```c++
for each time_step t:
    for each pedestrian p:

        reset_social_force(p)

        // (1)
        compute_acceleration_term(p)

        // (2)
        compute_repulsive_effects_from_pedestrians(p, pedestrians)

        // (3)
        compute_repulsive_effects_from_borders(p, board)

    for each pedestrian p:
        // next pos, desired dir, desired v, curr v
        update_state(p)
```


(1) $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) \vec{e}_\alpha(t) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$

(2) $\sum_{\beta} \vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta})$

(3) $\sum_{B} \vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{B})$