class Circle
  def initialize(radius)
    @radius = radius
  end

  def draw
    unless @canvas
      diameter = 2 * @radius
      @canvas = Array.new(diameter + 1){ ' ' * (2 * (diameter + 1)) }
      key_points.each do |kx, ky|
        [kx, diameter - kx].product([ky, diameter - ky]).each do |x, y|
          @canvas[x][2 * y] = @canvas[y][2 * x] = '*'
        end
      end
    end

    puts @canvas.join "\n"
  end

  private

  def key_points
    q = (1 - 0.5 * (2 ** 0.5)) * @radius # (1 - cos45) * radius
    [*q.floor..@radius].product([*0..q.ceil]).select{|x, y| lies_on_circle? x, y }
  end

  # Detects if point is closest to the circle edge by checking the devitaion of points above and below
  def lies_on_circle?(x, y)
    cx, cy = @radius, @radius # central point
    dx2, r2 = (x - cx) ** 2, @radius ** 2
    [y - 1, y, y + 1].min_by {|y| (dx2 + (y - cy) ** 2 - r2) ** 2 } == y
  end
end

Circle.new(ARGV[0].to_i).draw

# ruby circle.rb 7
#           * * * * *           
#       * *           * *       
#     *                   *     
#   *                       *   
#   *                       *   
# *                           * 
# *                           * 
# *                           * 
# *                           * 
# *                           * 
#   *                       *   
#   *                       *   
#     *                   *     
#       * *           * *       
#           * * * * *