## 3 Results
### Accuracy Validation of the Maxillofacial Reconstruction 3D Model  
As mentioned in Section 2.5, the accuracy of the maxillofacial reconstruction models generated by the maxillofacial reconstruction surgery simulator was evaluated. A maxillofacial surgeon applied medical CAD software, Mimics 17.0, and the implemented simulator to create reconstruction models based on 10 patient datasets. The maxillofacial reconstruction models generated using Mimics 17.0 were defined as the target models, while those generated by the simulator were defined as the test models. First, surface distance analysis was performed by applying the target and test models to CloudCompare v2.14. To ensure accurate results, fine registration was conducted to align the positions of the target and test models, and surface distances between the two models were calculated using the Mesh Distance function. Table 7 shows the results of the surface distance calculations between the 10 target and test models. The average Min dist. of 0 mm indicates that, in all 10 comparison groups, there are locations where the models align perfectly. Although the number of exact matching points varies across the comparison groups, all test models have areas that precisely match the shape of the target models. In the 10 comparison groups, the Max dist. values ranged from approximately 0.962 mm to approximately 2.375 mm. While there are variations in Max dist. among the comparison groups, the relatively small difference between the minimum and maximum Max dist. values suggests that the shape differences between the target and test models in these 10 groups are not significant. This implies that the maxillofacial reconstruction models generated by the simulator have the potential to produce results at the level of CAD software models. The average Avg dist. across the 10 comparison groups is approximately 0.0118 mm, with most groups maintaining an average distance of less than 0.01 mm. This indicates that the surface points of the two models in each comparison group are generally close to each other, meaning that the shape differences between the models are minimal overall. The Sigma values ranged from approximately 0.0134 mm to approximately 0.238 mm. A lower standard deviation signifies that the distances between the surfaces of the two models are closer to the average distance. Comparison Groups 8, 9, and 10 show a higher standard deviation compared to other groups, suggesting that there are inconsistent distance differences in certain regions. Finally, the average Max error is approximately 0.499 mm, indicating that the Max error values across the groups do not vary greatly from the average Max error, thus suggesting an overall reliable surface distance calculation. In summary, the target and test models in the 10 comparison groups have a low average distance and a minimum distance of 0, indicating that the models are generally similar in shape. However, since some maximum distances exceed 2 mm, there may be localized shape differences in certain areas. These localized differences can be difficult to interpret solely from distance calculations, so analyzing key difference regions through visually interpretable heatmap visualizations is necessary. Figure 11 shows the heatmap results of six representative models from the 10 comparison groups.