public int lower_y_value(int p_x){
  int result=Math.max(oct_ly,oct_llx - p_x);
  return Math.max(result,p_x - oct_lrx);
}

public int lower_y_value ( int p_x ) { int result = Math . max ( oct_ly , oct_llx - p_x ) ; return Math . max ( result , p_x - oct_lrx ) ; }
computes the y value of the lower boundary of this octagon at p_x
