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

// return the direction between curr position and destination
// $\vectorarrow{e}_\alpha(t)$
Vector2d get_desired_direction(Pedestrian &p)
{
  Vector2d diff = p.desired_next_node - p.curr_pos;
  double length = diff.norm();
  return (p.desired_next_node - p.curr_pos) / length;
}

// return the direction between curr position and destination
// $\vectorarrow{e}_\alpha(t)$
Vector2d get_actual_direction(Pedestrian &p)
{
  Vector2d diff = p.actual_next_node - p.curr_pos;
  double length = diff.norm();
  return (p.actual_next_node - p.curr_pos) / length;
}

// double w(Vector2d e, Vector2d f) {
//
//   if (e.dot(f) >= f.norm() * PHI_DEG) return 1.0;
//   return C;
//
// }
double w(Vector2d e, Vector2d f)
{
  // The w() function should check if the angle between the desired direction e and the force f is within the field of view.
  //  Per equation (7), the condition is:
  //  e · f ≥ ||f|| * cos(phi)
  //  where phi = 100° (half of the 200° field of view (PHI_DEG)).
  const double phi = (PHI_DEG / 2.0) * M_PI / 180.0; // half-angle in radians
  if (e.dot(f) >= f.norm() * cos(phi))
    return 1.0;
  return C;
}

// F_i is the current position resp. direction vector of pedestrian p in time i?
//
// $\vectorarrow{F}_\alpha(\vectorarrow{v}_\alpha, v^0_\alpha \vectorarrow{e}_\alpha) \vectorarrow{e}_\alpha(t) = \frac{1}{\tau_\alpha}(v^0_\alpha \vectorarrow{e}_\alpha - \vectorarrow{v}_\alpha)$
//
void compute_acceleration_term(Pedestrian *p)
{

  Vector2d desired_velocity = get_desired_direction(*p) * p->desired_v0;

  // TODO: How to get this number
  // Probably needs to lookup the map and see if the desired position is reachable
  Vector2d actual_velocity = get_actual_direction(*p) * p->actual_v0;

  double tau_inv = 1 / TAU;

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

// $\vectorarrow{f}_{\alpha \beta}(\vectorarrow{r}_{\alpha \beta}) = -\gradient_{\vectorarrow{r}_{\alpha \beta}} V_{\alpha \beta}[b(\vectorarrow{r}_{\alpha \beta})]$
void compute_repulsive_effects_from_pedestrians(Pedestrian *P, Pedestrian *p, int N)
{
  double delta_t = 0.5; // assuming 0.5 seconds steps
  for (int i = 0; i < N; i++)
  {
    // TODO: add check for $\vectorarrow{e} * \vectorarrow{f} >= \Arrowvert \vectorarrow{f} \Arrowvert \cos(\phi) $
    // only consider close pedestrians
    if (P + i == p)
      continue;
    if ((P[i].curr_pos - p->curr_pos).norm() < DISTANCE)
    {
      //
      // $2b = \sqrt{(\Arrowvert \vectorarrow{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vectorarrow{r}_{\alpha \beta} - v_\beta \Delta t \vectorarrow{e}_\beta \Arrowvert)^2 - (v_\beta \Delta t)^2}$
      //
      // $\Arrowvert \vectorarrow{r}_{\alpha \beta} \Arrowvert$
      Vector2d r_ab = p->curr_pos - P[i].curr_pos;
      double r_ab_norm = (p->curr_pos - P[i].curr_pos).norm();

      // $\Arrowvert \vectorarrow{r}_{\alpha \beta} - v_\beta \Delta t \vectorarrow{e}_\beta \Arrowvert$
      Vector2d e_beta = get_actual_direction(P[i]);
      Vector2d r_ab_something = p->curr_pos - P[i].curr_pos - (e_beta * (P[i].actual_v0 * delta_t));
      double r_ab_something_norm = (p->curr_pos - P[i].curr_pos - (e_beta * (P[i].actual_v0 * delta_t))).norm();

      // $v_\beta \Delta t$
      double v_beta_delta_t = P[i].actual_v0 * delta_t;

      double b = sqrt((r_ab_norm + r_ab_something_norm) * (r_ab_norm + r_ab_something_norm) - (v_beta_delta_t) * (v_beta_delta_t)) / 2;

      //
      // $\vectorarrow{f}_{\alpha \beta}(\vectorarrow{r}_{\alpha \beta}) = \frac{V^0_{\alpha \beta}}{\sigma}e^{-b / \sigma} \grad_{\vectorarrow{r}_{\alpha \beta}}b$
      //
      // TODO: what is $V^0_{\alpha \beta}$ probably some number?
      //
      //
      // $\grad_{\vectorarrow{r}_{\alpha \beta}} = \frac{(\Arrowvert \vectorarrow{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vectorarrow{r}_{\alpha \beta} - v_\beta \Delta t \vectorarrow{e}_\beta \Arrowvert) (\frac{\vectorarrow{r}_{\alpha \beta}}{\Arrowvert \vectorarrow{r}_{\alpha \beta} \Arrowvert} + \frac{\vectorarrow{r}_{\alpha \beta} - v_\beta \Delta t \vectorarrow{e}_\beta}{\Arrowvert \vectorarrow{r}_{\alpha \beta} - v_\beta \Delta t \vectorarrow{e}_\beta \Arrowvert})}{4b}$
      //
      Vector2d delta_r_alpha_beta = (((r_ab / r_ab_norm) + (r_ab_something / r_ab_something_norm)) * (r_ab_norm + r_ab_something_norm)) / (4 * b);

      // $\vectorarrow{f}_{\alpha \beta}$
      Vector2d f_alpha_beta_r_alpha_beta = delta_r_alpha_beta * ((V0_AB / SIGMA) * (exp(-b / SIGMA)));

      p->F_i += f_alpha_beta_r_alpha_beta * w(get_desired_direction(*p), f_alpha_beta_r_alpha_beta * -1);
    }
  }
}

// TODO: missing
void compute_repulsive_effects_from_borders(Sidewalk &S, Pedestrian *p)
{

  Vector2d *obstacles = S.obstacles;
  int n_obs = S.n_obstacles;

  for (int i = 0; i < n_obs; i++)
  {
    Vector2d obstacle = obstacles[i];
    // TODO: find out the variables and parameters
    //
    // $\vectorarrow{F}_{\alpha B}(\vectorarrow{r}_{\alpha B}) = \frac{U^0_{\alpha B}}{R} e^{- \Arrowvert \vectorarrow{r}_{\alpha B} \Arrowvert / R} \frac{\vectorarrow{r}_{\alpha B}}{\Arrowvert \vectorarrow{r}_{\alpha B} \Arrowvert}$
    //
    // double e = 2.718;
    // we could just use exp

    // $\vectorarrow{r}_{\alpha B}$
    Vector2d r_ab = p->curr_pos - obstacle;
    // $\Arrowvert \vectorarrow{r}_{\alpha B} \Arrowvert$
    double r_ab_norm = r_ab.norm();
    if (r_ab_norm < 1e-6)
      continue;
    // repulsive force vector (Direction * Magnitude) (Edquation 6)
    Vector2d f_ab = (r_ab / r_ab_norm) * (U0_AB / R) * exp(-r_ab_norm / R);
    p->F_i += f_ab * w(get_desired_direction(*p), f_ab * -1);
  }
}