine like Unreal Engine recently developed tools to automatically optimize the geometries but in some cases, they still fail, and most importantly they are not compatible with all the devices, so, if possible, it is still preferable to optimize the models in advance). The most popular exchange formats to bring 3D models into game engines are those that support meshes and texture mapping (e.g., FBX, GLB, glTF, OBJ) because they not only import the geometry but also the shaders, the textures, and their parametrization (and in some cases also other properties such as animations and scene assets like cameras and lights).

AR: Augmented Reality is another common output for 3D models. Usually, the digital model is presented alone overlapped and tracked onto a real-world scene. The models need to be optimized according to the AR visualization devices of choice (e.g., headsets, HoloLenses, smartphones).

3D printing: printing is gaining importance in dissemination, especially as a response to blind people’s accessibility needs in museography and exhibitions. In the case of 3D printing of Raw Models, it is recommended to decimate them only up to the resolution of the 3D printer in order to avoid loss of detail; and in the case of 3D printing of Informative Models, it is recommended to model to a Level of Detail compatible with the resolution of the 3D printer to avoid modelling details that will not be visible in the final print. All the geometric details baked and embedded only into bump maps
- or normal maps are not considered in the 3D printing process, a good rule of thumb would be removing all the normal and bump maps before printing in order to have a more realistic preview of the result. The standard exchange formats for 3D printing are STL and PLY as printers most often work only with mesh geometries without textures.
- Animation: animation offers the opportunity to add the time dimension to the 3D space, making it a 4D model. It is an interesting output for reconstructions, as the virtual anastylosis or geometric complexion processes can be shown in a 3D timeline. Animations can be exported in various video formats, the most popular and widely supported is the MP4 with H.264 codec. Some 3D export formats recommended for 3D animated models are FBX, GLB and glTF, which support not only the model and its parametrized textures but also its animations.
- Web Storytelling: 3D models freely navigable in real time on the web can be implemented with additional information like texts and audio in order to add knowledge interactively to the experience (3D viewers like Sketchfab or Poly Viewer have plugins to insert the models in web pages that offer this kind of tools). This offers the possibility to elaborate storytelling through the 3D Model. Depending on the web service of choice, is possible to program the user navigation experience and synchronize it with the displaying of texts and images or the reproduction of audio tracks, to enhance the narrative and offer a meaningful experience.

Term

Documentation

Definition

In the field of 3D hypothetical virtual reconstructions, the documentation process concerns the careful and extensive description of the gathering and evaluating the sources used for the reconstruction, and the methods, techniques and working steps carried out to build the 3D digital model. More in general, it concerns the gathering and publication of all the metadata and paradata concerning the hypothetical reconstruction.

It provides the foundation for transparency and reproducibility of the study, which are cornerstone features of the scientific practice. Good documentation should take care not only of the textual descriptions, but also the references of the available sources used. Digital reconstructions are based on visual aspects, so it is desirable to include in the documentation other visual materials that can help to understand the research process. These can be multimedia materials (images, presentations, video, etc.) complementing the 3D reconstruction with additional information concerning the authenticity, hypotheses, source materials and their analysis, as well as archival, historical, archaeological and architectural research that has been conducted. For digital documentation, standardisation of the documentation process is crucial for the creation of an efficient research environment. The use of open exchange file formats capable of embedding metadata and paradata and relating them directly to the 3D elements is nowadays the best solution available for documenting the reconstruction process. Documentation prepared in this way should also be made available to others through publication in appropriate repositories that comply with FAIR Principles.

Term

Exchange File Format (CityGML, IFC, OBJ, glTF, PLY, IGES, STEP, STL, …)

Definition

An exchange file format, in the field of 3D modelling, refers to a 3D model file format that does not refer to any particular application. They are more effective than proprietary exclusive formats to store and share 3D data for future uses because they are most of the time open source and they should guarantee a better long-term preservation of the data. However, exchange file formats could lose specific proprietary data in the conversion process (e.g., specific metadata, modifiers, elements, filters), thus it is crucial to investigate which data a given exchange file format can carry before using it as the only vehicle of transmission of our 3D models.

FBX: stores a wide range of 3D data, including mesh geometry, animation, cameras, rigs, lights, and textures. Useful for games, XR and web visualisation.

GLB/glTF: store mesh geometry, animations, and textures using a small and compressed file size. Useful for games, XR and web visualisation and more supported by software and online viewers than FBX.

OBJ: stores mesh geometry and textures in separate files. Useful for storing the data and modifying textures.

STL: stores mesh geometry data without textures. Useful for 3D printing.

PLY: stores mesh geometry data and vertex colours. Useful for 3D printing but less supported than STL.

IGES / STEP: store NURBS geometries.

Definition

A geometric element is an element in space about which some transformation can be performed. Geometric elements are classified based on the dimensionality N of the space on which they act, the upper limit on the dimensionality of the symmetry element being N-1.

Point: the minimum element we can visualize. It represents a single exact position and has no dimension in Euclidean space.

Line is the trace of a trajectory between two points; this trajectory can be straight or curved. It has a single dimension in Euclidean space.

Plane: a set of points with just two dimensions.

Surface: the graphical element linking a series of points. Surface is also the term we generally use when we refer to the global boundary delimiting the outermost or uppermost layer of a physical object or space. Planes can be seen as a particular kind of surfaces: a flat surface, and surface as a generalization of planes. Edges can be defined as a particular type of line segment delimiting different planes or surfaces.

Manifold is a collection of points, lines or surfaces forming a certain kind of set, such as those of a topologically closed surface or an analogue of this in three or more dimensions.

Volume: a particular combination of planes and surfaces closing a particular space.

In practice, implicit representation methods describe the shape indirectly through mathematical equations or functions that define the relationship between the 3D space and the geometry of the object.

Implicit functions can describe the inside of a volume through mathematical formulas, this makes it suitable for applications where changes in the volume matter (e.g., creation of variable density 3D printing lattices, modelling of metaballs with marching cubes algorithms, reconstructing a surface from point clouds with the Poisson surface reconstruction methodology). The trade-off of this latter approach is that it is less suitable for visualisation purposes or for generating exact replicas of the boundaries of digital objects.

In the context of 3D hypothetical virtual reconstructions, solutions that use only implicit representations are of minor interest. Implicit representation is usually used in sub-steps of the reconstruction processes which are then converted into explicit representations for reproduction, manual manipulation, and visualisation purposes.

Term

Informative Model (IM)

Definition

Digital reconstructive architectural 3D models can be divided into two broad categories: Raw Models (RM) and Informative Models (IM).

The Informative Model (IM) is a digital information-enriched 3D model where the relevant information is available and accessible (Informed Model or Information Enriched Model are similar to informative models but have slightly different meanings because they do not require the information to be available and accessible).

An example of IM is any architectural source-based virtual hypothetical 3D reconstruction which is documented and published. Another example of IM is an architectonic survey that starts from raw data obtained through a laser scanning campaign which is then automatically processed to make an objective mesh model (RM), such mesh is then polished, rectified, segmented and redesigned by an author through a CAD software (IM).

The main difference between RM and IM is conceptual: the RM represents only dimensional data (and sometimes also colourimetric data) acquired from physical objects independently of any previous scientific interference. The IM, on the other hand, represents the complex interpretation process of various sources. The IM is a model obtained through a reverse engineering operation. There is also a technical difference. The RM is always discrete (numerical or polygonal). On the contrary, the IM can be represented with different digital representation methods (continuous or discrete) and built with various modelling techniques (e.g., parametric modelling, direct handmade modelling, polygonal modelling).

To sum up, the IM provides many types of information, such as metric, colorimetric, geometric, source-based. On the contrary the RM provides only metric and colorimetric information (e.g., if a chunk of a point cloud is interpreted to be interpolated with a cylindrical/planar/conical NURBS surface that interpolated 3D surface is already an IM).

Term

Informed Model / Information Enriched Model

Definition

Digital reconstructive architectural 3D models can be divided into two broad categories: Raw Models (RM) and Informative Models (IM).

LoD 100 (conceptual model where only the volumes are drafted, it is at the pre-design phase where only the designers interact);
LoD 200 (a schematic model where the dimensions, shapes, orientation and positioning are approximated, this LoD enables basic analysis of the design and preliminary coordination with other stakeholders);
LoD 300 (a developed model useful for a more accurate estimation of costs, this LoD enables coordination with the contractors and fabricators);
LoD 350 (this intermediate LoD adds the construction documentation to the previous LoD);
LoD 400 (model accurate not only in its shape and dimensioning but also with regards to construction requisites, this LoD enables the production);
LoD 500 (as-built, this LoD report all the information coherent with the constructed building, it is used for maintenance and facility management).

It is important to not confuse the LoD with the concept of the scale of representation, however, they are concepts that can be put into relation. Higher LoD (more complexity) can be related to representations at larger scales (e.g., 1:20, 1:10, 1:2), and lower LoD (less complexity) can be related to smaller scales (e.g., 1:100, 1:200, 1:300).

Level of Information Need (LOIN) is a terminology associated with BIM systems introduced as a new European Standard by the EN-ISO-19650 (2020) and defines the extent and granularity of information considering three different aspects, the geometric data, the alphanumeric data, and the unstructured graphical data (documents, sources). The standard was introduced with the goal to overcome the limitations of existing LoD definitions. With this standard, the International Organization of Standardisation asks to limit the use of acronyms as much as possible in order to reduce misinterpretations. An exhaustive literature review about this topic is the one by Abualdenien and Borrmann in 2022.

The use of the LOIN concept in the context of hypothetical 3D reconstruction is not very popular.

Term

London Charter

Definition

The London Charter is a document that aims to establish internationally recognised principles for the use of computer-based visualisation by researchers, educators and cultural heritage organisations. It was conceived, starting in 2006, to ensure the methodological rigour of computer-based visualisation as a means of researching and communicating cultural heritage. It also aimed at contributing to widespread recognition of this method.

The London Charter principles are the following and are valid whether the computer-based visualisation is applied to research or dissemination of cultural heritage:

implementation
aims and methods
research sources
documentation
sustainability
access

The principle of implementation deals with the awareness that the computer-based visualisation should follow the London Charter principles in order to be transparent and transmissible; furthermore, the costs of implementing of such a strategy should be considered from early stages in relation to the outputs. The principle of aims and methods illustrates that computer-based visualisation should be used only when it is the most appropriate for that purpose. The research sources principle illustrates the importance of properly research, analyse, structure, and communicate the sources to ensure intellectual integrity. The principle of documentation describes how to properly document and disseminate sufficient information about the process of reconstruction to make the computer-based visualisation understandable concerning its context and purposes. The principle of sustainability highlights the importance of ensuring the long-term sustainability of cultural heritage-related computer-based visualisations and relative documentation to avoid loss of knowledge. The access principle, lastly, illustrates the importance of ensuring the maximum possible benefits from the study, understanding, interpretation, preservation and management of cultural heritage and how this work of reconstruction can enhance dissemination, access and understanding.

Term

Machine Learning (ML)

Definition

Machine Learning is a subfamily of Artificial Intelligence systems (AI) which refers to all those algorithms capable of learning from reference data without needing specific instructions. This approach is mainly based on training the model by inputting huge data sets and setting some rules to evaluate the quality of the input and the output. The model is then set up to run millions of times to allow the machine to learn from its failures.

Term

Manifold

Definition

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point19. Examples of one-dimensional manifolds are (e.g.) the line and the circle. Examples of two-dimensional manifolds are (e.g.) the sphere and the torus.

In 3D modelling practice, manifold geometries are important because they can be rendered, 3D printed, and manipulated without errors. Non-manifold geometries in 3D modelling are for example two cubes attached only with an edge or a cylinder with an off-centred hole (with its axis parallel to the axis of the cylinder) that is tangent to the lateral face of the cylinder from the inside. Another example of non-manifold geometry is a mesh where three faces are attached to the same edge, in a manifold mesh each edge has two and only two faces attached.

Term

Mathematical Representation (3D Digital Representation Method)

Definition

Mathematical representation refers to the use of symbols, equations, and mathematical constructs to represent concepts and relationships. It is useful for formalising and analysing symbolic and abstract concepts. NURBS geometries are often called mathematical representations, since they are described by mathematical equations (and not numbers like meshes). Mathematical representation is often used as synonymous with parametric representation and is the counterpart of numerical representation. When 3D modelling applications implement tools based on the mathematical representation method, we can also talk about mathematical 3D modelling, which is the 3D modelling technique based on this representation method.

Term

Mesh Representation (3D Digital Representation Method)

Definition

A polygonal mesh (or simply mesh) is a 3D digital representation method where the three-dimensional shapes are described with collections of vertices, edges, and polygonal faces. Meshes always consist of triangular planar faces, nevertheless, most 3D modelling or rendering applications nowadays allow to hide some edges from the view in order to work with polygonal faces. Meshes composed mainly by quadrangular faces are often preferred to triangulated ones because they behave better in specific contexts, for example for visualisation purposes, in subdivision-based workflows, in soft body simulations, and in non-rigid animations. Mesh representations are described only with the coordinates of their vertices and by defining which vertices are connected with which other, this is why this way of representing a 3D model is considered a subset of discrete and numerical representation. Modern graphic cards are only capable of shading and rendering mesh models, thus mathematical continuous models such as NURBS must be converted into discretized polygonal meshes for any visualisation purpose. Meshes are more efficient for real-time rendering applications compared to NURBS models, especially if they have a low number of polygons, for this reason, they are preferred for computer games and any other real-time-rendering applications. Mesh models also have major cons, they are not capable of describing concepts like curvature and tangency since any curved surface in mesh 3D modelling is approximated with flat faces. Converting a NURBS model into a mesh model is an easy task that a computer can perform automatically because it is just a matter of placing points on the curved surface and connecting them with flat triangular faces. Doing the opposite is much harder, because there is no robust fully automatic algorithm capable of always accurately converting a mesh into a NURBS model yet.

Term

Parametric Representation (3D Digital Representation Method)

Definition

The Principles of Seville implements the principles already presented in the London Charter as follows:

Interdisciplinarity
Purpose
Complementarity
Authenticity
Historical rigour
Efficiency
Scientific transparency
Training and evaluation

In the context of architectural virtual hypothetical 3D reconstruction, raw data is defined as the unprocessed information instrumentally acquired from reality (e.g., from the preserved remains of built heritage through laser scanning or photogrammetry) necessary to create the Raw model (e.g., the photos for a photogrammetric campaign).

The raw data is independent of the user’s subjective influence by definition, namely, Raw data only represent metric and colourimetric information (that is objective up to the accuracy of the acquisition technology used) and does not contain any interpretative or creative addition by any author. If two different users acquire the same physical object through the same instrument with the same input settings and environmental/boundary conditions, the data from the two campaigns would be analogous. The difference between Raw Data and Raw Model is that the Raw Data does not necessarily have to be three-dimensional (e.g., the photographic set for photogrammetry before processing is raw data).

Term

Raw Model (RM)

Definition

Digital reconstructive architectural 3D models can be divided into two broad categories: Raw Models (RM) and Informative Models (IM).

The Raw Model is a digital 3D model obtained through quasi-automatic procedures starting from raw data captured from physical sources with minimal subjective interpretations by the operator (e.g., digital photogrammetry, laser scanning). For example, possible sources may be archaeological remains (e.g., the ruins of a Roman theatre) and in this case the RM could be a point cloud or a textured mesh model.

The main difference between RM and IM is conceptual: the RM represents only dimensional data (and sometimes also colorimetric data) acquired from physical objects. The IM, on the other hand, represents the complex interpretation process of various sources. The IM is a model obtained through a reverse engineering operation. There is also a technical difference. The RM is always discrete (numerical or polygonal). On the contrary, the IM can be represented with different digital representation methods (continuous or discrete) and built with various modelling techniques (e.g., parametric modelling, direct handmade modelling, polygonal modelling).

Reflectance Transformation Imaging (RTI) (or relightable imaging) is an acquisition technique, of quasi-planar manufacts, that captures the surface colour and surface ruggedness of an object and produces an enhanced 2D visualisation that enables the interactive re-lighting of the subject from any light direction22.

Taxonomic scheme of 3D digital representation methods, compared with 3D digital modelling
techniques.

The 3D digital representation method concern the intrinsic mathematical/geometrical nature of the 3D models, namely they are the languages (or set of rules) that the software uses to represent shapes in a three-dimensional space.

The naming 3D digital representation methods comes from their analogies with the traditional representation methods. The main analogy concerns the fact that both digital and traditional methods are sets of mathematical/geometrical rules developed to represent shapes, the former in 3D space, and the latter in 2D space. There are also analogies in the way they are used. For example, orthogonal views and axonometric projections are used to describe precisely the shape and dimensions of an object; on the other hand, perspective projections are used to describe how humans perceive space with sight. In the same way, the continuous/mathematical/parametric representation methods, for example, are used to precisely describe the shape and are more suitable to accurately control the geometric shape, while the discrete/numerical/non-parametric representation methods are used to approximate curved shapes and are more suitable for visualisation purposes (renderings).

The most relevant classification of representation methods used in the field of virtual hypothetical 3D reconstructions considers two methods: continuous representation (e.g., NURBS, Bézier, spline) and discrete representation (e.g., mesh, point clouds, voxels). Continuous and discrete representation methods are also known as, parametric representation and non-parametric representation respectively, however, we will suggest not using this latter naming in this context to avoid ambiguity with the parametric 3D modelling technique which has a completely different definition.

Another possible classification of the digital representation methods confronts the mathematical representation from the numerical representation. Since mathematical representation concerns equations (described with parameters), and numerical representation concerns numbers (coordinates), In the context of hypothetical virtual 3D reconstruction this classification overlaps with the continuous/parametric and discrete/non-parametric classifications.

Another possible classification of digital representations considers the forms of the equations used to describe the digital shapes: implicit representation, and explicit representation, this latter classification is not analogous to the previous ones, however, it is less interesting in the context of hypothetical virtual 3D reconstructions because it does not correspond to specific geometrical features of the models. For example, a curved smooth NURBS model and its mesh approximation can be both explicit representations of the same object, however, they have a very different geometrical nature, the former is a continuous smooth accurate description of the shape, while the latter is its approximation with flat faces (discretization).

There are many possible ways to classify representation methods, the last presented here concerns the differentiation of methods that represent the 3D models as boundary representations, solids, volumes or wireframes.

Retopology is the process of modifying or recreating a 3D mesh model in order to improve its geometric structure (e.g., edge flow, quadrangular faces, loops and rings), for future processing that requires a specific configuration/organisation of the model topology (e.g., subdivision surface, soft-body animation).

While the decimation of a 3D model means the reduction of the polygon count of the model, the retopology implies the re-creation of a new and cleaner mesh from scratch, for this reason is considered a 3D modelling technique. It is highly recommended for improving hardware performances and visual quality, especially if the model comes from automatic or semi-automatic digitisation methodologies (photogrammetry and laser scanning). The reason is that digitisation automatic and semi-automatic procedures produce triangulated 3D models, while for visualization and animation, quadrangular faces are preferred. Quads-based meshes provide improved behaviour in UV mapping, smooth shading, subdivision surface workflows, and soft body animation.

In architectural drawing, the scale of representation is used to determine the size of the object or architectural space based on its drawn reproduction on a bi-dimensional media (e.g., a sheet of paper). In this context, the representation scale of 3D models has a direct analogy with the representation scale of 2D drawings. Generally, when building a 3D model, it is necessary to set a reference unit of measurement in the virtual space (for example, one unit of the virtual system corresponds to one centimetre of the metric system). Furthermore, it is necessary to set a tolerance which establishes the software’s accuracy when performing the calculations.

The choice of the reference unit of measurement (centimetre, metre, kilometre, Roman feet and more) must be based on the target Level of Detail. Therefore, for example, the reference unit will be centimetres if the target scale of the details is equivalent to a 1:50 scaled print; or the reference unit will be kilometres if the target scale of the details is equivalent to 1:10000 scaled print. In conclusion, when working in a digital space, the concept of scale is not any more strictly related to the size of the represented object because through displays digital objects can change in size based on the zoom level, on the contrary, it would be related to the maximum scale at which the 3D digital model could be printed without loss of detail. So instead of saying “The model is in scale 1:1”, one could say “The model was built in cm without reduction or multiplication factor, and its LoD is comparable to that of a drawing in scale 1:100”.

Term

Scientific 3D Hypothetical Reconstruction

Definition

In the context of 3D hypothetical virtual reconstruction, the subjectivity of the operator is an unavoidable factor. For this reason, the use of the adjective scientific in this contest is widely debated.

Defining the word scientific can be a big challenge by itself, because it covers a vastity of subjects and many scientists, thinkers and philosophers gave innumerable definitions with slight differences which for reasons of space we cannot enumerate all here. However, a good synthesis is given by the AI tool Chat GPT24: “The term scientific pertains to anything that is related to or based on the principles and methods of science. Science is a systematic and organized approach to acquiring knowledge and understanding the natural world through observation, experimentation, and logical reasoning. It involves formulating hypotheses, conducting experiments or making observations to test those hypotheses, and analysing the data to draw conclusions.”

The canonical steps of the scientific process consist of:

defining a question to investigate,
making predictions,
gathering data,
analysing the data,
drawing conclusions.

Some authors also add a further step, which is the sharing of the results with the reference scientific community, which validates them by reproducing the experiment/procedure and comparing the results.

Solid Representation (3D Digital Representation Method)

Definition

Figure 7: an example of an uncertainty scale where the uncertainty is related to the type, authorship and quality of the reference sources used. This scale is conceived for 3D hypothetical virtual reconstruction of architectural heritage. In cases where authors are unknown (such as in some archaeological periods) the five-levels scale presented in [Apollonio et al., 202432] could be more appropriate.

The uncertainty scale (sometimes it is called the reliability scale which is opposite to uncertainty) is an analysis and visualisation strategy for hypothetical source-based reconstruction aimed at evaluating the level of accuracy and consistency of interpretation and historical plausibility based on some related data (e.g., historical documental sources). Different scales could exist based on the different objectives of the reconstruction.

The uncertainty scale is based on the definition of a multi-step sorted list, where every item of the list is related to a certain level of uncertainty described textually and/or numerically and assigned to specific elements/areas of the hypothetical reconstructive model (an example of uncertainty scale is in Figure 6). In order to visualise the assigned levels of uncertainty the textual definitions are usually paired with colours (or other similar graphical artifices: e.g., different patterns, level of transparency, silhouette lines), that are assigned to the various elements of the model through false-colour shading. Over the years several scales have been developed, for example, some measured the uncertainty based on the type of sources, others by following fuzzy logic approaches, others by relating their levels to the amount of available physical ruins.

The various one-dimensional scales developed over the years (simple lists of elements) sometimes evolved into n-dimensional matrices (tables with multiple entrances). Uncertainty matrices are able to cross-reference multiple factors at the same time, this approach is harder to read and apply but is capable of transmitting more information.

Virtual hypothetical 3D reconstruction refers to the process of digitally recreating or constructing a three-dimensional representation of an object, structure, or environment that may no longer exist or is inaccessible in its original form. It involves using available data, such as historical sources, photographs, archaeological findings, or physical remnants, to create a virtual representation of the object.

The process of virtual hypothetical 3D reconstruction usually involves the following steps:

Data Collection: relevant historical or archaeological data, including photographs, drawings, measurements, or written accounts, are collected to provide a basis for the reconstruction. This data serves as a reference for understanding the original form and characteristics of the subject.
3D Modelling: using specialized software, a 3D model is created based on the collected data. This involves recreating the shape, structure, and appearance of the subject using various 3D modelling techniques and methods of representation.
Texture mapping and definition of material properties: sometimes the 3D model is further enhanced by applying textures, colours, and material properties to enhance the visual appearance of the subject; textures can be derived from historical images or artistic interpretations. Sometimes this step is completely skipped if the initial sources do not provide enough information, and a neutral mono-material is applied instead (white, grey).
Addition of contextual assets: sometimes additional elements such as characters, furniture, products, and vegetation, are added in order to achieve a better placemaking and depict the atmosphere of the represented time by adding a further layer of complexity considering perception and/or social relations between people and artefacts.
Presentation/visualisation and interaction: the reconstructed 3D model can be presented/visualised by means of various methods and technologies. It can be rendered as static images depicting it from different angles; animated and presented in a video fort; or presented in an interactive virtual environment.

Virtual hypothetical 3D reconstruction plays a significant role in disciplines such as archaeology, cultural heritage preservation, architecture, history, and education. It allows researchers, historians, and the public to experience and understand historical or archaeological subjects that may no longer exist in their original form. Virtual hypothetical reconstructions help visualise and communicate the past, provide insights into lost civilizations, architectural marvels, or significant historical events, and contribute to the preservation and documentation of cultural heritage.

Wireframe representation is a 3D digital representation method where the 3D models are represented as cages of vertices connected with straight segments. Wireframe representation is different from the mesh representation because in wireframe representation there are no faces and thus edges in front or behind the 3D shape are visible all at once without any hierarchy.