# Repair of Voids in Multi-Labeled Triangular Mesh
## 5 Results  
We implemented the mesh repairing algorithm in C++ and tested it on a Windows 64-bit PC with 3.80 GHz Intel(R) Core(TM) i7-10,700K and 32 GB RAM. To verify the reliability of our method, we tested the method on several geological datasets generated from geological sampling data using an implicit modeling method [4]. In addition, we compared the repairing results with the input meshes, as shown in Figures 6-9. Tables 1-4 show the parameters of the four experiments.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Meshes**} & \multirow{2}{*}{**Colors**} & \multirow{2}{*}{\(N_{V}\)} & \multirow{2}{*}{**Time (s)**} & \multicolumn{2}{c}{**Facets**} & \multicolumn{2}{c}{**Vertexes**} \\ \cline{5-8}  & & & & **Original** & **Repaired** & **Original** & **Repaired** \\ \hline
**Mesh 1** & red & & & & & & \\
**Mesh 2** & blue & 2 & 0.344 & 83,260 & 62,254 & 41,636 & 30,661 \\
**Mesh 3** & purple & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the multi-labeled mesh with input three sub-meshes. \(N_{V}\) is the number of voids, the Time is the time consumed in repairing the mesh, the Facets is the number of the triangular facets in multi-labeled mesh, the Vertexes is the number of mesh vertexes in multi-labeled mesh.  
Figure 8: The multi-labeled mesh with input four sub-meshes.  
Figure 7: The multi-labeled mesh with input three sub-meshes.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Meshes**} & \multirow{2}{*}{**Colors**} & \multirow{2}{*}{\(N_{V}\)} & \multirow{2}{*}{**Time (s)**} & \multicolumn{3}{c}{**Facets**} & \multicolumn{3}{c}{**Vertexes**} \\ \cline{5-8}  & & & & **Original** & **Repaired** & **Original** & **Repaired** \\ \hline
**Mesh 1** & blue & & & & & & \\
**Mesh 2** & purple & & & & & & \\
**Mesh 3** & yellow & 4 & 0.347 & 78,590 & 57,770 & 39,305 & 28,239 \\
**Mesh 4** & red & & & & & & \\
**Mesh 5** & green & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of the multi-labeled mesh with input five sub-meshes. \(N_{V}\) is the number of voids, the Time is the time consumed in repairing the mesh, the Facets is the number of the triangular facets in multi-labeled mesh, the Vertexes is the number of mesh vertexes in multi-labeled mesh.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Meshes**} & \multirow{2}{*}{**Colors**} & \multirow{2}{*}{\(N_{V}\)} & \multirow{2}{*}{**Time (s)**} & \multicolumn{3}{c}{**Facets**} & \multicolumn{3}{c}{**Vertexes**} \\ \cline{5-8}  & & & & **Original** & **Repaired** & **Original** & **Repaired** \\ \hline
**Mesh 1** & red & & & & & \\
**Mesh 2** & green & & & & & \\
**Mesh 3** & blue & & & & & \\
**Mesh 4** & purple & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of the multi-labeled mesh with input four sub-meshes. \(N_{V}\) is the number of voids, the Time is the time consumed in repairing the mesh, the Facets is the number of the triangular facets in multi-labeled mesh, the Vertexes is the number of mesh vertexes in multi-labeled mesh.  
Figure 9: The multi-labeled mesh with input five sub-meshes.  
To test the universality of the algorithm, we implemented another three sets of experiments. Figures 7-9 shows the examples of the repairing results using the multi-labeled mesh generated from more sub-meshes. With the increase of the input meshes, the repairing algorithm can still repair the voids in the multi-labeled model.  
The performance of the repairing method mainly depends on the number of facets and the meshes vertexes in the multi-labeled mesh, as shown in Tables 1-4. The experimental results of several datasets show that our method can repair the voids in multi-labeled mesh efficiently.