3D Modeling

Abstract

The chapter introduces the concepts of the raw model and informative model; it clarifies the concept of semantic segmentation and defines the digital representation methods and 3D modeling techniques; finally, it lists the different configuration spaces of a 3D model in different software packages.

Guiding questions

• What are the methods of digital representation?

• What are the 3D modeling techniques?

• What are the differences between representation methods and 3D modeling techniques?

Basic terms

• Raw Model (acquisition/digitization)

• Informative Model (information enriched reconstruction)

• Discrete and Continuous modeling

• Semantic segmentation

• Mesh

• Non-Uniform Rational B-Spline (NURBS)

• Tessellation (discretization)

• Level of Detail (LoD)

6.1 The Raw Model and the Informative Model

Retro-digitization is the process of conversion into the digital format of a work designed and published in an earlier era. There are several approaches for converting a real object into digital form; sometimes, the raw data captured from reality has to be interpreted and manipulated to produce a critical digital version of the object. At other times the object is no longer extant or was never realized and the 3D information must be extracted from documental sources, critically analyzed, and used as a starting point to reconstruct the 3D model [1].

According to this premise, two main models within retro-digitization can be defined in this context: the digitization, or Raw Model, and the reconstruction, or Informative Model. This classification is proposed for the first time in this book, and it is aimed to emphasize their different natures. The Raw Model (RM) is the unprocessed digital survey of real sources (e.g., the point cloud/textured mesh resultant from the laser scanning of the remains of a Roman theatre). The Informative Model (IM) is the critical rationalized hypothetical virtual reconstruction.

The RM is based on data that can now be obtained almost automatically using the tested digital methodologies of architectural survey. Raw means unprocessed, thus this model is based on the captured original data and it is not equivalent to the ultimate result of an architectural survey which is usually interpreted and processed by the operator (e.g., the points that are coplanar or colinear in a point cloud are approximated with a plane or a line [2]). The RM is data obtained with automated procedures. The precision and accuracy of this data are linked to the correctness of the survey procedures adopted and the tools used.

The two most used techniques to generate a RM are digital photogrammetry and digital scanning. Both produce a 3D point cloud that can be automatically (or semi-automatically) transformed into a textured polygonal 3D model. Digital photogrammetry calculates 3D information of the displayed objects from photographs taken at different angles and returns 3D models of remarkable graphic quality that embed information even on the material surface of the artifact. The technique is based on capturing and processing photographs; therefore, it is relatively inexpensive because the tools needed are a camera and a computer to run the processing program, which is less expensive than a laser scanner. There are several applications on the market and the cost is easily managed by any architectural firm or university research department. Digital scanning uses laser scanners which gathers information about the geometry of objects by sending a laser beam at different angles and measuring the distance between the laser emitter and the object's surface by the beam's time of flight. The cost and quality of the scans are related to the type of scanner used. These tools are considerably more costly than photogrammetry but return metrically very accurate data. Today when it is economical and practical, these two techniques are used together. Those techniques are described in the literature [3,4,5,6].

The IM is built from a series of inferences based on reference data. This concept, therefore, can be compared to what is known as reverse engineering. This process starts from a reference in its final form with missing data and tries to deduce what was the process that generated it. The RM lacks any semantic segmentation and organization and can be used as a source to build the IM. Several studies are attempting to automate the creation of a semantically structured IM starting from the RM data, e.g. by identfying architectural segments from point clouds by using AI [7]. To date, these studies have not produced satisfactory results, at least for application to architectural cultural heritage. The current algorithms are not capable of identifying with sufficient efficiency the complexity and the variety of architectural typologies. Will it be possible to automate this step in the future? This question cannot be answered now, but the complexity of virtual reconstructions is similar to the complexity of any creative act; therefore, it requires a certain amount of creative and analogical intelligence which is typical of the complexity of the human mind.

Further reading: Research on modeling

The research on technologies for 3D modeling and 3D digitization has been important for decades. In recent decades, various large-scale projects on the EU level on 3D modeling in cultural heritage primarily focused on 3D digitization from contemporary survey data [8]. A major objective during the FP7 to Horizon 2020 framework programs was to ease use, reduce costs, and increase quality. With the following transition to the Horizon Europe framework, valorization, and wide use became the focus. As recent projects on the EU level, the VIGIE study [9] examines use cases for 3D/4D digitization of tangible heritage and the EU DT–20 competence center [10] investigates and develops support structures for 3D digitization from contemporary survey data. Various articles were published to provide an overview of particular technologies of relevance for 3D modeling and visualization, recently on laser scanning [11], photogrammetry [12], machine learning [13, 14], and extended reality technologies [15].

6.2 Semantic Description of the 3D Model

Semantic segmentation/organization of data is the act of logically subdividing and structuring information by making groups and naming each element according to similarities (shape, type, position, etc.). It is rooted in the scientific organization and systematization of knowledge, or taxonomy, which means a scheme of (hierarchical) classification in which things are organized into groups or types, uniquely named and identified. It allows for knowledge to be indexed and organized (e.g., a search engine taxonomy), so users can more easily find the information they are searching for (Fig. 6.1).

Fig. 6.1

(Image: Foschi)

Semantic segmentation of a 3D photogrammetric model

The semantic segmentation/organization of data is not only a matter of digital representation; it rather intrinsically belongs to architecture [16]. This structure must be linked to the language and type of architecture and must be as simple as possible. It is, therefore, important to build the Informative Model by individually modeling its architectural elements and keeping them well organized. The parts should be named clearly and unequivocally and grouped hierarchically [17, 18]. A building could be semantically segmented into its elements as follows: the roof, the attic, the base, the window, the door, the column, the wall, etc. Each element could be differentiated from the others by adding to its name an indication of the positioning or numbering it in the group of analogous elements. This first semantic structure is extremely important because it allows anyone to clearly name each part of the analyzed architecture and refer to it unequivocally. Only through clear and rational identification of these architectural elements it is possible to appropriately decoding the model. Building a 3D model by assembling single elements also simplifies and rationalizes the process of 3D modeling: it allows copy-pasting instances of parts that are equal/analogous, speeding up the modeling and analysis process, and decreasing the file size. Semantic reading, therefore, has its digital equivalent in the structure of 3D models like in any CAD and BIM software. This simple 3D model structure can be refined and hierarchically organized at a later stage. This second level of the semantic organization of the model can follow various paths, which are generally also linked to the purpose of virtual reconstruction. For example, in an antique building, the architectural elements could be organized according to the architectural order. We could create a column level, and below this column level, insert the elements of the shaft, the base, and the capital. Or we could divide and organize the elements according to the floors of the building, etc. Of course, these choices are linked to the architectural typology analyzed and the semantic choices must rationally reflect this important relationship.

Further reading: Algorithmic modeling and machine learning

• Algorithmic modeling: Traditional algorithmic-only approaches, as in photogrammetry, employ algorithms to complete a specific operation, e.g., to detect, describe, and match geometric features in images [19]. In contrast, machine learning uses algorithmic approaches to train a statistical model in a supervised or unsupervised way via training data—e.g., to detect features [20]. Current evolvements in computer vision are closely coupled to the massive renaissance in machine learning [21] with the use of convolutional neural networks (CNNs) [22] since 2012. Machine learning approaches are currently heavily researched and used for image and 3D point cloud analytics in cultural heritage [13], but also increasingly for 3D modeling tasks.

• 3D/4D model generation via machine learning: In 3D reconstruction of cultural heritage, machine learning-based technologies are primarily used for specific tasks within the modeling process: to preselect imagery [23, 24], in semantic segmentation to classify parts of images [25,26,27], and to recognize specific objects.[27,28,29,30] Another strand—bypassing the modeling stage—is generating visualizations directly from imagery [28, 31, 32]. Machine-learning-based technologies currently require large-scale training data [13, 27, 28] only capable of recognizing well-documented and visually distinctive landmark buildings [33]. Machine learning fails to deal with less distinctive architecture, such as houses of similar style. Regarding transparency, most machine learning approaches are applied within black box settings in a non-standardized way [13, 34]. Specifically, generative adversarial networks (GAN) as a combination of proposal and assessment components of machine learning are frequently employed in 3D modeling. Application scenarios are single photo digitization [35], completion of incomplete 3D digitized models [36, 37], or photo-based reconstructions [38]. Neural Radiance Fields (NeRF), which use viewpoint cuing [39], have gained importance since 2020. Although primarily an image transformation-based approach to calculate new viewpoints, NeRF enables, e.g., lighting changes [40] or 3D mesh calculation from sparse imagery.

The semantic construction of the 3D model is linked to the knowledge of architecture; not only its history but also all those qualities that define it: type, geometry, shape, architectural orders, etc. Therefore, the culture of the creator of the 3D model is an important aspect. A scholar reconstructing a Renaissance building will have to study the design of the architectural orders and the history of Renaissance architecture. The quality of a virtual reconstruction depends primarily on the scholar’s discipline culture and experience. For this reason, a multidisciplinary approach from different expertise is desirable: architects, historians, engineers, archaeologists, etc.

6.3 Traditional and Digital Representation Methods

Digital representation has somehow closed a cycle between the real physical model and its representation. From a 2D drawing, it is possible to construct a digital 3D model; this 3D model can be printed into a physical model ($\to$ Media and Interfaces); this physical model or maquette can be scanned and transformed into a digital point cloud; this point cloud can be transformed into a mesh model; the process can go on and the cycle repeats itself. Therefore, digital representation has not only increased the accuracy of the drawings but has also allowed transformations between the real physical model and its representation in a more fluid and versatile way.

Despite its importance, while there are shared standards and norms for traditional 2D drawings (plans and elevations), for the construction and evaluation of digital 3D models these norms have not yet been fully defined.

Scholars that use 3D models as tools hardly ever make explicit reference to the methods of representation and techniques they adopted to build them. Nevertheless, it would be advisable for scientists and researchers to always declare the techniques and methods used, to enhance transparency and interoperability of the 3D models ($\to$ Documentation). This is also an important prerequisite for the scientifical reuse of 3D models, made by others, as a source of knowledge. In the next few paragraphs, the representation methods and 3D modeling techniques are defined and illustrated.

The methods of digital representation concern the intrinsic mathematical/geometrical nature of the 3D models and are either continuous or discrete (Fig. 5.5):

• Continuous methods: the geometry is described in a continuous way with mathematical equations, the Mathematical /Surface Modelling is part of this category (e.g., Non-Uniform Rational B-Spline (NURBS) modeling)

• Discrete methods: the geometry is described in a discrete way, not with equations, but with points described by coordinates (vertices), lines (edges), and planar faces (polygons); numerical/polygonal modeling is part of this category (e.g., mesh modeling).

All the other methods mostly used in the architectural world can be considered subsets of one of these two. For example, point cloud modeling is a subset of mesh modeling, and spline and Bezier modeling are subsets of NURBS modeling (Fig. 6.2).

Fig. 6.2

(Image: Foschi)

Continuous (NURBS, on the left) and discrete (mesh) 3D models with different tesselation

Parametric modeling, handmade modeling, digital sculpting, etc. are not methods of digital representation, they are  3D modeling techniques ($\to$ 6.4 3D Modeling Techniques) to create models of continuous or discrete nature.

Continuous and discrete modeling have analogies with the traditional methods of representation. Some scholars [41] propose to consider them as a direct addition to the traditional representation methods which are:

• Double orthogonal projection

• Axonometric projection

• Perspective projection

• Topographic terrain projection (with contour lines).

Choosing between the discrete or continuous method has similar implications as choosing to use an axonometry or a perspective. What is this method useful for? Why is it more useful than the other/s? What aspects are you highlighting by choosing it? Even if the final appearance of an object represented with one method or the other might be similar (or even the same), the implications of using one or the other methods are different, due to the scope and the data that the method carries.

For example, if we represent the front view of the same cube in double, axonometric, and perspective projections, the resulting image is the same, a square. Yet, the constructions that generated those results are different, and so are the purposes that lead us to choose one method over the other. We use double orthogonal projections to study and check the measurements and proportions of the object; we use axonometric projection to represent the relationship between volumes or the mechanism of the object; we use perspective projection to mimic how the object is perceived by human eyes. Axonometric and double projections are widely used in mechanical drawings and executive architectural drawings, while perspective projection is widely used in painting and architectural renderings. Similarly, we use the digital methods of mathematical representation (NURBS) to describe the form accurately and continuously. Instead, we use the polygonal method (mesh) to build organic shapes or produce renderings.

3D models can also be generated with hybrid methods, i.e., a model can be formed from mathematical solids and mesh solids. This also happens in traditional representation methods: for example, a perspective section includes both the section in true form, as in double orthogonal projections, and the perspective view to formally evaluate the space (Fig. 6.3). Mastering all representation methods (both digital and traditional) is important because each of them has a specific vocation and is more effective than another only in some contexts.

Fig. 6.3

(Image: Fallavollita)

Perspective section of the never-built church of S. Margherita, Bologna, 1685 (Agostino Barelli), informative reconstructive model

To sum up, the methods of digital representation can be classified into two distinct families: continuous and discrete. Continuous methods describe the shape continuously and accurately through mathematical equations; the NURBS mathematical representation is the most popular today. Discrete methods describe the shapes in an approximate and discrete way through a list of vertices, described through their coordinates, and a list of edges/faces that connect them; mesh polygonal modelling is the most popular today. The point cloud is a subset of the numerical representation in which the shape is described solely by a list of points in space (Fig. 6.4).

Fig. 6.4

(Image: Fallavollita and Foschi)

Conceptual scheme of 3D modeling classification

To give a clarifying example, imagine modeling a sphere. With the continuous method, the sphere will consist of a mathematical equation that describes the surface continuously and accurately. With the discrete method, the sphere will consist of a set of vertices connected by edges filled with triangular faces (some applications support polygonal faces with more than three edges but they always hide triangles inside) which discretizes the surface with a certain approximation (Fig. 6.2). Naturally, the more tessellated the surface of the sphere (more vertices, or smaller triangular faces), the less approximated the surface will be with respect to the ideal sphere.

6.4 3D Modeling Techniques

3D modeling techniques are the practices, processes, and norms used to create the 3D models described with any of the digital representation methods (continuous or discrete). To make an analogy with traditional drawing: the watercolor technique can be applied to realize perspective views, axonometric views, or double projections and it is used to obtain a shaded image. Analogously, the technique of parametric modeling can be used to generate both mesh and NURBS models. The 3D modeling techniques describe the act of constructing the shapes. These must not be confused with the digital representation methods that define how the computer represents the mathematical nature of the shapes.

Given this assumption we can define the following 3D modeling techniques:

• Procedural algorithmic modeling

  Software programs are e.g., McNeel Rhinoceros + Grasshopper, Autodesk Revit + Dynamo, Blender + Geometry Nodes;

• Parametric modeling

  Software programs are e.g., Autodesk Inventor, Dassault Catia, PTC Creo Parametric;

• Automatic reality-based modeling

  Software programs are e.g., Agisoft Metashape, Reality Capture;

• Direct handmade modeling

  Software programs are e.g., Rhinoceros, Autodesk Autocad, Maxon Zbrush, Blender, Autodesk 3D Studio Max, Maxon Cinema 4D;

• Hybrid modeling

  Nowadays supported by almost all commercial software packages. Almost all commercial software packages, nowadays, are considered hybrid modellers.

It is important to note that the classification proposed here is provisional. Professional 3D modelling applications are constantly evolving and the list of techniques and methods supported is subject to change.As a result, the software examples provided are for guidance only and are not exclusive.

6.4.1 Procedural and Algorithmic Modeling

Procedural/algorithmic modeling is when the 3D model is generated through the definition of an ordered set of non-destructive actions/operations/steps/commands that are memorized, and each step can always be accessed and modified to update the final output. The actions can be in the form of strings of text, mathematical formulas, nodes connected with wires, and so on. This technique is used when dynamic manipulation of the process is a key factor in defining the final form (Fig. 6.5).

Fig. 6.5

(Image: Foschi)

Creating a 3D model with an algorithm in a graphical scripting language

Applications that allow modeling through a graphical programming interface, such as Revit + Dynamo, Houdini, Blender + Geometry Nodes, and Rhinoceros + Grasshopper [42], are considered algorithmic modelers. All these applications share the same approach, where each command is in the form of a node that is connected chronologically to other operations through wires. This makes the algorithm easier to create, explore, investigate, modify, and share. More apps are nowadays integrating this type of interface because it enables modeling very complex 3D objects with much less effort than hand-made direct approaches. Furthermore, the algorithms can be shared, to allow others to reuse and modify them without needing to reproduce the same process step by step.

“Procedural” means made with/through a procedure, so procedural modeling should be synonymous with algorithmic modeling, but is sometimes used with a different connotation. For example, in software such as Cinema 4D and 3DS Max, it is possible to model in a non-destructive way by applying and stacking modifiers on simpler starting 3D geometries. This approach is much less versatile than that with a graphical programming interface. Nevertheless, both methods can be used to store the whole modelling process, and access and modify it at each point, so they can be considered as part of the same category.

MathWorks, MATLAB and GeoGebra can be used to generate a 3D model through a sequence of non-destructive commands that are always accessible and modifiable, but the command needs to be inputted in the form of strings of text or mathematical formulas, so they are less popular for digital 3D reconstruction of cultural heritage but are still part of the same category.

Each modeling technique has algorithms or code hidden inside its commands, but in 3D modeling in the past few decades algorithmic modeling has acquired a specific connotation with applications that focus on the algorithm, and it is findable, accessible, and modifiable at any time. If the algorithms are hidden from users and a lot of manual interaction is needed to create the 3D model, the technique would rather be categorized as direct handmade modeling.

6.4.2 Parametric Modeling

Parametric modeling is similar to algorithmic/procedural modeling and sometimes these terms are interchangeable, despite slight differences. In parametric modeling, it is not always possible to access each step of the process and modify it non-destructively. For example, in applications such as Autodesk Fusion 360, PTC Creo, and Inventor, it is possible to create a 3D object and change the initial parameters (size, position, generative curves, etc.). However, it is not possible to access the chronological sequence of the operations performed on the model from the beginning; only some parameters are modifiable, and it is not possible to add additional operations in between other operations already performed. This is what differentiates parametric modeling from algorithmic/procedural 3D modeling, although each technique could be used to produce similar results [43]. Their focus is different: parametric modeling focuses on the input parameters and the outcome; algorithmic/procedural modeling focuses on the process (Fig. 6.6).

Fig. 6.6

(Image: Fallavollita and Foschi)

Parametric modeling of a Ionic column, by chaning the parameter of the height we can update the 3D model

6.4.3 Automatic Reality-Based Modeling

In automatic reality-based modeling, the 3D model is generated through the application of a set of computer-based analyses and elaborations (Fig. 6.7), predefined by the developer of the software, starting from a set of input data (e.g., point clouds or images) captured by the user from reality with minimal manual interaction. Two main approaches that make use of automatic reality-based modeling are photogrammetry and laser scanning.

Fig. 6.7

(Image: Foschi)

Automatic reality-based modeling using photogrammetry. Top left: aligned photo and sparse point cloud; top right: aligned photo and dense cloud; bottom left: mesh; bottom right: textured model

Someone could claim that user interaction is still necessary to tell the computer how to use the captured data and to validate the result, however, the polygonal shape and textures of the model could potentially be automatically generated from start to finish without needing any interaction. Every other manipulation of the point cloud or the mesh model itself is not part of the automatic reality-based modeling algorithm, but it rather must be considered as direct handmade modeling.

6.4.4 Direct Handmade Modeling

Direct handmade 3D modeling is probably the most popular way to generate a shape with a computer. It consists of generating the 3D model manually by using the tools provided by the software (Fig. 6.8). It requires constant mouse and keyboard navigation of the 3D space and interaction of the 3D model, and most of the changes to the model are destructive, meaning that the model cannot be updated by changing parameters that were inputted in previous steps. For example, the CAD modeling of a house, the 3D mesh sculpting of a character, or the low poly polygonal modeling for video games assets can be performed entirely through direct handmade modeling. Digital sculpting is also considered as direct handmade modeling because the tools that are mainly used specifically resemble the tools of a sculptor (e.g., scalpel, brushes, scrapers).

Fig. 6.8

(Image: Foschi)

Handmade modeling through digital sculpting and polygonal modeling

Nowadays applications that only provide direct handmade modeling tools are hard to find; almost every application integrates some non-destructive workflows for specific operations because they speed up the shape-finding process. The reverse is also true: modeling applications that define themselves as algorithmic, automatic reality-based, or parametric modelers almost always integrate direct handmade modeling tools.

6.4.5 Hybrid Modeling

All the modeling techniques that make use of multiple approaches are considered hybrids. For example, a model can be generated by using direct handmade modeling for the preliminary shape and algorithmic modeling for adding more complex details. So basically, most of the software packages and applications nowadays are probably adopting hybrid approaches.

Among hybrid techniques, building information modeling (BIM) has to be considered as a special case. It deals with modeling, because the BIM method is more about data organization, automatization, and interoperation, including information about materials, prices, forces, technical systems, and construction site facilities. Thus, BIM is mainly used for the holistic management of architectural projects, and it is not exclusively dedicated to modeling.

6.5 Configuration Space

Other than classifying the models by their level of interpretation (raw or informative), the digital representation method adopted (continuous or discrete), and the technique used to generate them (procedural, algorithmic, etc.), we can also differentiate models by how the software considers their configuration space. There are four main ways that applications are used to describe the configuration space of 3D models (Fig. 6.9):

Fig. 6.9

(Image: Foschi)

Surface, solid, wireframe, and volumetric modeling

• Surface modeling (B-rep)

• Solid modeling (closed and manifold B-rep)

• Wireframe modeling (interlinked edges)

• Volumetric modeling (voxels).

Surface modeling or boundary modeling (B-rep) describes the models as collections of connected surfaces. This way of considering the models allows open and non-manifold geometries, in other words, geometries that do not have a clear distinction between the inside and the outside and thus have no calculable volume.

Solid modeling describes shapes as volumes and has a predilection for Boolean operations. It can also be generated by B-reps: this changes how the software checks the validity of the geometry generated, which basically would not allow generating any open or non-manifold geometry.

Most 3D modeling applications adopt hybrid approaches. Computer applications that define themselves as surface modelers can be used to connect single surfaces and generate closed poly-surfaces to then apply Boolean operations that by definition can only be performed between watertight solids. Other applications that define themselves as solid modelers allow the user to split the solids into the single boundary surfaces that enclose the volume. These ambiguities that can be observed in many applications are mostly due to the fact that software developers try to meet users’ needs by implementing new commands.

Volumetric models and wireframes of 3D models are other two ways of describing the configuration space. In volumetric modeling, the volume is usually occupied by points (points sometimes are shaped like cubes or spheres: then they are called voxels and thus there is a discrete volume), and each of these points is enriched with specific data, such as structural stresses, temperature, type of material, density, and so on. This type of model is mostly used to store and visualize data from tomographic surveys in engineering, archeology, and medicine, or for physical simulations (fluids, rigid bodies, etc.). Lastly, wire modeling only provides the cage of a 3D model, made of edges that meet at vertices. In this case, there is no distinction between the outside and inside of the configuration space and thus it has no calculable volume.

6.6 Best Practices

There are five main aspects to consider for properly designing the model:

• Semantic organization

• Scale and level of detail

• Solid modeling

• Model tessellation

• Interoperability

The semantic organization of a 3D model mostly uses one of two methods: philological and constructive/semantic. The two options may be coincident in some cases but in most cases, they return differently segmented models. The creator has to decide which path to choose and how to organize the semantic and logical structure of the model. To give an example, think of a reconstruction of a column of an Ionic order (it could be a Corinthian or Doric order, it does not matter). In constructive semantic logic, the base of the column generally includes the initial part of the column, the attachment to the base formed by a strip (listello) and an arched connection (apophyge/cavetto/fillet). In philological logic, however, the base will stop exactly below the shaft of the column and the listello + apophyge will be part of the shaft and not of the base (Fig. 6.10).

Fig. 6.10

(Image: Fallavollita and Foschi)

Different segmentation of the column base: constructive semantic approach on the left, philological approach on the right

The second aspect concerns the scale and the level of detail (LoD). It is generally said that in virtual space one draws on a scale of 1:1. This statement is misleading because in architecture the representation is generally on a reduced scale, also in 3D digital modeling. As in traditional drawing, there are different scales of representation, and thus of LoD. For example, we could define that a certain model has a LoD comparable to a scale of 1:100 while another 3D model is equivalent to a scale of 1:20 because it has greater detail. Certain modeling applications, e.g., BIM applications and game engines, allow for multiple LoDs within the same model. It must be remembered that these different levels are nothing more than different models that are displayed when different scales are requested. Again, the analogy with traditional methods is still valid both in theory and in practice.

Further reading: Level of detail

Level of detail and/or development (LoD) is used to differentiate between multiple variants of the same model with a different number of polygons or different levels of complexity [44]. Some systems distinguish between five gradations (Fig. 6.11). Since these are only roughly described in terms of graduation, in practice this often leads to intermediate levels, such as LoD 2.5 as a model of the building exterior envelope including window partitioning. Specific LoD classifications have been developed in some fields of application, as described for BIM [45] or, with different LoD scales, CityGML for GIS [46].

Fig. 6.11

(Image: Foschi)

Model detail qualities of virtual 3D reconstruction according to City GML [46]

Solid modeling is the third aspect of architectural modeling [47]. One way to obtain traditional and manageable models is to conceive and draw a 3D model composed of closed, non-self-intersecting solids. There are two main reasons for following this procedure: conceptual and technical. The conceptual is most important and concerns the logical construction of architecture. The real world of constructions is made up of solid objects that cannot under any circumstances interpenetrate or be “floating”: physical and static laws do not allow exceptions. Of course, in the virtual world, these exceptions are allowed: we can construct two solids that intersect or are hovering in space; moreover, we can conceive objects composed of single surfaces or open poly-surfaces. These exceptions must be avoided because they would have no possible equivalent in architectural reality. The technical reason concerns some consequences that these exceptions could have in digital representation. If a 3D model contains some parts composed of open surfaces or open meshes, they will not be 3D printable. In addition, open or self-intersecting poly-surfaces may cause errors and glitches in the rendering phase. If two surfaces overlap, they will be likely displayed as a patchy or flickering surface; this is because the computer does not know which surface is on top and returns a confused surface (known as z-fighting effect). Moreover, where the light hits open poly-surfaces there may be unrealistic shadow effects or light leaking. For these technical reasons, it is useful to conceive and build architectural digital 3D models according to non-self-intersecting closed and manifold solids. The possible objection to this simple solid modeling principle could be that in some cases computer graphics requires specific measures to obtain rendering effects or to lighten the model. For example, when you need to render a glass object that contains a liquid such as a glass of wine, the element of the wine should slightly be interpenetrated to (or moved away from) the solid of the glass. Or in video games, all the surfaces that are not visible are eliminated to make the game lighter to run. These exceptions should not undermine or weaken the solid modeling principle as they are usually implemented at a later stage if needed.

The fourth aspect concerns tessellation, the process of transforming mathematical models into polygonal models. Switching from a mathematical environment to a polygonal one is easy because it is just a matter of populating the continuous surfaces with points and connecting them with edges and planar faces. The inverse is hard because as soon as they are converted into polygonal models, NURBS models lose all the information about the curvature of their surfaces. Nevertheless, even if this conversion is destructive and passes from a continuous to a discretized model, it is necessary both to produce shaded rendered images and to eventually be able to 3D print the model. In fact, each 3D modeling software that handles NURBS internally converts them into meshes in real time to allow the graphic cards to shade and display the models in the interactive view while working on the model. Because of that, someone might say that to produce images it is more convenient to directly model with discretized surfaces. This might be true sometimes, but if the discretized model turns out to be too much or too little tessellated at the end of the modeling process, the only way to update it is to entirely remodel it from scratch, which is why the NURBS model is almost always preferable at least when aiming to accuracy and versatility.

Summary

The chapter deals with the concepts of raw model and informative model; it clarifies the concept of semantic segmentation and defines the digital representation methods and 3D modeling techniques; finally, it lists the different configuration spaces of a 3D model in different software packages.

Standards and guidelines

• Beacham, R.; Denard, H.; Niccolucci, F. An Introduction to the London Charter. In Papers from the Joint Event CIPA/VAST/EG/EuroMed Event, Ioannides, M., Arnold, D., Niccolucci, F., Mania, K., Eds.; 2006; pp. 263–269.

• Denard, H. (2009) “The London Charter. For the Computer-Based Visualization of Cultural Heritage, Version 2.1.” (https://www.londoncharter.org, accessed on 1.2.2023).

• Principles of Seville. International Principles of Virtual Archaeology. Ratified by the 19th ICOMOS General Assembly in New Delhi, December 2017 (http://sevilleprinciples.com, accessed on 1.2.2023).

Key literature

• Albisinni, P. and L.D. Carlo, eds. Architettura disegno modello: Verso un archivio digitale dell’opera di maestri del XX secolo. 2011, Gangemi Editore (2011) [47].

• Aubin, P.F. (2013). Renaissance Revit: Creating Classical Architecture with Modern Software. G3B Press [43].

• Apollonio, FI. (2012). Architettura in 3D. Modelli digitali per i sistemi cognitivi. Milano: Bruno Mondadori [16].

• Migliari, R., Geometria Descrittiva—vol. 1, vol. 2—Metodi e costruzione. 2009: Città Studi Edizioni [48].

• Pottmann, H., Architectural geometry. 2007: Bentley institute press [49].

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