text: """Computational processing related to image processing."""
  
  from typing import Tuple
  
  
  def _calc_internally(p1: float, p2: float, ratio: Tuple[float, float]) -> float:
      """Calculate the point that divides internally.
  
      Args:
          p1 (float): point 1
          p2 (float): point 2
          ratio (float): ratio of division
  
      Returns:
          float: divided point
      """
      num_ratio = ratio[0] / (ratio[0] + ratio[1])
      assert 0 <= num_ratio <= 1
      if p1 < p2:
          dist = p2 - p1
          return p1 + dist * num_ratio
      else:
          dist = p1 - p2
          return p1 - dist * num_ratio
  
  
  def divide_internally(p1: Tuple[int, int], p2: Tuple[int, int], ratio: Tuple[float, float]) -> Tuple[int, int]:
      """Obtain internally division point.
  
      obtain the point that divides internally
  
      Args:
          p1 (Tuple[int, int]): point 1
          p2 (Tuple[int, int]): point 2
          ratio (float): ratio of division
  
      Returns:
          Tuple[int, int]: divided point
  
      """
      x = _calc_internally(p1[0], p2[0], ratio)
      y = _calc_internally(p1[1], p2[1], ratio)
  
      return (int(x), int(y))
  
  
  def _calc_externally(p1: float, p2: float, ratio: Tuple[float, float]) -> float:
      """Calculate the point that divides externally.
  
      Args:
          p1 (float): point 1
          p2 (float): point 2
          ratio (float): rate of division
  
      Returns:
          float: divided point
      """
      if ratio[0] >= ratio[1]:
          num_ratio = ratio[0] / (ratio[0] - ratio[1])
          assert num_ratio >= 1
          if p1 < p2:
              dist = p2 - p1
              return p1 + dist * num_ratio
          else:
              dist = p1 - p2
              return p2 + dist * num_ratio
      else:
          num_ratio = ratio[1] / (ratio[1] - ratio[0])
          assert num_ratio >= 1
          if p1 < p2:
              dist = p2 - p1
              return p1 + dist * num_ratio
          else:
              dist = p1 - p2
              return p2 + dist * num_ratio
  
  
  def divide_externally(p1: Tuple[int, int], p2: Tuple[int, int], ratio: Tuple[float, float]) -> Tuple[int, int]:
      """Obtain externally division point.
  
      obtain the point that divides internally
  
      Args:
          p1 (Tuple[int, int]): point 1
          p2 (Tuple[int, int]): point 2
          ratio (float): ratio of division
  
      Returns:
          Tuple[int, int]: divided point
  
      """
      x = _calc_externally(p1[0], p2[0], ratio)
      y = _calc_externally(p1[1], p2[1], ratio)
  
      return (int(x), int(y))
  