# Characterization of Driver Dynamic Visual Perception Under Different Road Linearity Conditions
## 4 Model Construction
### Modeling of Average Fixation Duration over Time Under Different Road Sections  
After importing the processed data into Origin software for cubic polynomial fitting, the trend of average fixation duration over time under different road conditions was calculated and is shown in Figure 6, the fitted model showed excellent fitting effect, and its specific fitting parameters are shown in Table 4. The models for average fixation duration under different roadway segments and their fitting results are presented in Table 4. For the straight road section, the fitted model is:  
\[\mathrm{y}=1.62437\times 10^{-5}\mathrm{t}^{3}-0.00204\mathrm{t}^{2}+0.0772 \mathrm{t}+0.46727 \tag{1}\]  
Figure 6: Model of average fixation duration under different road sections: (a) straight ahead; (b) turning; (c) climbing; (d) downhill.  
The R\({}^{2}\) value of this model was 0.843, which indicated that the model can fit the data well, indicating that, in the straight road section, the driver's cognitive load was low, and the fixation duration showed a smooth increase over time.  
For the turning section, the fitted model is  
\[\mathrm{y}=6.0543\times 10^{-6}\mathrm{t}^{3}-7.72704\times 10^{-4}\mathrm{t}^{2}+ 0.02957\mathrm{t}+0.12151 \tag{2}\]  
The R\({}^{2}\) value of this model was 0.701, and the relatively low R\({}^{2}\) value indicates that driver fixation duration fluctuated more in the turning road section, and the fitting effect was not as good as in the straight road section. This is due to the fact that drivers need to adjust their vision frequently when turning and the task complexity was higher, which resulted in increased data volatility.  
For the climbing section, the fitting model is:  
\[\mathrm{y}=2.43225\times 10^{-6}\mathrm{t}^{3}-2.98094\times 10^{-4}\mathrm{t}^{2 }+0.01557\mathrm{t}+0.47329 \tag{3}\]  
The R\({}^{2}\) value of this model was 0.815, which indicated that the fitting effect was better for the climbing section, even though there was some data volatility and the driver's cognitive load was higher at the beginning of the ramp but gradually decreased as he or she adapted to the ramp environment.  
For the downhill section, the fitting model is:  
\[\mathrm{y}=9.01659\times 10^{-6}\mathrm{t}^{3}-0.00112\times 10^{-4}\mathrm{t}^{2 }+0.04226\mathrm{t}+0.23338 \tag{4}\]  
The model had an R\({}^{2}\) value of 0.731, and the relatively low R\({}^{2}\) value indicated that the fixation duration changes were more complicated in the downhill section. Drivers' cognitive load was higher and fixation duration fluctuates more at the beginning of the downhill section due to the need to control speed and cope with potential hazards, while drivers' cognitive load gradually decreased as the gradient decreases or the complexity of the environment decreases.  
Overall, the model fitted well to the data points under the four road conditions, especially in the straight ahead and climbing segments, showing high prediction accuracy. However, the complexity of the task was greater in the turning and downhill segments, the data points fluctuated more, and the fitted model had some deviations. In addition, the graphs also showed that the average fixation duration gradually increases with the continuation of time for the four road conditions, which may be due to the fatigue caused by the drivers driving for a long time, which reduces the frequency of the fixation behavior and the intensity of the attention allocation.