determine the best approach path based on where the plane/last waypoint is

[Pomax]

// quarter turn
double Q4 = PI/2;

// some random airport orientation
double randomAngle = random(0, TAU);

// distance from approach point to offset point
double R = 50;

// distance from offset point to secondary offset
// (to force the plane to fly towards the offset)
double R2 = R + 10;

Point end, start, M = new Point(0,0), anchor, o1, o2;

void determineCriticalPoints(int x, int y) {
  Point cursor = new Point(x, y);

  double ca = cos(randomAngle);
  double sa = sin(randomAngle);

  // even though M is (0,0), it won't be in the game.
  double mx = M.x;
  double my = M.y;

  start = new Point(mx - 150 * ca, my - 150 * sa);
  end = new Point(mx - 200 * ca, my - 200 * sa);
  anchor = new Point(mx + 150 * ca, my + 150 * sa);
  o1 = null;
  o2 = null;

  double ax = anchor.x;
  double ay = anchor.y;

  double v1 = M.x - ax;
  double v2 = M.y - ay;

  double w1 = cursor.x - ax;
  double w2 = cursor.y - ay;

  double r = randomAngle;
  double a = atan2(w2*v1 - w1*v2, w1*v1 + w2*v2);

  Point p = cursor.project(M, anchor);
  double d = dist(p, cursor);

  if (a > Q4 || a < -Q4) {
    o1 = new Point(ax + R * cos(r), ay + R * sin(r));
  } else {
    if (a > 0) {
      r -= Q4;
      double cr = cos(r);
      double sr = sin(r);
      o1 = new Point(ax + R * cr, ay + R * sr);
      if (d < 50) o2 = new Point(ax + R2 * cr, ay + R2 * sr);
    } else {
      r += Q4;
      double cr = cos(r);
      double sr = sin(r);
      o1 = new Point(ax + R * cr, ay + R * sr);
      if (d < 50) o2 = new Point(ax + R2 * cr, ay + R2 * sr);
    }
  }
}

[Pomax]

[Pomax]

added