push x y with spline.cpp

// define the (x,y) points we will use for the planner
vector<double> next_x_vals;
vector<double> next_y_vals;
// start with previous path points from above
for (int i = 0; i < prev_size; i++)
{
  next_x_vals.push_back(previous_path_x[i]);
  next_y_vals.push_back(previous_path_y[i]);
}
// calculate how to break up spline points to travel at desired reference velocity
double target_x = 30.0;
double target_y = s(target_x);
double target_dist = sqrt(target_x * target_x + target_y * target_y);
double x_add_on = 0;
// fill up the rest of path planner after filling with previous points
for (int i = 1; i < 50 — prev_size; i++) // 50 points
{
  // ramp up speed
  ref_vel += speed_diff;
  if (ref_vel > max_vel) // until hitting limit
  {
    ref_vel = max_vel; // then hold
  }
  else if (ref_vel < max_acl) // if hitting max acceleration
  {
    ref_vel = max_acl; // keep at max acceleration
  }
  double N = target_dist / (0.02 * ref_vel / 2.24);
  double x_point = x_add_on + target_x / N;
  double y_point = s(x_point);
  x_add_on = x_point;
  double x_ref = x_point;
  double y_ref = y_point;
  // now rotate BACK to normal
  x_point = x_ref * cos(ref_yaw) — y_ref * sin(ref_yaw);
  y_point = x_ref * sin(ref_yaw) + y_ref * cos(ref_yaw);
  x_point += ref_x;
  y_point += ref_y;
  next_x_vals.push_back(x_point);
  next_y_vals.push_back(y_point);
}