## 3 Results
Despite the magnet remaining in a relatively constant starting position and the magnetometer being calibrated consistently, variations in the measurements among users are evident. The disparities are notably visible in the readings \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Measurement** & **Axis** & **Intra-Person** & **Inter-Person** \\ \hline \multirow{4}{*}{Stylus rotation [rad]} & X & 9.11 & 18.83 \\ \cline{2-4}  & Y & 7.33 & 14.68 \\ \cline{1-1} \cline{2-4}  & Z & 2.18 & 4.37 \\ \cline{1-1} \cline{2-4}  & Magnitude & 5.42 & 18.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Intra-person and inter-person variability of the rotation vector for stylus tilt data across different axes (X, Y, Z) and magnitude. Data for finger writing were not available. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & & \multicolumn{2}{c}{**Stylus**} & \multicolumn{2}{c}{**Finger**} \\ \hline \multirow{2}{*}{**Measurement**} & \multirow{2}{*}{**Axis**} & **Intra-Person** & **Inter-Person** & **Intra-Person** & **Inter-Person** \\ \hline \multirow{4}{*}{Relative Position (X,Y) [pixel]} & X & 101.73 & 306.44 & 93.27 & 219.74 \\ \cline{2-4}  & Y & 79.34 & 129.70 & 99.56 & 202.03 \\ \cline{1-1} \cline{2-4}  & Magnitude & 103.37 & 220.40 & 100.89 & 226.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of intra-person and inter-person variability in relative position measurements (X, Y) and magnitudes for stylus and finger inputs based on 5 trials from each of the 5 participants. of the magnetic field along the X and Y axes, while the measurements along the Z axis show less variation. Additionally, the minimum and maximum values for the same users do not show a noticeable deviation from the mean value across all five writing trials. The graph shows that each user may have an activity surface, which reflects a distinct set of writing attempts. In order to authenticate, the current write attempt has to reside inside the existing activity surface for a particular user. Figure 12 illustrates the comparison of averaged magnetometer readings when the distinct user wrote the same sentence five times using both a stylus and a finger. Predictably, the magnetometer measurements for the aforementioned two input modalities differ noticeable for the same user. Writing with a stylus is considerably different from writing with a finger in terms of the orientation and location of the magnet, which explains the findings. The blue lines representing the stylus exhibit more consistent and smoother patterns compared to the orange lines representing the finger, suggesting that using a stylus provides more stable and accurate input. Moreover, the bending motions of the finger when writing have distinct effects on the magnetometer readings compared to the rigid and inflexible stylus. \begin{table}
\begin{tabular}{l l l l} \hline \hline \multicolumn{1}{c}{**Measurement**} & **Axis** & **Intra-Person** & **Inter-Person** \\ \hline \multirow{3}{*}{Stylus translation [mm]} & X & 0.65 & 2.62 \\ \cline{2-4}  & Y & 0.85 & 3.52 \\ \cline{2-4}  & Z & 1.62 & 6.78 \\ \cline{2-4}  & Magnitude & 1.94 & 8.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Intra-person and inter-person variability of the translation vector for stylus tilt data across different axes (X, Y, Z) and magnitude. Data for finger writing were not available. Figure 10: The X and Y coordinates of the stylus tilt are determined by using the ArUco marker positioned on the tip of the stylus. Distinct hues of a single color signify multiple trials of the same person, whereas varying colors denote the inclinations of the stylus for different individuals. \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & \multicolumn{3}{c}{**Stylus**} & **Finger** \\ \hline
**Measurement** & **Intra-Person** & **Inter-Person** & **Intra-Person** & **Inter-Person** \\ \hline \multicolumn{1}{c}{Stylus orientation [rad]} & 0.28 & 2.76 & N/A & N/A \\ \hline \hline \end{tabular}
\end{table}