## 3 Results  
Table 1 shows the median and the 25 th and 75 th percentiles of the differences between the virtual planning and postoperative results for each cephalometric point in the three axes for all patients. The median distances are also displayed in Figure 6.  
The overall analysis showed good accuracy, with all median differences below 1 mm. The highest median differences were seen at point A and Pog in the anteroposterior direction, which were 0.835 mm and 0.780 mm, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Landmark** & & & \\
**(Measured Axis)** & **Percentile 25 (mm)** & **Median (mm)** & **Percentile 75 (mm)** \\ \hline _A point (X)_ & 0.077 & 0.239 & 0.360 \\ _A point (Y)_ & 0.297 & 0.835 & 0.400 \\ _A point (Z)_ & 0.075 & 0.280 & 0.600 \\ _B point (X)_ & 0.020 & 0.070 & 0.330 \\ _B point (Y)_ & 0.162 & 0.480 & 0.885 \\ _B point (Z)_ & 0.036 & 0.150 & 0.292 \\ _Pogoonion (X)_ & 0.013 & 0.079 & 0.190 \\ _Pogoonion (Y)_ & 0.175 & 0.780 & 1.160 \\ _Pogoon (Z)_ & 0.070 & 0.200 & 0.625 \\ _Right upper first molar (X)_ & 0.257 & 0.770 & 1.445 \\ _Left upper first molar (X)_ & 0.186 & 0.665 & 1.222 \\ _Right lower first molar (X)_ & 0.100 & 0.310 & 0.370 \\ _Left lower first molar (X)_ & 0.150 & 0.580 & 0.850 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Median and 25 th and 75 th percentiles for all differences between surgical planning and actual postoperative results at the selected landmarks for the 40 patients. The \(x\) axis represents the mediolateral (or horizontal) direction, the \(y\) axis, the anteroposterior direction, and the \(z\) axis, the inferosuperior (or vertical) direction. Figure 6: Median distance (mm) for all cephalometric points in the \(x\), \(y\), and \(z\) axes. The \(x\) axis represents the mediolateral (or horizontal) direction, the \(y\) axis, the anteroposterior direction, and the \(z\) axis, the inferosuperior (or vertical) direction. The highest accuracy was observed at point B and Pog in the mediolateral direction (0.070 mm and 0.079 mm, respectively), followed by point B in the vertical direction (0.150 mm). The overall accuracy in the mediolateral direction was very good for all cephalometric points. The differences in the bone margin over the upper first molars were slightly higher compared to the mandibular first molars: 0.770 mm and 0.665 mm for the right and left upper first molars, and 0.310 mm and 0.580 mm for the right and left lower molars, respectively. Then, we computed the absolute 3D distance for point A, point B, and Pog. The median and 25 th and 75 th percentiles for such values were calculated and are presented in Table 2. The median 3D values for point A, point B, and Pog were 0.934 mm, 0.613 mm, and 1.034 mm, with the highest differences found at Pog. Furthermore, we calculated the weight of each axis to the overall 3D distance using multivariate analysis for point A, point B, and Pog (Figure 7). For point A, the axis that weighed the most was the \(y\) axis (anetroposterior), with a coefficient of 0.885 (meaning that for each unit that the distance increased in the \(y\) axis, the 3D distance increased by 0.885 mm), which was statistically significant (\(p<0.001\)). For point B, it was the \(z\) axis (vertical) that had the most influence on the 3D distance, with a coefficient of 0.813, which was also statistically significant (\(p<0.001\)). In the case of Pog, the highest input was given by the \(y\) axis as well (anetroposterior), with a coefficient of 0.726, which was statistically significant (\(p<0.001\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Landmark** & & & \\
**(3D Absolute Measure)** & **Percentile 25 (mm)** & **Median (mm)** & **Percentile 75 (mm)** \\ \hline A point & 0.344 & 0.934 & 1.719 \\ B point & 0.367 & 0.613 & 1.107 \\ Pog & 0.405 & 1.034 & 1.513 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Median and 25 th and 75 th percentiles of 3D absolute differences at landmarks point A, point B, and Pog.