# Characterization of Driver Dynamic Visual Perception Under Different Road Linearity Conditions
## 4 Model Construction
### Modeling of saccade Amplitude over Time Under Different Road Sections  
Figure 8 demonstrated the trend of driver saccade amplitude over time for different roadway conditions. The fitting results are shown in Table 6, where the driver saccade amplitude for the three roadway segments, except for the straight roadway segment, exhibited significant volatility.  
\begin{table}
\begin{tabular}{c c c} \hline
**Section of Road** & **Pupil Diameter Model** & \(\mathbf{R^{2}}\) \\ \hline Straight Movement & \(y=1.35886\times 10^{-5}\mathrm{t}^{3}-0.0016\mathrm{t}^{2}+0.0601\mathrm{t}+2.3468\) & 0.813 \\ Turn & \(y=2.67826\times 10^{-5}\mathrm{t}^{3}-0.00326\mathrm{t}^{2}+0.11417\mathrm{t}+3.717 \mathrm{\tau}\mathrm{\tau}\mathrm{\tau}\mathrm{\tau}\mathrm{\tau}\mathrm{\tau}\) & 0.772 \\ Climbing & \(y=5.1995\times 10^{-6}\mathrm{t}^{3}-6.16309\ast 10^{-4}\mathrm{t}^{2}+0.02224 \mathrm{t}+3.23528\) & 0.794 \\ Downhill & \(y=1.8722\times 10^{-7}\mathrm{t}^{3}-4.36681\ast 10^{-4}\mathrm{t}^{2}+0.028 \mathrm{t}+3.56532\) & 0.753 \\ \hline \end{tabular}
\end{table}
Table 5: Model of the change in pupil diameter for different road sections.  
The fitting model for the straight roadway section is:  
\[y=2.35796\times 10^{-4}t^{3}\ -0.02682t^{2}+0.91661t+39.98236 \tag{9}\]  
The R\({}^{2}\) value of this model was 0.842, which indicated a good fitting effect. In the straight road section, the driver's attention was focused on the centerline of the road ahead, the cognitive load was low, the saccade amplitude was small and stable, and the fitting curve showed a smooth state.  
In the turning section, the fitting model is:  
\[y=8.24778\times 10^{-4}t^{3}-0.09047t^{2}+2.83902t+97.6021 \tag{10}\]  
\begin{table}
\begin{tabular}{c c c} \hline
**Section of Road** & **Saccade Amplitude Model** & \(R^{2}\) \\ \hline Straight Movement & \(y=2.35796\times 10^{-4}t^{3}\ -0.02682t^{2}+0.91661t+39.98236\) & 0.842 \\ Turn & \(y=8.24778\times 10^{-4}t^{3}-0.09047t^{2}+2.83902t+97.6021\) & 0.713 \\ Climbing & \(y=6.81582\times 10^{-4}t^{3}-0.07598t^{2}+2.42437t+60.45934\) & 0.729 \\ Downhill & \(y=0.00108t^{3}-0.13295t^{2}+4.77193t+84.71186\) & 0.721 \\ \hline \end{tabular}
\end{table}
Table 6: Modeling of saccade amplitude under different road sections.  
Figure 8: Model of saccade range under different road sections: (**a**) straight ahead; (**b**) turning; (**c**) climbing; (**d**) downhill.  
The R\({}^{2}\) value of the model was 0.713, and the relatively low fitting accuracy indicated that the data were more volatile. During the turning process, drivers needed to frequently shift their eyes to cope with the changing environment and path selection, which resulted in increased saccade amplitude and high volatility.  
For the climbing section, the fitted model was:  
\[y=6.81582\times 10^{-4}t^{3}-0.07598t^{2}+2.42437t+60.45934 \tag{11}\]  
The R\({}^{2}\) value of this model was 0.729, which indicated a relatively poor fitting effect. During the climbing course, the drivers needed to perform power control and speed adjustment, and the saccade amplitude gradually increased with time, but with the adaptation to the ramp, the saccade amplitude gradually stabilized.  
For the downhill section, the fitting model is:  
\[y=0.00108t^{3}-0.13295t^{2}+4.77193t+84.71186 \tag{12}\]  
The R\({}^{2}\) value of the model was 0.721, and the relatively low fitting accuracy indicated that the driver's saccade amplitude was more volatile during the downhill section, especially in the initial period, when the drivers needed to adjust their vision frequently to cope with the potential speed and hazard control needs, which resulted in a poor model fitting.  
Overall, the fitted models in Table 6 showed high prediction accuracy in the straight ahead and climbing segments, while in the turning and downhill segments, the data points fluctuate more, resulting in a poorer fit. This suggested that drivers had increased cognitive loads and greater fluctuations in saccade amplitude in such complex sections of turning and downhill, which affected the model fitting accuracy.