## 4 Discussion  
The attachments used in clear aligner therapy are intended to enhance the clinical performance of orthodontic treatment. The inadequate design or placement of these attachments could hinder their ability to exert the necessary force to achieve the desired dental \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Materials** & **Tooth** & **OverPuffPoint** & & & **GverPuffPoint** & \\ \hline \multirow{6}{*}{Vertical} & \multirow{6}{*}{MM-TA} & Mean \(\pm\) SD & Min & Max & Mean \(\pm\) SD & Min & Max \\  & & & (mm) & (mm) & (mm) & (mm) & (mm) & (mm) \\  & & MM-TA & 2.6 & 0.39 \(\pm\) 0.34 & 0.1 & 0.87 & 0.65 \(\pm\) 0.42 & 0.05 & 1.02 \\  & MM-TA & 2.1 & 0.29 \(\pm\) 0.01 & 0.28 & 0.3 & 0.32 \(\pm\) 0.08 & 0.21 & 0.42 \\  & MM-TA & 1.1 & 0.34 \(\pm\) 0.08 & 0.28 & 0.47 & 0.42 \(\pm\) 0.22 & 0.27 & 0.8 \\  & MM-TA & 1.6 & 0.27 \(\pm\) 0.14 & 0.08 & 0.4 & 0.31 \(\pm\) 0.14 & 0.2 & 0.55 \\  & MM-CA & 2.6 & 0.28 \(\pm\) 0.24 & 0.1 & 0.68 & 0.48 \(\pm\) 0.35 & 0.08 & 0.92 \\  & MM-CA & 2.1 & 0.34 \(\pm\) 0.19 & 0.18 & 0.66 & 0.16 \(\pm\) 0.1 & 0.09 & 0.32 \\  & MM-CA & 1.1 & 0.28 \(\pm\) 0.12 & 0.17 & 0.43 & 0.20 \(\pm\) 0.07 & 0.11 & 0.29 \\  & MM-CA & 1.6 & 0.26 \(\pm\) 0.19 & 0.01 & 0.5 & 0.43 \(\pm\) 0.27 & 0.15 & 0.74 \\ \hline \hline \multicolumn{8}{c}{**DhorPuffPoint**} & \multicolumn{4}{c}{**MhorPuffPoint**} \\ \hline \multirow{6}{*}{Horizontal} & \multirow{6}{*}{MM-TA} & Mean \(\pm\) SD & Min & Max & Mean \(\pm\) SD & Min & Max \\  & & & (mm) & (mm) & (mm) & (mm) & (mm) \\  & MM-TA & 2.6 & 0.28 \(\pm\) 0.13 & 0.09 & 0.44 & 0.35 \(\pm\) 0.09 & 0.24 & 0.45 \\  & MM-TA & 2.1 & 0.41 \(\pm\) 0.05 & 0.34 & 0.47 & 0.26 \(\pm\) 0.06 & 0.17 & 0.31 \\  & MM-TA & 1.1 & 0.20 \(\pm\) 0.06 & 0.15 & 0.3 & 0.43 \(\pm\) 0.07 & 0.33 & 0.5 \\  & MM-TA & 1.6 & 0.30 \(\pm\) 0.17 & 0.14 & 0.5 & 0.24 \(\pm\) 0.05 & 0.17 & 0.31 \\  & MM-CA & 2.6 & 0.18 \(\pm\) 0.07 & 0.1 & 0.29 & 0.21 \(\pm\) 0.07 & 0.09 & 0.27 \\  & MM-CA & 2.1 & 0.3 \(\pm\) 0.06 & 0.24 & 0.38 & 0.24 \(\pm\) 0.1 & 0.1 & 0.38 \\  & MM-CA & 1.1 & 0.25 \(\pm\) 0.19 & 0.09 & 0.58 & 0.34 \(\pm\) 0.19 & 0.13 & 0.62 \\  & MM-CA & 1.6 & 0.24 \(\pm\) 0.2 & 0.02 & 0.5 & 0.29 \(\pm\) 0.15 & 0.08 & 0.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Vertical and horizontal outcomes considered in the puff analysis. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**MM-TA vs. MM-CA**} \\ \hline \multirow{2}{*}{Vertical CUTTING PLANE} & OverShape Point & OverShape Point & OverPuff Point & GverPuff Point \\ \hline \multirow{2}{*}{Vertical CUTTING PLANE} & 0.01 \({}^{\text{a}}\) & 0.02 \({}^{\text{a}}\) & 0.032 \({}^{\text{a}}\) & 0.47 \({}^{\text{b}}\) & 0.05 \({}^{\text{a}}\) \\ \hline \multirow{2}{*}{Horizontal CUTTING PLANE} & \multirow{2}{*}{0.432 \({}^{\text{b}}\)} & \multirow{2}{*}{0.01 \({}^{\text{a}}\)} & \multirow{2}{*}{0.07 \({}^{\text{a}}\)} & \multirow{2}{*}{0.22 \({}^{\text{a}}\)} & \multirow{2}{*}{0.083 \({}^{\text{b}}\)} \\  & & & & & & \\ \hline \multicolumn{8}{c}{MM-TA vs. MM-CA} \\ \multicolumn{8}{c}{**Vertical**} & \multirow{2}{*}{**Horizontal**} \\ Analysis of the Shape & & 0.01 \({}^{\text{a}}\) & 0.01 \({}^{\text{a}}\) & & \\ \multicolumn{8}{c}{Analysis of the Puff} & 0.031 \({}^{\text{a}}\) & 0.048 \({}^{\text{a}}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Inferential statistics and multiple comparisons (univariate ANOVA). \({}^{\text{a}}\) means significant differences with \(p<\) 0.05 were detected; \({}^{\text{b}}\) means no significant differences were detected. positioning [11]. Another factor influencing the effectiveness of clear aligner treatment and its clinical results is the accuracy of replicating the shape of the attachments [17; 19]. Many studies have assessed the effects of various forms of attachments on dental movement [13; 18; 20; 21]. However, only a limited number of studies have evaluated the accuracy of reproducing the programmed shape required for the desired tooth displacement [17; 19].