# Voxel-Based Digital Twin Framework for Earthwork Construction
## 4 Implementation of the Proposed System
### Graphical Simulation Environment for Model-Equipment Interaction
#### 4.1.3 Model Integration in Platform
The total quantity of the earthwork to be removed was 65 m\({}^{3}\). The excavated volume design is shown using a target surface representation, and schedules are embedded into the model for the as-planned state using voxels. After finishing the work in actuality on the construction site, the site images were taken, and a point cloud was generated. The point cloud was converted into a surface model, which was then voxelized to achieve an as-built voxel model. The experiments performed in this scenario are explained in Table 3, along with the progress and productivity information. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Time** & **Model Visualization** & **Model Quantification** & **Remarks** \\ \hline Time-0 & Total volume = 65 m\({}^{3}\) & Before construction \\ Time-1 & As-planned voxels = 65 m\({}^{3}\) & On schedule \\ Time-2 & As-planned voxels = 14.45 m\({}^{3}\) & On schedule \\ Tracked material = silty voxels & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Progress visualization and quantification using an integrated model. #### 4.2.3 Accuracy Evaluation

The proposed method uses point cloud data for as-built voxel generation. However, while UAV-based or laser scanners provide data with sub-centimeter accuracy, raw data typically contains noise, incomplete regions, and redundant points, particularly in areas of steep ground. Additionally, the data is converted into voxels, and this process introduces some inaccuracy, which is inherent in the modeling process. For example, the sources of the as-built data collection (UAVs and laser scanners) may introduce some errors. Furthermore, converting the point cloud data into a TIN surface incorporates interpolation errors, especially in areas where point data is missing or in complex terrains. Moreover, creating voxels from this data introduces discretization errors because there are voxels that are outside of the as-built TIN surface. Hence, to ensure geometric fidelity and reliability of the voxel results, the raw data must undergo a structured preprocessing workflow prior to conversion into the as-built model. Firstly, point cloud preprocessing begins with noise filtering, where statistical outlier removal is applied to eliminate sparse points that lie significantly outside the neighboring points. This step normalizes the data points, reducing as-built surface roughness and preventing voxel misclassification, making the process efficient for comparing as-planned and as-built voxels. To reduce computational burden and manage data scalability, point cloud decimation/subsampling is applied using a distance-based method. The distance-based method uses a predefined distance between 3D points, and points are subsampled based on the minimum distance. In this method, the points are retained after the minimum distance is achieved, and the interior points are excluded [49]. For example, a sampling percentage of 20% refers to a large inter-point distance, resulting in a sparser point cloud, whereas a higher sampling percentage (e.g., 70%) corresponds to denser point clouds with smaller inter-point distances. The method was selected based on simplicity, and other \begin{table}
\begin{tabular}{c c c} \hline
**Time** & **Model Visualization** & **Model Quantification** & **Remarks** \\ \hline Time-3 & As-planned voxels = 39.13 m\({}^{3}\) & \\  & As-built voxels = 12.87 m\({}^{3}\) & Behind schedule \\  & Tracked material = silty voxels & \\ \hline Time-4 & As-planned voxels = 51.55 m\({}^{3}\) & \\  & As-built voxels = 14.45 m\({}^{3}\) & Behind schedule \\  & Tracked material = silty voxels & \\ \hline Time-5 & As-planned voxels = 18.75 m\({}^{3}\) & \\  & As-built voxels = 21. 38 m\({}^{3}\) & Behind schedule \\  & Tracked material = silty voxels & \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._methods, such as random point or cell-based approaches, can also be adopted to achieve the output sparser point cloud [50]. The method is applied inside CloudCompare, a commercial tool, allowing users to manipulate point cloud datasets.