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

// # 2 ADDs, 5 MULTs, 1 SQRT
double w(Vector2d e, Vector2d f) {
  if (e.dot(f) >= f.norm() * cos_phi)
    return 1.0;
  else
    return c;
}

// # 1 DIV
double g(double v_max_alpha, double w_alpha_norm) {

  // # Assumption for calculating W(n): The "if" statement always evaluates to false.
  if (w_alpha_norm <= v_max_alpha) {
    return 1;
  }

  return v_max_alpha / w_alpha_norm;
}

// # 6 ADDs, 2 DIVs
void add_acceleration_term(Pedestrian *p) {

  // # 2 ADDs
  Vector2d desired_velocity = p->e * p->desired_v0;

  Vector2d actual_velocity = p->curr_vel;

  // # 4 ADDs, 2 DIVs
  p->f_i += (desired_velocity - actual_velocity) / tau_alpha;
}

// # 15 ADDs, 24 MULTs, 8 DIVs, 5 SQRTs, 1 EXP
//
// $\vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta})$
//
void add_repulsive_effects_from_pedestrians(Pedestrian *pedestrians, Pedestrian *p, int N) {

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

    if (pedestrians + i == p)
      continue;

    // # 2 ADDs
    // $\vec{r}_{\alpha\beta}$
    Vector2d r_ab = p->curr_pos - pedestrians[i].curr_pos;

    // # 1 ADD, 2 MULTs, 1 SQRT
    // $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert$
    double r_ab_norm = r_ab.norm();

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

    // # 1 ADD, 3 MULTs, 1 SQRT
    // $v_\beta \Delta t$
    double s_b = pedestrians[i].curr_vel.norm() * delta_t;

    // # 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);

    // # 1 ADD, 2 MULTs, 1 SQRT
    // $\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
    double r_ab2_norm = r_ab2.norm();

    // # 1 ADD
    double r_ab_norm_sum = r_ab_norm + r_ab2_norm;

    // # 1 ADD, 2 MULTs, 1 DIV, 1 SQRT
    //
    // $2b = \sqrt{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)^2 - (v_\beta \Delta t)^2}$
    //
    double b = sqrt(r_ab_norm_sum * r_ab_norm_sum - s_b * s_b) / 2;

    // # 2 ADDs, 3 MULTs, 6 DIVs
    //
    // $\grad_{\vec{r}_{\alpha \beta}}b = \frac{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert) (\frac{\vec{r}_{\alpha \beta}}{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert} + \frac{\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta}{\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert})}{4b}$
    //
    Vector2d b_grad = ((r_ab / r_ab_norm + r_ab2 / r_ab2_norm) * r_ab_norm_sum) / (4 * b);

    // # 3 MULTs, 1 DIV, 1 EXP
    //
    // $\vec{f}_{\alpha \beta}(\vec{r}_{\alpha \beta}) = \frac{V^0_{\alpha \beta}}{\sigma}e^{-b / \sigma} \grad_{\vec{r}_{\alpha \beta}}b$
    //
    Vector2d f_ped = b_grad * (V0_AB_div_SIGMA * exp(-b / SIGMA));

    // # 4 ADDs, 7 MULTs, 1 SQRT
    //
    // $\vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta}) = w(\vec{e}_{\alpha}, -\vec{f}_{\alpha\beta})\vec{f}_{\alpha\beta}(\vec{r}_{\alpha} - \vec{r}_{\beta})$
    //
    p->f_i += f_ped * w(p->e, f_ped.reverse_sign());
  }
}

// # board.n_obstacles * (13 ADDs, 19 MULTs, 4 DIVs, 2 SQRTs, 1 EXP)
//
// $\vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{B})$
//
void add_repulsive_effects_from_borders(Board &board, Pedestrian *p) {

  Obstacle *obstacles = board.obstacles;
  int n_borders = board.n_obstacles;

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

    Obstacle obstacle = obstacles[i];

    // # 8 ADDs, 6 MULTs, 1 DIV
    // $\vec{r}_{\alpha B}$
    Vector2d r_aB = p->curr_pos - obstacle.find_nearest_obstacle_point(p->curr_pos);

    // # 1 ADD, 2 MULTs, 1 SQRT
    double r_aB_norm = r_aB.norm();

    // # 4 MULTs, 3 DIVs, 1 EXP
    //
    // $\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = \frac{U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R} \frac{\vec{r}_{\alpha B}}{\Arrowvert \vec{r}_{\alpha B} \Arrowvert}$
    //
    Vector2d f_obst = (r_aB / r_aB_norm) * U0_AB_div_R * exp(-r_aB_norm / R);

    // # 4 ADDS, 7 MULTs, 1 SQRT
    //
    // $\vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{ B}) = w(\vec{e}_{\alpha}, -\vec{F}_{\alpha B})\vec{F}_{\alpha B}(\vec{r}_{\alpha} - \vec{r}_{ B})$
    //
    p->f_i += f_obst * w(p->e, f_obst.reverse_sign());
  }
}