## 2 Materials and Methods
### Analyzing Methods and Measuring Instruments
\begin{table}
\begin{tabular}{r r r r r r r r r} \hline  & & \multicolumn{6}{c}{**Surface Difference Comparison**} \\
**Individual** & \multicolumn{3}{c}{**Upper Jaw**} & \multicolumn{3}{c}{**Bottom Jaw**} \\  & **Points** & **Median** & **Mean** & **Std** & **Points** & **Median** & **Mean** & **Std** \\ \hline _05_ & 239,340 & 0.0060 & 0.0128 & 0.1317 & 222,690 & 0.0168 & 0.0163 & 0.1282 \\ _08_ & 181,522 & \(-\)0.0122 & \(-\)0.0121 & 0.2163 & 187,267 & \(-\)0.0041 & \(-\)0.0081 & 0.1684 \\ _09_ & 234,314 & \(-\)0.0166 & \(-\)0.0209 & 0.1212 & 209,048 & 0.0443 & 0.0330 & 0.1433 \\ _12_ & 197,424 & \(-\)0.0172 & \(-\)0.0261 & 0.2311 & 208,471 & 0.0114 & 0.0057 & 0.1748 \\ _15_ & 228,273 & \(-\)0.0047 & \(-\)0.0292 & 0.2155 & 220,984 & \(-\)0.0353 & \(-\)0.0845 & 0.3617 \\ _16_ & 236,978 & \(-\)0.0424 & \(-\)0.0317 & 0.2742 & 232,064 & 0.0128 & 0.0051 & 0.1504 \\ _17_ & 278,309 & \(-\)0.0316 & \(-\)0.0470 & 0.3280 & 256,598 & \(-\)0.0213 & \(-\)0.0315 & 0.2336 \\ _18_ & 206,480 & \(-\)0.0198 & \(-\)0.0228 & 0.1032 & 195,661 & 0.0227 & 0.0345 & 0.3595 \\ _19_ & 275,752 & \(-\)0.0349 & \(-\)0.0280 & 0.2214 & 245,881 & 0.0008 & \(-\)0.0009 & 0.1412 \\ _20_ & 253,589 & \(-\)0.0162 & \(-\)0.0189 & 0.1149 & 230,604 & \(-\)0.0220 & \(-\)0.0092 & 0.1402 \\ _21_ & 254,839 & \(-\)0.0280 & \(-\)0.0264 & 0.1180 & 209,657 & \(-\)0.0028 & \(-\)0.0263 & 0.1248 \\ _22_ & 269,743 & \(-\)0.0142 & \(-\)0.0190 & 0.1340 & 229,829 & \(-\)0.0060 & \(-\)0.0100 & 0.2710 \\ _23_ & 280,864 & \(-\)0.0404 & \(-\)0.0174 & 0.2135 & 268,421 & \(-\)0.0018 & \(-\)0.0070 & 0.1566 \\ _25_ & 227,458 & \(-\)0.0066 & 0.0032 & 0.0969 & 199,842 & \(-\)0.0018 & \(-\)0.0028 & 0.1550 \\ _28_ & 242,926 & \(-\)0.0180 & \(-\)0.0248 & 0.1581 & 256,832 & \(-\)0.0018 & \(-\)0.0097 & 0.2219 \\ _29_ & 235,302 & \(-\)0.0091 & \(-\)0.0046 & 0.2089 & 207,356 & 0.0036 & 0.0014 & 0.1285 \\ _30_ & 198,720 & \(-\)0.0035 & \(-\)0.0080 & 0.1305 & 172,267 & \(-\)0.0059 & \(-\)0.0195 & 0.1338 \\ _32_ & 253,200 & \(-\)0.0338 & \(-\)0.0466 & 0.1790 & 235,288 & \(-\)0.0309 & \(-\)0.0286 & 0.1612 \\ _34_ & 243,778 & \(-\)0.0129 & 0.0978 & 0.5841 & 230,922 & \(-\)0.0163 & \(-\)0.0097 & 0.1345 \\ _36_ & 237,367 & \(-\)0.0017 & \(-\)0.0095 & 0.1283 & 224,377 & \(-\)0.0131 & \(-\)0.0228 & 0.1982 \\ _37_ & 237,520 & \(-\)0.0295 & \(-\)0.0268 & 0.0951 & 199,934 & \(-\)0.0031 & \(-\)0.0121 & 0.1382 \\ _40_ & 268,848 & \(-\)0.0052 & \(-\)0.0083 & 0.1454 & 245,285 & 0.0216 & 0.0247 & 0.0954 \\ \hline
**Mean** & **240,116** & \(-\)**0.0178** & \(-\)**0.0143** & **0.1886** & **222,240** & \(-\)**0.0013** & **0.0152** & **0.1695** \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of the plaster cast and virtual model surface for 22 individuals with number of data points, medians, means, and standard deviations of their difference for the upper and bottom jaws. To align the virtual casts, modifications were made using the best-fit algorithm in Autodesk Meshmixer 3.5 (Autodesk, Inc., San Rafael, Kaliforni, USA). The reference mesh (plaster model) was adjusted to be clearly larger than the compared mesh. Subsequently, the models were imported into CloudCompare 2.13, where the final fine registration was conducted using the iterative closest point (ICP) algorithm. The inaccuracy of the virtual casts was determined by calculating the cloud-mesh distances using the root mean square method:  
\[RMS=\frac{1}{\sqrt{N}}\sqrt{\sum_{i=1}^{N}D_{i}^{2}} \tag{1}\]  
for \(N\) cloud-cloud differences \(\{D_{i}\}_{i=1}^{N}\), evaluated for each point of the compared cloud, searching the nearest triangle in the reference mesh. The presentation of the cloud-cloud and cloud-mesh distances is shown in Figure 2.  
Figure 1: Principle of the 3D dental models construction using the printed 3D model based on data acquired by the 3D scanner and the plaster cast model and their comparison by the laboratory scanner and the appropriate software tools. Figure 2: Comparison of the cloud–cloud distance and cloud–mesh distance to evaluate the inaccuracy of the virtual casts.