#include "forces.hpp"
#include <math.h>

// # Done
double w(Vector2d e, Vector2d f) {
  if (e.dot(f) >= f.norm() * cos_phi)
    return 1.0;
  return c;
}

// # Done
//
// $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) \vec{e}_\alpha(t) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$
//
void compute_acceleration_term(Pedestrian *p) {

  // $v_{\alpha}^{0}\vec{e}_{\alpha}$
  Vector2d desired_velocity = p->e * p->desired_v0;

  // $\vec{v}_{\alpha}(t)$
  Vector2d actual_velocity = p->curr_vel;

  double tau_alpha_inv = 1 / tau_alpha;

  p->F_i += (desired_velocity - actual_velocity) * tau_alpha_inv;
}

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

void compute_repulsive_effects_from_pedestrians(Pedestrian *pedestrians, Pedestrian *p, int N) {

  for (int i = 0; i < N; i++) {

    if (pedestrians + i == p)
      continue;

    // # Optional: Do not consider far away pedestrians from current pedestrian
    // # Might get better speed up, remove if not
    // if ((pedestrians[i].curr_pos - p->curr_pos).norm() > DISTANCE) {
    //   continue;
    // }

    // $\vec{r}_{\alpha\beta}$
    Vector2d r_ab = p->curr_pos - pedestrians[i].curr_pos;

    // $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert$
    double r_ab_norm = r_ab.norm();

    // $\vec{e}_{\beta}$
    Vector2d e_beta = pedestrians[i].e;

    // $v_\beta \Delta t$
    double v_beta_delta_t = pedestrians[i].desired_v0 * delta_t;

    // $\vec{r}_{\alpha\beta} - \vec{v}_{\beta}\varDelta_{t}\vec{e}_{\beta}$
    Vector2d r_ab_minus_v_beta_delta_t_e_beta = r_ab - (e_beta * v_beta_delta_t);

    // $\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
    double r_ab_minus_v_beta_delta_t_e_beta_norm = r_ab_minus_v_beta_delta_t_e_beta.norm();

    // (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_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;

    // (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 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);

    // (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_alpha_beta_r_alpha_beta = delta_r_alpha_beta_b * ((V0_AB / SIGMA) * (exp(-b / SIGMA)));

    // (11):
    //
    // $\vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta}) = w(\vec{e}_{\alpha}, -\vec{f}_{\alpha\beta})\vec{f}_{\alpha\beta}(\vec{r}_{\alpha} - \vec{r}_{\beta})$
    //
    // Add repulsive effects from other pedestrians to current pedestrian's social force
    p->F_i += f_alpha_beta_r_alpha_beta * w(p->e, f_alpha_beta_r_alpha_beta * -1);
  }
}

// # Done
void compute_repulsive_effects_from_borders(Board &B, Pedestrian *p) {

  Vector2d *borders = B.borders;
  int n_borders = B.n_borders;

  for (int i = 0; i < n_borders; i++) {

    Vector2d border = borders[i];

    // $\vec{r}_{\alpha B}$
    Vector2d r_alpha_B = p->curr_pos - border;

    //
    // $\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = \frac{U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R} \frac{\vec{r}_{\alpha B}}{\Arrowvert \vec{r}_{\alpha B} \Arrowvert}$
    //

    Vector2d F_alpha_B = (r_alpha_B / r_alpha_B.norm()) * (U0_AB / R) * std::exp(-r_alpha_B.norm() / R);

    // (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_alpha_B * w(p->e, F_alpha_B * (-1));
  }
}