# A Fast Hole-Filling Method for Triangular Mesh in Additive Repair
## 6 Experimental Results and Discussion
### Other Examples  
To further demonstrate the efficiency, robustness and shape-recovery ability of our method, four non-mechanical models were tested. For each model, it contains at least one of the three types of holes with different sizes, and then our algorithm is applied to fill them. Figure 16 shows a hole-filling gallery on these four models. Figure 16a illustrates the incomplete models, and it can be seen that most of them suffer from at least one or more types of holes, e.g., small-sized, middle-sized, and large-sized holes. In particular, the ones contained in the statue and head models are divergent holes. The cleaned meshes are shown in Figure 16b, and from the results, it can be observed that all the tooth faces occurring on the hole boundaries have been completely removed, which provides smooth inputs for the next processing step. The final filling results obtained by our method are illustrated in Figure 16c,d. From the viewpoint of visualization check, all the holes have been successfully closed by our method, besides, it can also ensure the filling patches to be compatible with surrounding meshes well. Table 2 gives the statistics of the hole-filling results obtained by our method on these four models. Regarding the head model, although it contains a large and divergent hole with a boundary vertex size of 160, our algorithm takes only 91.83 \(ms\) to close it. Unlike the [PERSON]'s algorithm, the closing and refining stages for a large hole are completed in a single step for our method, which can significantly reduce the hole filling times, especially for large ones. Compared with the [PERSON]'s algorithm, our method strictly limits the processing region to its adjacent area of one large hole, which can prevent the non-hole regions from being modified. From the ninth column of Table 2, it can be seen that the triangle quality evaluation results on all testing models are greater than 76%, which proves that the filling patch generated by our method is mainly composed of regular triangles. Furthermore, Figures 17-20 present the statistics of the vertex valence computation results obtained by our method on these models. From these results, it can be seen that the vertex valence of the filling vertices obtained by our method only ranges from four to eight, and the vertices with vertex valence of six account for more than 71 % of the total number of the newly inserted vertices. These results demonstrate that our method can guarantee the majority of the newly added vertices to be high regular ones.  
Figure 16: Hole filling results on four example models. (**a**) The incomplete models. (**b**) The results after hole boundary clean. (**c**) The results of our method in one view. (**d**) The results of our method in another view.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Incomplete Model**} & \multicolumn{2}{c}{**Hole Number**} & \multicolumn{2}{c}{**Large-Sized Hole Size**} & \multicolumn{2}{c}{**Total Filling Time (ms)**} & \multicolumn{2}{c}{**Triangle Quality Evaluation (\%)**} \\ \cline{2-9}  & \(N_{\text{c}}\) & \(N_{\text{f}}\) & **Small-Sized** & **Middle-Sized** & **Large-Sized** & \(N_{\text{c}}\) & **Total Filling Time (ms)** & **Triangle Quality Evaluation (\%)** \\ \hline Dog & 12,800 & 25,508 & 0 & 1 & 1 & 61 & 15.97 & 76.89 \\ Burny & 28,599 & 57,007 & 2 & 2 & 1 & 79 & 40.88 & 86.24 \\ Statue & 19,293 & 38,453 & 4 & 1 & 107 & 40.93 & 89.99 \\ Head & 21,755 & 43,254 & 2 & 4 & 1 & 160 & 91.83 & 81.29 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistics of the hole-filling results on example models.  
Figure 19: Vertex valence statistics of the filling patch for the statue model.  
Figure 17: Vertex valence statistics of the filling patch for the dog model.  
Figure 18: Vertex valence statistics of the filling patch for the bunny model.