## 2 Materials and Methods
### Validation of Simulator Performance and Model Accuracy
For shape comparison, CloudCompare v2.14 is used to perform surface distance analysis and generate heatmaps, quantifying the differences by calculating the distance between the surfaces of the two models and visually comparing them through heatmaps. The surface distance analysis confirms the geometric precision of the simulator-based maxillofacial reconstruction model, and the model overlay analysis evaluates the surface congruency of the simulator-based model. Table 4 shows information derived from the distance calculations, and Figure 8 shows an example of heatmap generation using iliac models. \begin{table}
\begin{tabular}{c c} \hline \hline
**Dist. Item** & **Feature** \\ \hline Min dist. & This is the minimum distance between the closest points on the surfaces of the two models. \\  & A value of 0 indicates that there is a point where the surfaces of the two models coincide. \\ \hline Max dist. & This represents the distance between the farthest points on the surfaces of the two models. \\  & A larger value implies a greater discrepancy in certain areas between the models. \\ \hline Avg. dist. & This is the average distance between the surface points of the two models, providing a general indication of how closely the models match overall. \\ \hline Sigma & This is the standard deviation of the distance values. A smaller sigma indicates consistent distance differences between the models, while a larger sigma suggests significant discrepancies at certain points. \\ \hline Max error & This represents the maximum possible error that may occur in the distance calculations between the models. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Information derived from surface distance analysis. \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Evaluation** \\ \hline FPS & The simulation is performed for 10 min, recording FPS values and calculating the average. \\ \hline CPU usage & The simulation is performed for 10 min, recording CPU usage values every 30 s and calculating the average. \\ \hline GPU usage & The simulation is performed for 10 min, recording GPU usage values every 30 s and calculating the average. \\ \hline Memory usage & The simulation is performed for 10 min, recording memory usage values every 30 s and calculating the average. \\ \hline Resection time & Resection was performed on 20 facial and iliac bone models, recording the time required for resection on each model, and then calculating the average time. \\ \hline Recognition accuracy & For each cycle, 100 rays were cast from the controller to detect the model accurately, counting the number of successful recognitions. This was repeated for a total of 10 cycles, and the average number of recognitions was calculated. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation methods for selected performance metrics. The heatmap shown in Figure 8 uses colors to represent the congruence between the two models. Higher congruence is represented by blue, while lower congruence is indicated by green, yellow, and red in that order. In the example, the overall presence of green suggests that the two iliac models share a similar shape, while the occurrence of yellow and red in certain areas indicates regions with significant differences.