# Behavioral Dynamics of Pedestrians Crossing between Two Moving Vehicles
## 3 Results
### Parameters Fall within Affordance  
Due to the accuracy of the simple crossing model, we expect Equations (3) and (4) to hold for the fitting parameters derived from the data. Figure 6a presents the affordance boundaries in the 3D parameter space. The curved surfaces depict the boundaries specified by Equation (3), and each data point plots the parameters corresponding to a single crossing. For comparison, data for two-step crossings (crosses) as well as simple crossings (circles) are displayed. It is observed that the circles, corresponding to simple crossings indeed lie within the volume between the boundaries. In contrast, most of the crosses are located outside, above the higher surface. This indicates that the subject is on route to collide with the leading vehicle and therefore deceleration is necessary.  
Figure 6: Data plotted with boundaries representing the affordance of the gap. (**a**) data plotted with surfaces in the three-dimensional parameter space \((\tau,v_{\text{max}},t_{a})\) defined by Equation (3). Data points for \(l_{g}=25\,\text{m}\) and \(y_{0}=-3.5\,\text{m}\) are plotted for all age groups; dots represent simple crossings and crosses represent two-step crossings; (**b**) data plotted with boundaries on the two-dimensional plane \((v_{\text{max}},t_{a})\) defined by Equation (4). To illustrate the effects of a shift in affordance, data and boundaries for \(l_{g}=25\,\text{m}\) and \(y_{0}=-3.5\,\text{m}\) (black) are plotted with those for \(l_{g}\) changed to \(33.3\,\text{m}\) and for \(y_{0}\) changed to \(-6.5\,\text{m}\) are shown in red and in blue, respectively. Triangles indicate average parameter values.  
Plotting Equation (4) on the 2D parameter plane \((v_{\text{max}},t_{a})\) corresponds to the projection of the 3D plot in Figure 6a onto the plane defined by \(\tau=0\). This results in Figure 6b, where two more cases have been included in addition to the case of the gap length \(l_{g}=25\,\text{m}\) and the initial position \(y_{0}=-3.5\,\text{m}\) presented in Figure 6a. Namely, to probe how the distribution of parameter values shifts with \(l_{g}\) and \(y_{0}\), we consider the data for a larger gap \(l_{g}=33.3\,\text{m}\) and for a farther initial position \(y_{0}=-6.5\,\text{m}\). Accordingly, Figure 6b presents data for three sets of the gap length and initial position together with the corresponding boundaries (lines instead of surfaces in Figure 6a) determined by Equation (4). Specifically, the cases of \((l_{g}=33.3\,\text{m},y_{0}=-3.5\,\text{m})\) and \((l_{g}=25\,\text{m},y_{0}=-6.5\,\text{m})\) are plotted in red and in blue, respectively, as well as the case of \((l_{g}=25\,\text{m},y_{0}=-3.5\,\text{m})\) plotted in black. It is observed that, as the gap is widened, the average behavior (designated by red triangles) shifts toward smaller \(t_{a}\) and larger \(v_{\text{max}}\). This reflects the tendency of the pedestrian to cross early before the gap center when possible. On the other hand, in the case that the initial position becomes farther from the intersection point, the pedestrian must compensate by either beginning to walk earlier or walking faster. Data in blue indeed exhibit on average a decrease in \(t_{a}\) and a slight increase in \(v_{\text{max}}\) (which is, however, not statistically significant). We remark that Figure 6b corresponds directly to Figures 3C and 3D of [13] while Figure 6a is a generalization.