#include "forces.hpp"
#include "constants.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 DT;
  else
    return C_TIMES_DT;
}

// # 4 ADDs, 4 MULTs
void add_acceleration_term(Pedestrian *p) {

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

  Vector2d actual_velocity = p->curr_vel;

  // # 4 ADDs, 2 MULTs
  p->f_i += (desired_velocity - actual_velocity) * DT_TIMES_TAU_ALPHA_INV;
}

// # (N - 1) * (14 ADDs, 23 MULTs, 1 DIV, 4 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();

    // # 2 ADDs
    // $\vec{r}_{\alpha\beta} - \vec{v}_{\beta}\varDelta_{t}\vec{e}_{\beta}$
    Vector2d r_ab2 = r_ab - pedestrians[i].s_b_e_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
    // $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
    double r_ab_norm_sum = r_ab_norm + r_ab2_norm;

    // # 1 ADD, 1 MULT, 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 two_b = sqrt(r_ab_norm_sum * r_ab_norm_sum - pedestrians[i].s_b_sq);

    // # 3 MULTs, 1 DIV
    //
    // $\frac{-V^0_{\alpha\beta}}{\sigma} \frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b \Arrowvert \vec{r}_{\alpha \beta} \Arrowvert \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}$
    //
    double common_factor = NEG_V0_AB_DIV_TWO_SIGMA * r_ab_norm_sum / (two_b * r_ab_norm * r_ab2_norm);

    // # 2 ADDs, 4 MULTs
    // $2\grad_{\vec{r}_{\alpha \beta}}b$
    // See: derivations.jpg
    Vector2d A = (r_ab * r_ab2_norm + r_ab2 * r_ab_norm) * common_factor;

    // # 4 MULTs, 1 EXP
    //   $-\vec{f}_{\alpha \beta}(\vec{r}_{\alpha \beta})$
    //
    // $= \frac{-V^0_{\alpha \beta}}{\sigma}e^{-b / \sigma} \grad_{\vec{r}_{\alpha \beta}}b$
    //
    //
    // $= \frac{-V^0_{\alpha \beta}}{2\sigma}e^{-b / \sigma} 2\grad_{\vec{r}_{\alpha \beta}}b$
    //
    Vector2d neg_f_ped = A * exp(two_b * NEG_ONE_DIV_TWO_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 -= neg_f_ped * w(p->e, neg_f_ped);
  }
}

// # board.n_obstacles * (12 ADDs, 18 MULTs, 1 DIV, 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];

    // # 7 ADDs, 5 MULTs
    // $\vec{r}_{\alpha B}$
    Vector2d r_aB = p->curr_pos - obstacle.find_nearest_obstacle_point(p->curr_pos);

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

    // # 4 MULTs, 1 DIV, 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 neg_f_obst = r_aB * (NEG_U0_AB_DIV_R * exp(r_aB_norm * NEG_R_INV) / r_aB_norm);

    // # 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 -= neg_f_obst * w(p->e, neg_f_obst);
  }
}