Update board.hpp, forces.hpp, forces.cpp, main.cpp, pedestrian.hpp: correct some bugs in implementation
This commit is contained in:
AKallala
@@ -1,9 +1,41 @@
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#pragma once
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#include "vector2d.hpp"
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struct Obstacle {
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Vector2d start;
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Vector2d end;
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Obstacle() : start(0, 0), end(0, 0) {}
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Obstacle(Vector2d s, Vector2d e) : start(s), end(e) {}
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// find the point of the obstacle that is nearest to p
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Vector2d find_nearest_obstacle_point(Vector2d p) {
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Vector2d obstacle_v = end - start;
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double projection = (p - start).dot(obstacle_v) / obstacle_v.dot(obstacle_v);
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if (projection < 0.0)
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projection = 0.0;
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if (projection > 1.0)
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projection = 1.0;
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return start + obstacle_v * projection;
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}
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};
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struct Board {
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double length, width;
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Vector2d *borders; // array containing the position of each obstacle
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int n_borders; // number of obstacles
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Board(double l, double w, int n, Vector2d *border) : length(l), width(w), n_borders(n), borders(border) {}
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Obstacle *obstacles; // array of obstacles (represented as lines) that are present on the board
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int n_obstacles; // number of obstacles
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Board(double l, double w, int n, Obstacle *o) : length(l), width(w), n_obstacles(n + 4) {
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obstacles = new Obstacle[n + 4];
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for (int i = 0; i < n; i++) {
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obstacles[i] = o[i];
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}
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// borders of the board: bottom, right, top, left
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obstacles[n] = Obstacle(Vector2d(0, 0), Vector2d(l, 0));
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obstacles[n + 1] = Obstacle(Vector2d(l, 0), Vector2d(l, w));
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obstacles[n + 2] = Obstacle(Vector2d(l, w), Vector2d(0, w));
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obstacles[n + 3] = Obstacle(Vector2d(0, w), Vector2d(0, 0));
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}
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~Board() { delete[] obstacles; }
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};
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+25
-71
@@ -1,35 +1,26 @@
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#include "forces.hpp"
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#include <math.h>
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// # Done
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double w(Vector2d e, Vector2d f) {
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if (e.dot(f) >= f.norm() * cos_phi)
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return 1.0;
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return c;
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else
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return c;
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}
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double g(double v_max_alpha, double w_alpha_norm) {
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if (w_alpha_norm <= v_max_alpha) {
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return 1;
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}
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return v_max_alpha / w_alpha_norm;
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}
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// # Done
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//
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// $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) \vec{e}_\alpha(t) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$
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//
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void compute_acceleration_term(Pedestrian *p) {
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// $v_{\alpha}^{0}\vec{e}_{\alpha}$
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Vector2d desired_velocity = p->e * p->desired_v0;
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// $\vec{v}_{\alpha}(t)$
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Vector2d actual_velocity = p->curr_vel;
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double tau_alpha_inv = 1 / tau_alpha;
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p->F_i += (desired_velocity - actual_velocity) * tau_alpha_inv;
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p->f_i += (desired_velocity - actual_velocity) / tau_alpha;
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}
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// # Done
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//
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// $\sum_{\beta} \vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta})$
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//
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void compute_repulsive_effects_from_pedestrians(Pedestrian *pedestrians, Pedestrian *p, int N) {
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for (int i = 0; i < N; i++) {
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@@ -43,78 +34,41 @@ void compute_repulsive_effects_from_pedestrians(Pedestrian *pedestrians, Pedestr
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// continue;
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// }
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// $\vec{r}_{\alpha\beta}$
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Vector2d r_ab = p->curr_pos - pedestrians[i].curr_pos;
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// $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert$
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double r_ab_norm = r_ab.norm();
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// $\vec{e}_{\beta}$
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Vector2d e_beta = pedestrians[i].e;
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Vector2d e_b = pedestrians[i].e;
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// $v_\beta \Delta t$
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double v_beta_delta_t = pedestrians[i].desired_v0 * delta_t;
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double s_b = pedestrians[i].desired_v0 * delta_t;
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// $\vec{r}_{\alpha\beta} - \vec{v}_{\beta}\varDelta_{t}\vec{e}_{\beta}$
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Vector2d r_ab_minus_v_beta_delta_t_e_beta = r_ab - (e_beta * v_beta_delta_t);
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Vector2d r_ab2 = r_ab - (e_b * s_b);
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// $\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
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double r_ab_minus_v_beta_delta_t_e_beta_norm = r_ab_minus_v_beta_delta_t_e_beta.norm();
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double r_ab2_norm = r_ab2.norm();
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// (4):
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//
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// $2b = \sqrt{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)^2 - (v_\beta \Delta t)^2}$
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//
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double b = sqrt(pow(r_ab_norm + r_ab2_norm, 2) - pow(s_b, 2)) / 2;
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double b = sqrt((r_ab_norm + r_ab_minus_v_beta_delta_t_e_beta_norm) * (r_ab_norm + r_ab_minus_v_beta_delta_t_e_beta_norm) - (v_beta_delta_t) * (v_beta_delta_t)) / 2;
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Vector2d b_grad = (r_ab / r_ab_norm + r_ab2 / r_ab2_norm) * (r_ab_norm + r_ab2_norm) / (4 * b);
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// (7):
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//
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// $\grad_{\vec{r}_{\alpha \beta}}b = \frac{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert) (\frac{\vec{r}_{\alpha \beta}}{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert} + \frac{\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta}{\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert})}{4b}$
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//
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//
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Vector2d delta_r_alpha_beta_b = (((r_ab / r_ab_norm) + (r_ab_minus_v_beta_delta_t_e_beta / r_ab_minus_v_beta_delta_t_e_beta_norm)) * (r_ab_norm + r_ab_minus_v_beta_delta_t_e_beta_norm)) / (4 * b);
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Vector2d f_ped = b_grad * ((V0_AB / SIGMA) * (exp(-b / SIGMA)));
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// (5):
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//
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// $\vec{f}_{\alpha \beta}(\vec{r}_{\alpha \beta}) = \frac{V^0_{\alpha \beta}}{\sigma}e^{-b / \sigma} \grad_{\vec{r}_{\alpha \beta}}b$
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//
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//
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Vector2d f_alpha_beta_r_alpha_beta = delta_r_alpha_beta_b * ((V0_AB / SIGMA) * (exp(-b / SIGMA)));
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// (11):
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//
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// $\vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta}) = w(\vec{e}_{\alpha}, -\vec{f}_{\alpha\beta})\vec{f}_{\alpha\beta}(\vec{r}_{\alpha} - \vec{r}_{\beta})$
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//
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// Add repulsive effects from other pedestrians to current pedestrian's social force
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p->F_i += f_alpha_beta_r_alpha_beta * w(p->e, f_alpha_beta_r_alpha_beta * -1);
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p->f_i += f_ped * w(p->e, f_ped * -1);
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}
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}
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// # Done
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void compute_repulsive_effects_from_borders(Board &B, Pedestrian *p) {
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void compute_repulsive_effects_from_borders(Board &board, Pedestrian *p) {
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Vector2d *borders = B.borders;
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int n_borders = B.n_borders;
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Obstacle *obstacles = board.obstacles;
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int n_borders = board.n_obstacles;
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for (int i = 0; i < n_borders; i++) {
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Vector2d border = borders[i];
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Obstacle obstacle = obstacles[i];
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// $\vec{r}_{\alpha B}$
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Vector2d r_alpha_B = p->curr_pos - border;
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Vector2d r_aB = p->curr_pos - obstacle.find_nearest_obstacle_point(p->curr_pos);
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//
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// $\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = \frac{U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R} \frac{\vec{r}_{\alpha B}}{\Arrowvert \vec{r}_{\alpha B} \Arrowvert}$
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//
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Vector2d f_obst = (r_aB / r_aB.norm()) * (U0_AB / R) * std::exp(-r_aB.norm() / R);
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Vector2d F_alpha_B = (r_alpha_B / r_alpha_B.norm()) * (U0_AB / R) * std::exp(-r_alpha_B.norm() / R);
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// (12):
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//
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// $\vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{ B}) = w(\vec{e}_{\alpha}, -\vec{F}_{\alpha B})\vec{F}_{\alpha B}(\vec{r}_{\alpha} - \vec{r}_{ B})$
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//
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p->F_i += F_alpha_B * w(p->e, F_alpha_B * (-1));
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p->f_i += f_obst;
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}
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}
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+5
-18
@@ -3,46 +3,33 @@
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#include "pedestrian.hpp"
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#include <cmath>
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// $\tau_{\alpha}$
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// https://arxiv.org/pdf/cond-mat/9805244, page 8
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const double tau_alpha = 0.5;
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// $V^0_{\alpha \beta}$
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// https://arxiv.org/pdf/cond-mat/9805244, page 8
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const double V0_AB = 2.1;
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// $\sigma$
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// https://arxiv.org/pdf/cond-mat/9805244, page 8
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const double SIGMA = 0.3;
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// $U^0_{\alpha B}$
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// https://arxiv.org/pdf/cond-mat/9805244, page 8
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const double U0_AB = 10.0;
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// $R$
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// https://arxiv.org/pdf/cond-mat/9805244, page 8
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const double R = 0.2;
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// $c$
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// https://arxiv.org/pdf/cond-mat/9805244, page 8
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const double c = 0.5;
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// $\varphi$
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// https://arxiv.org/pdf/cond-mat/9805244, page 8
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const double phi = 100.0;
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const double phi = 100.0 / 180.0 * M_PI;
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const double cos_phi = cos(phi);
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// $\varDelta_{t}$
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// step size = 0.2 seconds
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// https://arxiv.org/pdf/cond-mat/9805244, page 8
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const double delta_t = 2;
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const double dt = 0.01;
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// # Optional (forces.cpp: compute_repulsive_effects_from_pedestrians)
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// const double DISTANCE = 2.0;
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double w(Vector2d e, Vector2d f);
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double g(double v_max_alpha, double w_alpha_norm);
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void compute_acceleration_term(Pedestrian *p);
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void compute_repulsive_effects_from_pedestrians(Pedestrian *P, Pedestrian *p, int N);
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@@ -4,12 +4,8 @@
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#include "pedestrian.hpp"
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#include "vector2d.hpp"
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double g(double v_max_alpha, double w_alpha_norm) {
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if (w_alpha_norm <= v_max_alpha) {
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return 1;
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}
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return v_max_alpha / w_alpha_norm;
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}
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#define BOARD_WIDTH 10.0
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#define BOARD_LENGTH 50.0
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using namespace std;
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@@ -23,67 +19,58 @@ using namespace std;
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Pedestrian *init_pedestrians(int n_p) {
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Pedestrian *P = new Pedestrian[n_p];
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for (int i = 0; i < n_p; i++) {
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P[i] = Pedestrian();
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std::random_device rd; // use for truly random simulation
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std::mt19937 gen(rd()); // use rd instead of 42 as seed for real randomness
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std::normal_distribution<double> velocity_gen(1.34, 0.26); // 1.34 and 0.26 are the mean and stdrd deviation used in paper
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std::uniform_real_distribution<double> x_gen(2, BOARD_LENGTH - 2);
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std::uniform_real_distribution<double> y_gen(2, BOARD_WIDTH - 2);
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for (int i = 0; i < n_p / 2; i++) {
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Vector2d start_pos = Vector2d(1, y_gen(gen));
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Vector2d destination = Vector2d(BOARD_LENGTH - 1, y_gen(gen));
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double desired_v0 = velocity_gen(gen);
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double v_max = 1.3 * desired_v0;
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P[i] = Pedestrian(WHITE, (destination - start_pos) / (destination - start_pos).norm() * desired_v0, start_pos, (destination - start_pos) / (destination - start_pos).norm(), v_max, desired_v0, destination, Vector2d());
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}
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for (int i = n_p / 2; i < n_p; i++) {
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Vector2d start_pos = Vector2d(BOARD_LENGTH - 1, y_gen(gen));
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Vector2d destination = Vector2d(1, y_gen(gen));
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double desired_v0 = velocity_gen(gen);
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double v_max = 1.3 * desired_v0;
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P[i] = Pedestrian(BLACK, (destination - start_pos) / (destination - start_pos).norm() * desired_v0, start_pos, (destination - start_pos) / (destination - start_pos).norm(), v_max, desired_v0, destination, Vector2d(0, 0));
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}
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return P;
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}
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Board init_board(int width, int length) {
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Vector2d obs[] = {Vector2d(2.0, 1.0), Vector2d(4.0, 1.0), Vector2d(6.0, 2.0), Vector2d(6.0, 4.0)};
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return Board(width, length, 4, obs);
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}
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int main(int argc, const char *argv[]) {
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int main(int argc, const char* argv[]) {
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Board B = init_board(10, 15);
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Obstacle obs[] = {};
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Board board = Board(BOARD_LENGTH, BOARD_WIDTH, 0, obs);
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int n_p = atoi(argv[1]);
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int n_iter = atoi(argv[2]);
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Pedestrian *pedestrians = init_pedestrians(n_p);
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for (int t = 0; t < n_iter; t++) {
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for (int i = 0; i < n_p; i++) {
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Pedestrian &p = pedestrians[i];
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p.F_i.reset();
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p.f_i.reset();
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//
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// $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) \vec{e}_\alpha(t) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$
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//
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compute_acceleration_term(&p);
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//
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// $\sum_{\beta} \vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta})$
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//
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compute_repulsive_effects_from_pedestrians(pedestrians, &p, n_p);
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//
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// $\sum_{B} \vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{B})$
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//
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compute_repulsive_effects_from_borders(B, &p);
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compute_repulsive_effects_from_borders(board, &p);
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//
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// $\vec{w}_i = \vec{v}_i + \vec{F}_idt$
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//
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p.w_alpha = p.curr_vel + p.F_i * delta_t;
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Vector2d w_alpha = p.curr_vel + p.f_i * dt;
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//
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// $\vec{v}_i^{t+1} = \vec{w}_ig(\frac{v^{max}_i}{\Arrowvert \vec{w}_i \Arrowvert}) $
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//
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p.next_vel = p.w_alpha * g(p.v_max, p.w_alpha.norm());
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p.curr_vel = w_alpha * g(p.v_max, w_alpha.norm());
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//
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// $\vec{r}_i^{t+1} += \vec{r}^t_i + v^t_idt$
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//
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p.curr_pos = p.curr_pos + p.curr_vel * delta_t;
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}
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p.curr_pos = p.curr_pos + p.curr_vel * dt;
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for (int i = 0; i < n_p; i++) {
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pedestrians[i].update();
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p.e = (p.destination - p.curr_pos) / (p.destination - p.curr_pos).norm();
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}
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}
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+7
-71
@@ -1,85 +1,21 @@
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#pragma once
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#include "vector2d.hpp"
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#include "random"
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#include "vector2d.hpp"
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// For visual simulation
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enum Color { BLACK, WHITE };
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struct Pedestrian {
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// TODO: Update initial values
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Pedestrian() :
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curr_vel(),
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curr_pos(),
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e(),
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v_max(1.34 * 1.3),
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desired_v0(1.34),
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destination(),
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F_i(),
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next_pos(),
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next_vel(),
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w_alpha()
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{}
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Pedestrian(
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Vector2d c_v,
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Vector2d c_p,
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Vector2d e,
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Vector2d d,
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Vector2d f,
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Vector2d n_p,
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Vector2d n_v,
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Vector2d w_alpha
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) :
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curr_vel(c_v),
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curr_pos(c_p),
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e(e),
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v_max(),
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desired_v0(),
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destination(d),
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F_i(f),
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next_pos(n_p),
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next_vel(n_v),
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w_alpha(w_alpha)
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{}
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// $\vec{v}_{\alpha}(t)$
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Color color;
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Vector2d curr_vel;
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// $\vec{r}_\alpha(t)$
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Vector2d curr_pos;
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// $\vec{e}_{\alpha}(t)$
|
||||
Vector2d e;
|
||||
|
||||
// $v_{\alpha}^{max} = 1.3 v^{0}_{\alpha}$
|
||||
double v_max;
|
||||
|
||||
// $v_\alpha^0$
|
||||
double desired_v0;
|
||||
|
||||
// # =============================================================
|
||||
|
||||
// $\vec{r}^0_\alpha$
|
||||
Vector2d destination;
|
||||
Vector2d f_i;
|
||||
|
||||
// social force
|
||||
Vector2d F_i;
|
||||
Pedestrian() : color(WHITE), curr_vel(0.0, 0.0), curr_pos(0.0, 0.0), e(0.0, 0.0), v_max(0.0), desired_v0(0.0), destination(0.0, 0.0), f_i(0.0, 0.0) {}
|
||||
|
||||
// # =============================================================
|
||||
|
||||
// $\vec{r}_\alpha(t+1)$
|
||||
Vector2d next_pos;
|
||||
|
||||
// $\vec{v}_{\alpha}(t + 1)$
|
||||
Vector2d next_vel;
|
||||
|
||||
// $\vec{w}_{\alpha}$
|
||||
Vector2d w_alpha;
|
||||
|
||||
// # =============================================================
|
||||
|
||||
void update() {
|
||||
curr_pos = next_pos;
|
||||
curr_vel = next_vel;
|
||||
e = (destination - curr_pos) / (destination - curr_pos).norm();
|
||||
}
|
||||
Pedestrian(Color clr, Vector2d c_v, Vector2d c_p, Vector2d e, double v_max, double desired_v0, Vector2d d, Vector2d f) : color(clr), curr_vel(c_v), curr_pos(c_p), e(e), v_max(v_max), desired_v0(desired_v0), destination(d), f_i(f) {}
|
||||
};
|
||||
|
||||
Reference in New Issue
Block a user