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added back formula

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This commit is contained in:
smail alijagic
2026-04-27 10:48:43 +02:00
parent a83aa654df
commit 2fe93b5c94
11 changed files with 1000154 additions and 1000002 deletions
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.DS_Store
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.vscode/c_cpp_properties.json
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.vscode/launch.json
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.vscode/settings.json
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forces.cpp
+34 -1
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@@ -18,15 +18,23 @@ double g(double v_max_alpha, double w_alpha_norm) {
}
// # 8 flops
//
// $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) \vec{e}_\alpha(t) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$
//
void compute_acceleration_term(Pedestrian *p) {
// # 2 flops
// $v_{\alpha}^{0}\vec{e}_{\alpha}$
Vector2d desired_velocity = p->e * p->desired_v0;
// $\vec{v}_{\alpha}(t)$
Vector2d actual_velocity = p->curr_vel;
// # 6 flops = 4 ADDs, 2 DIVs
p->f_i += (desired_velocity - actual_velocity) / tau_alpha;
}
// # 55(N - 1) = 55N - 55 flops
//
// $\sum_{\beta} \vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta})$
//
void compute_repulsive_effects_from_pedestrians(Pedestrian *pedestrians, Pedestrian *p, int N) {
for (int i = 0; i < N; i++) {
@@ -41,32 +49,50 @@ void compute_repulsive_effects_from_pedestrians(Pedestrian *pedestrians, Pedestr
// }
// # 2 ADDs
// $\vec{r}_{\alpha\beta}$
Vector2d r_ab = p->curr_pos - pedestrians[i].curr_pos;
// # 4 flops = 1 SQRT, 2 MULTs, 1 ADD
// $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert$
double r_ab_norm = r_ab.norm();
// $\vec{e}_{\beta}$
Vector2d e_b = pedestrians[i].e;
// # 2 MULTs
double s_b = pedestrians[i].desired_v0 * delta_t;
// $v_\beta \Delta t$
double s_b = pedestrians[i].curr_vel.norm() * delta_t;
// # 4 flops = 2 ADDs, 2 MULTs
// $\vec{r}_{\alpha\beta} - \vec{v}_{\beta}\varDelta_{t}\vec{e}_{\beta}$
Vector2d r_ab2 = r_ab - (e_b * s_b);
// # 4 flops = 1 SQRT, 2 MULTs, 1 ADD
// $\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
double r_ab2_norm = r_ab2.norm();
// # 7 flops = 1 SQRT, 3 ADDs, 2 MULTs, 1 DIV
//
// $(4):2b = \sqrt{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)^2 - (v_\beta \Delta t)^2}$
//
double b = sqrt((r_ab_norm + r_ab2_norm) * (r_ab_norm + r_ab2_norm) - s_b * s_b) / 2;
// # 12 flops = 6 DIVs, 3 ADDs, 3 MULTs
//
// $(7):\grad_{\vec{r}_{\alpha \beta}}b = \frac{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert) (\frac{\vec{r}_{\alpha \beta}}{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert} + \frac{\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta}{\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert})}{4b}$
//
Vector2d b_grad = (r_ab / r_ab_norm + r_ab2 / r_ab2_norm) * (r_ab_norm + r_ab2_norm) / (4 * b);
// # 6 flops = 3 MULTs, 2 DIVs, 1 EXP
//
// $(5):\vec{f}_{\alpha \beta}(\vec{r}_{\alpha \beta}) = \frac{V^0_{\alpha \beta}}{\sigma}e^{-b / \sigma} \grad_{\vec{r}_{\alpha \beta}}b$
//
Vector2d f_ped = b_grad * ((V0_AB / SIGMA) * (exp(-b / SIGMA)));
// # 14 flops: 9 MULTs, 4 ADDs, 1 SQRT
//
// $(11):\vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta}) = w(\vec{e}_{\alpha}, -\vec{f}_{\alpha\beta})\vec{f}_{\alpha\beta}(\vec{r}_{\alpha} - \vec{r}_{\beta})$
//
p->f_i += f_ped * w(p->e, f_ped * -1);
}
}
@@ -83,9 +109,13 @@ void compute_repulsive_effects_from_borders(Board &board, Pedestrian *p) {
Obstacle obstacle = obstacles[i];
// # 17 flops
// $\vec{r}_{\alpha B}$
Vector2d r_aB = p->curr_pos - obstacle.find_nearest_obstacle_point(p->curr_pos);
// # 17 flops = 2 DIVs, 1 SQRT, 2 MULTs, 1 ADD, 2 MULTs, 1 DIV, 2 MULTs, 1 EXP, 1 SQRT, 2 MULTs, 1 ADD, 1 DIV
//
// $\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = \frac{U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R} \frac{\vec{r}_{\alpha B}}{\Arrowvert \vec{r}_{\alpha B} \Arrowvert}$
//
Vector2d f_obst = (r_aB / r_aB.norm()) * (U0_AB / R) * std::exp(-r_aB.norm() / R);
// # 2 ADDs
@@ -95,6 +125,9 @@ void compute_repulsive_effects_from_borders(Board &board, Pedestrian *p) {
// However, the formulas above for attractive and repulsive effects only hold for situations that are perceived in the desired direction e_alpha(t) of motion.
// I assumed that with formulas above its also meant for equation 8 (even though not explicitly mentioned their)
// # 14 flops: 9 MULTs, 4 ADDS, 1 SQRT
//
// $(12):\vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{ B}) = w(\vec{e}_{\alpha}, -\vec{F}_{\alpha B})\vec{F}_{\alpha B}(\vec{r}_{\alpha} - \vec{r}_{ B})$
//
p->f_i += f_obst * w(p->e, f_obst * -1);
}
}
forces.hpp
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@@ -3,25 +3,34 @@
#include "pedestrian.hpp"
#include <cmath>
// $\tau_{\alpha}$
const double tau_alpha = 0.5;
// $V^0_{\alpha \beta}$
const double V0_AB = 2.1;
// $\sigma$
const double SIGMA = 0.3;
// $U^0_{\alpha B}$
const double U0_AB = 10.0;
// $R$
const double R = 0.2;
// $c$
const double c = 0.5;
// $\varphi$
const double phi = 100.0 / 180.0 * M_PI;
const double cos_phi = cos(phi);
// $\varDelta_{t}$
// step size = 0.2 seconds
const double delta_t = 2;
const double dt = 0.01;
const double dt = 0.001;
// # Optional (forces.cpp: compute_repulsive_effects_from_pedestrians)
// const double DISTANCE = 2.0;
main.cpp
+13 -1
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@@ -67,7 +67,7 @@ int main(int argc, const char *argv[]) {
int n_iter = atoi(argv[2]);
// Logic to get/dump the simulation data
const int dump_interval = 5; // dump every 5 iterations -> 20 fps (since dt = 0.01)
const int dump_interval = 50; // dump every 5 iterations -> 20 fps (since dt = 0.01)
const char *dump_path = (argc >= 4) ? argv[3] : nullptr;
std::vector<std::tuple<int, int, double, double, int>> samples; // t, id, x, y, color
@@ -89,12 +89,21 @@ int main(int argc, const char *argv[]) {
p.f_i.reset();
// # 8 flops
//
// $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) \vec{e}_\alpha(t) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$
//
compute_acceleration_term(&p);
// # 55N - 55 flops
//
// $\sum_{\beta} \vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta})$
//
compute_repulsive_effects_from_pedestrians(pedestrians, &p, n_p);
// # 192 flops
//
// $\sum_{B} \vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{B})$
//
compute_repulsive_effects_from_borders(board, &p);
}
// Pass2: integrate the forces and update the current state
@@ -109,6 +118,9 @@ int main(int argc, const char *argv[]) {
p.curr_vel = p.w * g(p.v_max, p.w.norm());
// # 4 flops = 2 ADDs, 2 MULTs
//
// $\vec{r}_i^{t+1} += \vec{r}^t_i + v^t_idt$
//
p.curr_pos = p.curr_pos + p.curr_vel * dt;
// how to handle if a pedestrian reached the end of our simulation/end of the hallway
main_test_visualisation
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pedestrian.hpp
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@@ -7,13 +7,21 @@ enum Color { BLACK, WHITE };
struct Pedestrian {
Color color;
// $\vec{v}_{\alpha}(t)$
Vector2d curr_vel; // v_alpha (actual, ≤ v_max)
// $\vec{w}_{\alpha}$
Vector2d w; // w_alpha (preferred, integrates force)
// $\vec{r}_\alpha(t)$
Vector2d curr_pos;
// $\vec{e}_{\alpha}(t)$
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;
// social force
Vector2d f_i;
Pedestrian() : color(WHITE), curr_vel(0.0, 0.0), w(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) {}
positions.csv
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test_run_out.mp4
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