*2.1. BIM*

The topic of the paper [1] is the integration of BIM with the issue of reverse engineering. It is about improving the sub-phases of the information flow throughout the entire project cycle. The aim is to reduce the errors and increase efficiency by supporting technologies, such as prefabrication, virtual reality, 3D printing, etc. The proposed methodology also includes tools for managing and organizing the entire workflow. The results can be used in projects for the renewal of towns and municipalities. The article [7] deals with Historic Building Information Modeling (HBIM). It is special library of historical architectural elements, from which it is possible to reconstruct entire historical buildings and complexes. The library was created in ArchiCAD GDL (Geometric Description Language). These are parametric elements whose specific geometry is defined by the user. The resulting model is composed of laser scanning surveying or photogrammetric data and is completed with elements from library. The resulting model serves for conservation purposes. The publication [8] is a continuation

of the research that was presented in the previous paper [7]. The method for HBIM creation was supplemented by algorithms of data segmentation from point clouds that were obtained by ground laser scanning of buildings. This is a difficult task to be solved by algorithm, therefore a heuristic method was used.

#### *2.2. Reverse Engineering*

Article [2] deals with reverse engineering technology. The topic is terrestrial 3D laser scanning. There are latest technologies of point cloud processing by powerful technical and software tools described. The work [9] proposes a special procedure for laser scanning of buildings. The method consists in optimizing the arrangement of devices in the space by means of a telecommunication device located on the roofs of buildings. It is a virtual simulation of antenna sites, which generates a 3D scenario of the process. The method was verified at a project at the Technical University of Madrid. [10] is another work that belongs to the field of reverse engineering. It proposes an algorithm for comparing the actual state of the pipe design with the state in the Computer-Aided Design (CAD) system. 3D model is obtained from laser scanning. The method is used for reconstruction of buildings or verification of quality in construction. In the work [11] is described a new method of reverse engineering combined with knowledge engineering of construction. It deals with a definition of inverse CAD process while using topology and tree structure of design process. A specific geometry of the model is then created from this general concept.

#### *2.3. Terrestrial Laser Scanning*

The study [12] presents a new methodology for creating a 3D model of wooden structures. This is a quick procedure based on generative algorithms. Terrain data are obtained while using Terrestrial Laser Scanning. The method was verified in the framework of a research project of wooden roof structures in Bologna. A new algorithm for transforming point clouds into a 3D model while using parametric tools was developed. The model is created, in general, and other building elements can be modeled by changing of input parameters. The work [13] deals with the creation of a 3D model of the church that was obtained by Terrestrial Laser Scanning. There are described methods of point cloud analysis and digitization in CAD system.

#### *2.4. New Methods for 3D Models Creation*

In the paper [14] is proposed a method for reconstruction of geometry of 3D object and its components. The object is surveyed by geodetic terrestrial methods and obtained list of points is processed by object methods. The paper describes strategies for recognizing elements in objects and develops new algorithms that improve existing methods. The article [15] describes the method of reconstruction of reinforced concrete arch bridge. The technology is based on the smallest element method. The aim is to identify the structure of the building and create a 3D model of its actual execution. The work also presents an analysis of the accuracy of the geometric method that was used in object surveying. The content of the article [16] is a new technology for the surveying of historical buildings in hard to reach places. It is a photogrammetric method that uses fish-eye lenses. The advantage of the method is the speed of data acquisition and optimization of the data volume. It is an alternative method to Unmanned Aerial Vehicles (UAV). The paper [17] describes the monitoring of buildings by using of the methods of engineering geodesy. Buildings are geodetically surveyed and 2D or 3D models can be obtained from the data. The models are also used for the stage of structure protection and safety of buildings. The method of laser scanning of buildings is described in detail. It is also possible to create drawings, which include views and sections, from the data. Close-range photogrammetry can also be used to create orthoimage and linear drawing. This method is particularly suitable for surveying historical buildings that do not have building documentation.

Ref. [18] describes a special approach to 3D modeling. It is a new method of hybrid 3D reconstruction of objects, which is a combination of building elements, and computer graphics methods. This integrated method takes advantage of the geometry, topology, and visualization of building objects in the process of 3D model creation.

#### *2.5. Visualization of 3D Objects*

The paper [19] deals with the analysis of 3D objects visualization. A new method that is based on the analysis of topology and time series of the object is proposed. The method does not need its own 3D model; the information is directly obtained from the data. Visualization is used to obtain new functional relationships within an object. The method is verified on a case study. Article [20] deals with the reconstruction of architectural elements of historical buildings from a cloud of points that were obtained by laser scanning. It is a high resolution 3D model in Triangular Irregular Network (TIN) format. The benefit is the high speed of algorithm and realistic visualization of the object. The method is used in architecture for the reconstruction of historical buildings. The paper [21] describes a method for approximating the surface of 3D models in CAD software. The method allows for creating a surface from suitably randomly selected points that were obtained from reverse engineering or from the design process. Geodesy algorithms motivated the technology, e.g., the creation of a digital terrain model. The paper [22] presents a design of an algorithm based on Gaussian map. It is a procedure that is suitable for visualization of ancient architecture. Technology has been proven during archaeological research of ancient cities. Experiments show that the method is accurate enough, with minimum noise, and no need for user intervention.

### **3. Materials and Methods**

#### *3.1. Problems Description*

The process of creating a 3D model of a geographic object (GO) is simplified according to the diagram presented in Figure 1. The GO can represent any real object of interest (e.g., building or other construction). A general and not yet fully solved problem is to create a 3D model in suitable software (SW) with given accuracy.

Let *I* = *{(xi, yi, zi*)|*i* = 1, 2, ... , *n*} is a set of vectors (input) that represent the points of the GO in the real world, *O* = *{(xo, yo, zo*)|*o* = 1, 2, ... , *n*} is a set of vectors (output), describing the points in a digital database of a 3D model in suitable software. Subsequently, mapping function *f* from real space to the digital database of 3D model

$$O = f(I) \tag{1}$$

must fulfill the following conditions:


After generalization in software (Figure 1) the mapping function can be described with following equation:

$$O' = \mathcal{g}(I) \tag{2}$$

where *O'* = *U(O)* and *U* represents neighborhood of vectors that display the input vectors of GO from the real space to the digital database. The neighborhood size of *U* then represents the true accuracy of the 3D model in used SW. This accuracy is less, and then the a priori accuracy of the geodetic survey of GO in field. The mapping function g then describes the functional repository of the used SW (CAD, GIS), while *g* ⊂ *f* is valid.

A closed set of functions *g* though to describe the topology of GO, but it is necessary to generalize the 3D model in many cases. That means *O'* ⊂ *O* ⊆ *I*. In fact, we lose not only the accuracy of the position of points, but also some details of GO, which is a big disadvantage for further use of 3D models in engineering practice.

Another problem when creating a 3D model is the visualization of the results. This mainly involves rendering surfaces that represent the surface of an object. The problem can be divided into two categories:


*3.2. Posibility of Solutions*

Replacing complex elements with simple entities where there is no further need for generalization can solve the problem of the geometric accuracy of a 3D model in suitable software. E.g. composite arcs or larger degree curves can be replaced with polyline elements. For the model [6], the authors used the method of topological coding [23]. The main principle consists in adding special codes into list of coordinates of points, according to field sketch:

topological code: **L**/**x,y** or **S**/**x**

where,

**L** refers to line **S** refers to surface (polygon), **x** is unique identifier of the line (integer), and **y** is order number of the point in the line segment.

Format of the list of coordinates is following:

**Point ID, Y, X, Z [, code1, code2,** ... **, coden]**

Every attribute is separated by comma, while topological codes in square brackets are optional. The application in the form of the script in Python language was created for points input into graphic editors. This script offers automatic creation of topologically correct drawing in CAD or GIS-based software. The script also checks duplicities of entities and provides full topology of the drawing. Figure 2 presents the chart diagram.

**Figure 2.** Flow chart of Python script for topological drawing in Quantum GIS.

The problem of visualization of the produced 3D model can be solved in two ways:

	- (a) used build-in modules with customary texture models in given software, and
	- (b) create your own set of textures and import them into the software (if the program product has the appropriate features for this purpose).

In models [3–5], variant 1 (a) was used to represent the surface, in model [6] variant 1 (b).

*3.3. Transformation of Point Cloud into 3D Model*

Creating a 3D model by terrestrial laser scanning technology has several phases:

