1. Introduction

Currently, construction industry projects are becoming more complex and more difficult to control ^{(Machado and Vilela, 2020)}. As construction projects become larger and more sophisticated, various technologies are being developed to manage the vast amount of information generated by these projects more efficiently. Among the various technologies in use at present, augmented reality (AR) and building information modeling (BIM) are expanding in the construction industry. According to a survey by the UK’s fastest-growing Building Information Modeling (BIM) library, the BIM utilization rate was only 13 % in 2011, though it increased to 73 % in 2020 ^{(NBS Enterprises Ltd., 2020)}. And as a result of examining the augmented reality technology, widely used in many fields currently, the market size is expected to grow by 2025, and this technology is expected to be widely used in the construction and industrial fields (Software Policy and Research Institute, SPRI).

AR provides virtual information on physical surfaces, assisting with interactions with the real environment through a combination of virtual information and real information ^{(Karji et al., 2017)}. BIM technology utilizes parametric modeling technology to link and manage various 3D shape information and attribute information of a construction project, not only providing functions such as automatic drawing creation, quality improvement, quantity calculation, process management, and inter-process interference reviews but also making various simulations possible in the design and construction stages ^{(An et al., 2010)}. Integration between BIM and AR can serve as a reliable tool for visualizing the construction and improving the identification, handling and communication of progress discrepancies at the construction site. Numerous means by which to integrate AR with BIM have been proposed by the scholars. For example, ^{Chai et al.(2019)} showed that BIM is compatible and thus can be integrated with the AR platform through their proposed AR-BIM system.

Various methods already exist for projecting BIM data into AR ^{(An et al., 2010)}. In order to convert a BIM model to AR, the created BIM model must be transferred from each BIM authoring tool (e.g., Revit, Civil 3D) to one game engine (e.g., Unity, Unreal). In addition, conversion to a neutral format such as FBX, OBJ, and IFC is essential to create a single unified model based on it. However, during the process of converting the BIM model to a neutral format, the shape of the model can break, become deformed, or is duplicated frequently, which can seriously degrade the performance when running in an AR environment. To solve this problem, it is necessary to reduce the number of meshes in the BIM model by using commercial software or by developing a program directly.

The most dominant and fastest approach to keeping the overall polygon count low is to use a mesh optimization algorithm to generate a low-poly version of an existing high-poly model ^{(Bahirat et al., 2018)}. From 1993 to the present (2021), many researchers have conducted mesh optimization studies ^{(Hoppe et al., 1993)}. However, most existing mesh simplification algorithms are complex and are limited in their ability to handle meshes properly while maintaining the baseline shape of the 3D model ^{(Luebke, 2001)}. Therefore, this study developed an algorithm to reduce the mesh of BIM models by utilizing deep learning for high- performance AR visualization (see Fig. 1).

Fig. 1. Conceptual Framework for the Mesh Optimization Algorithm

2. Technical Background of Relevant Methods for Mesh Optimization

2.1 K-nearest Neighbors

K-nearest neighbors (KNN) is a supervised and pattern classification learning algorithm that helps us find the class of the new input (test value) when k-nearest neighbors are chosen, with the distance then calculated between them. KNN is useful for classification and regression owing to its versatility ^{(Cao et al., 2019)}. The k-nearest-neighbor classifier is usually based on the Euclidean distance between a test sample and the specified training samples ^{(Peterson, 2009)}. Let $x_{i}$ be an input sample with p features $(x_{i1},\: x_{i2},\: ...,\: x_{ip})$, n be the total number of input samples (i=1,2,…,n) and p be the total number of features (j=1,2,…,p). The Euclidean distance between sample $x_{i}$ and $x_{l}$ (l=1,2,…,n) is then defined as shown below.

(1)

$d(x_{i},\: x_{l})=\sqrt{(}x_{i 1}- x_{l1})^{2}+(x_{i 2}- x_{l2})^{2}+ ... +(x_{i p}- x_{lp})^{2}$

A graphic depiction of the nearest neighbor concept is illustrated by the Voronoi tessellation ^{(Peterson, 2009)} depiction shown in Fig. 2.

Fig. 2. Voronoi Tessellation Showing Voronoi Cells of 19 Samples Marked with a "+"(Peterson, 2009)

3. Mesh Optimization Algorithm Approach

The mesh optimization algorithm was designed to create a low-poly version of a 3D model effectively and accurately, proposing triangle combining and vertex merging using reconstructions of common vertices for merged triangles. This type of algorithm can merge three triangles into one triangle using the triangle centroid principle via calculations that take the average of the x-coordinate, y-coordinate, and z-coordinate of the triangle vertex (see Fig. 3).

Fig. 3. Steps of the Optimization Process and Concept

Our algorithm is based on the Unity C\# code based on the mesh finder and mesh level of details (LOD) technique, which is capable of finding, merging and reconstructing the triangular vertices of the 3D model using the triangular centroid calculation principle composed of three points. We used the triangle center principle in the mesh finder code, which counts the vertices and triangles of the model and draws a line between the vertices and reconstructs three center points. In the mesh LOD code, codes were written to add the ability to export the mesh code and divide the model into whole/part models.

Unity, a cross-platform game engine developed by Unity Technologies, can be used to create three-dimensional (3D) and two-dimensional (2D) games as well as interactive simulations and other experiences and can be used for video applications, such as those related to automobiles, architecture, engineering and construction ^{(Xie, 2012)}. It has been adopted in industries other than gaming. To call it from Unity, you need to attach a script to a Game Object (3D model) in your scene.

Scripts are written in a special language understandable by Unity, and the language used by Unity is called C\#. The written code C\# in our algorithm is responsible for finding, merging, and reconstructing the triangle vertices in the 3D model. For the final step, we used a KNN to test the classification based on the 3D model vertex distance dataset. A flow diagram of the proposed algorithm is shown in Fig. 4.

Fig. 4. Flowchart of the Proposed Algorithm

4. Experiment on the proposed mesh optimization algorithm

4.1 Specifications of the Test Model and 3D Modeling

A steel glass structure bridge with a length of 34 m, a height of 5 m, and a width of 2 m connecting Sungkyunkwan University’s No.1 Engineering Building 23 and No. 2 Engineering Building 25 was selected as the target model for our algorithm. It was modeled in Revit and passed to the Unity engine using the Unity Reflect process. Unity Reflect for Autodesk Revit, industry-leading BIM software, enables designers and engineers to transfer Revit models into real-time 3D experiences (2021 Unity Technologies). It is possible to check all types of structure details as well as multiple meshes and components (see Fig. 5).

Fig. 5. Target Model 3D Modeling

4.2 Data Collection and Processing Dataset using KNN Classification

KNN algorithms are used to find k-nearest neighbors of data points in a dataset, and the basic method of finding k-nearest neighbors of a point is to compute all Euclidean distances using data points ^{(Xia et al., 2015)}. The dataset is collected by running the target 3D model multiple times with a similar level of detail ^{(Wang et al., 2021)}. We can determine the class to which a new input (test value) belongs when k-nearest neighbors are chosen, and the distance is calculated between them. In our model, there are thousands of combinations possible when merging vertices. Thus, we use the KNN to determine the best fit to define the distance between the vertices. As a result of extracting the distance dataset of points from the selection model using the unity C\# code, we received a data set with 590,942 rows and four columns.

For data processing using KNN classification, the collected data mentioned earlier are divided into a training dataset (80 %) and a test dataset (20 %) through the Python package Scikit-learn. After the dataset train-test-split process, we used the sklearn KNeighbors Classifier and KNN-predict to make predictions. Based on our collected dataset, we obtained 90 % accuracy (see Fig. 6).

Fig. 6. Processing Dataset Using KNN Classification

4.3 Results and Discussion

As a result of our algorithm testing the SKKU steel bridge 3D model, although there may be some difficulties in checking with the naked eye, as shown in Fig. 7, blue is the model before reduction and green is the model after reduction. Moreover, there appears to be no problem in utilizing lightweight and original models for AR visualization, as there are no significant differences visually.

Fig. 7. Result of BIM Model Mesh Optimization

In addition to the entire model before and after optimization, the number of points and triangles before and after optimization for each structure could be checked immediately. As shown in Table 1, the vertex of the original model can be reduced by approximately 56 % and the triangle by about 42 %.

Table 1. Optimized Percentage Result of the Vertices and Triangles of the Model

$\dfrac{model\;Type}{Structure\;Type}$	Original model		Optimized model		Optimized % $$ \left(V=\frac{V_{2}}{V_{1}} \times 100 \%, T=\frac{T_{2}}{T_{1}} \times 100 \%\right) $$
	Vertices 1	Triangles 1	Vertices 2	Triangles 2	Vertices	Triangles
Glass Structure	7214	4804	4405	1921	61 %	40 %
Tube Structure	20310	10438	10628	4174	52 %	40 %
Full model	590942	335564	330116	140167	56 %	42 %

5. Conclusion

Recently, with the introduction of augmented reality in the fourth industrial revolution era, the construction industry is developing along with information and communication technology. AR applied to the construction field is used during the process of reviewing 3D models for architectural designs and is also used for construction management at construction sites.

In this paper, we proposed a new mesh reduction method based on central-triangular vertex decimation combined with a smart mesh finder and mesh LOD in order to automate the process of vertex merging by utilizing a KNN classification algorithm to optimize the imported BIM model with meta-data from an external program to visualize AR effectively. The classification operation well works on multi-hierarchy component 3D models and meshes, allowing it easily to find the most necessary parts for optimization. Some difficulty exists with regard to creating an easier import- export pipeline due to various file formats and corresponding underlying systems. This newer approach improves the topology preservation, and thus it is the best possible mesh reduction and reconstruction strategy. This study aimed to optimize the imported BIM model with meta data from an external program to visualize AR effectively, even on mobile devices with resource constraints.

For future work, the trained model will be uploaded onto a dedicated server for greater accessibility and availability. More diverse and complex mesh model testing will also be conducted for more accuracy. In addition, the optimized BIM models will be tested with an AR visualization device.