




'''simple docstring'''






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
lowercase	:      str				=       20

# Time between time steps in seconds
lowercase	:      List[str]				=       INTERVAL / 1000

class   SCREAMING_SNAKE_CASE_		:



 def __init__(  self   ,		A   ,		A   ,		A   ,		A   ,		A = 1.0   ,		A = 1.0   ,		A = "blue"   ,		):






        '''simple docstring'''




        lowercase  :		Optional[int]						=      position_x
        lowercase  :		Union[str, Any]						=      position_y
        lowercase  :		List[str]						=      velocity_x
        lowercase  :		Optional[Any]						=      velocity_y
        lowercase  :		List[str]						=      mass
        lowercase  :		int						=      size
        lowercase  :		List[str]						=      color



 @property
 def    SCREAMING_SNAKE_CASE(  self ):






        '''simple docstring'''




        return self.position_x, self.position_y



 @property
 def    SCREAMING_SNAKE_CASE(  self ):






        '''simple docstring'''




        return self.velocity_x, self.velocity_y



 def    SCREAMING_SNAKE_CASE(  self   ,		A   ,		A   ,		A ):






        '''simple docstring'''




        self.velocity_x += force_x * delta_time
        self.velocity_y += force_y * delta_time





 def    SCREAMING_SNAKE_CASE(  self   ,		A ):






        '''simple docstring'''




        self.position_x += self.velocity_x * delta_time
        self.position_y += self.velocity_y * delta_time






class   SCREAMING_SNAKE_CASE_		:



 def __init__(  self   ,		A   ,		A = 1.0   ,		A = 1.0   ,		A = 0.0   ,		):






        '''simple docstring'''




        lowercase  :		str						=      bodies
        lowercase  :		Union[str, Any]						=      gravitation_constant
        lowercase  :		Tuple						=      time_factor
        lowercase  :		List[str]						=      softening_factor



 def __len__(  self ):






        '''simple docstring'''




        return len(self.bodies )





 def    SCREAMING_SNAKE_CASE(  self   ,		A ):






        '''simple docstring'''




        for bodya in self.bodies:
               lowercase  :		Any						=      0.0
               lowercase  :		List[Any]						=      0.0
               for bodya in self.bodies:
                      if bodya != bodya:
                             lowercase  :		Tuple						=      bodya.position_x - bodya.position_x
                             lowercase  :		Any						=      bodya.position_y - bodya.position_y

                             # Calculation of the distance using Pythagoras's theorem
                             # Extra factor due to the softening technique
                             lowercase  :		str						=      (dif_x**2 + dif_y**2 + self.softening_factor) ** (
                                 1 / 2
                             )

                             # Newton's law of universal gravitation.
                             force_x += (
                                 self.gravitation_constant * bodya.mass * dif_x / distance**3
                             )
                             force_y += (
                                 self.gravitation_constant * bodya.mass * dif_y / distance**3
                             )

            # Update the body's velocity once all the force components have been added
               bodya.update_velocity(A   ,		A   ,		delta_time * self.time_factor )

        # Update the positions only after all the velocities have been updated
        for body in self.bodies:
               body.update_position(delta_time * self.time_factor )






def 		a_( lowerCamelCase   ,				lowerCamelCase   ,				lowerCamelCase      )				->Tuple:






       '''simple docstring'''




       body_system.update_system(lowercase__      )

       # Update the positions of the patches
       for patch, body in zip(lowercase__   ,				body_system.bodies      ):
              lowercase  :		List[str]						=      (body.position_x, body.position_y)




def 		a_( lowerCamelCase   ,				lowerCamelCase   ,				lowerCamelCase = -1   ,				lowerCamelCase = 1   ,				lowerCamelCase = -1   ,				lowerCamelCase = 1   ,				)				->Dict:






       '''simple docstring'''




       lowercase  :		List[Any]						=      plt.figure()
       fig.canvas.set_window_title(lowercase__      )
       lowercase  :		Dict						=      plt.axes(
           xlim=(x_start, x_end)   ,				ylim=(y_start, y_end)      )  # Set section to be plotted
       plt.gca().set_aspect('''equal'''      )  # Fix aspect ratio

       # Each body is drawn as a patch by the plt-function
       lowercase  :		List[Any]						=      [
           plt.Circle((body.position_x, body.position_y)   ,				body.size   ,				fc=body.color      )
           for body in body_system.bodies
       ]

       for patch in patches:
              ax.add_patch(lowercase__      )

       # Function called at each step of the animation
       def update(lowerCamelCase      ) -> list[plt.Circle]:
              update_step(lowercase__   ,				lowercase__   ,				lowercase__      )
              return patches

       lowercase  :		Any						=      animation.FuncAnimation(  # noqa: F841
           lowercase__   ,				lowercase__   ,				interval=lowercase__   ,				blit=lowercase__      )

       plt.show()




def 		a_( )				->Optional[Any]:






       '''simple docstring'''




       lowercase  :		Optional[Any]						=      0.9_70_04_36
       lowercase  :		List[str]						=      -0.24_30_87_53
       lowercase  :		Optional[Any]						=      0.4_66_20_36_85
       lowercase  :		List[Any]						=      0.43_23_65_73

       lowercase  :		List[str]						=      [
           Body(lowercase__   ,				lowercase__   ,				lowercase__   ,				lowercase__   ,				size=0.2   ,				color='''red'''      ),
           Body(-position_x   ,				-position_y   ,				lowercase__   ,				lowercase__   ,				size=0.2   ,				color='''green'''      ),
           Body(0   ,				0   ,				-2 * velocity_x   ,				-2 * velocity_y   ,				size=0.2   ,				color='''blue'''      ),
       ]
       return BodySystem(lowercase__   ,				time_factor=3      )




def 		a_( )				->int:






       '''simple docstring'''




       lowercase  :		int						=      7.3476E22
       lowercase  :		str						=      5.972E24
       lowercase  :		Any						=      1022
       lowercase  :		List[str]						=      3_8439_9000
       lowercase  :		Tuple						=      6.674E-11

       # Calculation of the respective velocities so that total impulse is zero,
       # i.e. the two bodies together don't move
       lowercase  :		Any						=      earth_mass * velocity_dif / (earth_mass + moon_mass)
       lowercase  :		Dict						=      moon_velocity - velocity_dif

       lowercase  :		Tuple						=      Body(-earth_moon_distance   ,				0   ,				0   ,				lowercase__   ,				lowercase__   ,				1000_0000   ,				'''grey'''      )
       lowercase  :		int						=      Body(0   ,				0   ,				0   ,				lowercase__   ,				lowercase__   ,				5000_0000   ,				'''blue'''      )
       return BodySystem([earth, moon]   ,				lowercase__   ,				time_factor=100_0000      )




def 		a_( )				->Dict:






       '''simple docstring'''




       lowercase  :		int						=      []
       for _ in range(10      ):
              lowercase  :		List[str]						=      random.uniform(-0.5   ,				0.5      )
              lowercase  :		Union[str, Any]						=      random.uniform(-0.5   ,				0.5      )

              # Bodies are created pairwise with opposite velocities so that the
              # total impulse remains zero
              bodies.append(
                  Body(
                      random.uniform(-0.5   ,				0.5      )   ,				random.uniform(-0.5   ,				0.5      )   ,				lowercase__   ,				lowercase__   ,				size=0.05   ,				)      )
              bodies.append(
                  Body(
                      random.uniform(-0.5   ,				0.5      )   ,				random.uniform(-0.5   ,				0.5      )   ,				-velocity_x   ,				-velocity_y   ,				size=0.05   ,				)      )
       return BodySystem(lowercase__   ,				0.01   ,				10   ,				0.1      )


if __name__ == "__main__":
      plot('''Figure-8 solution to the 3-body-problem''', example_a(), -2, 2, -2, 2)
      plot(
          '''Moon\'s orbit around the earth''',
          example_a(),
          -430000000,
          430000000,
          -430000000,
          430000000,
      )
      plot('''Random system with many bodies''', example_a(), -1.5, 1.5, -1.5, 1.5)











'''simple docstring'''






import numpy as np
from PIL import Image




def 		a_( lowerCamelCase      )				->np.array:






       '''simple docstring'''




       lowercase,     lowercase,     lowercase  :		Union[str, Any]						=      rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
       return 0.29_89 * r + 0.58_70 * g + 0.11_40 * b




def 		a_( lowerCamelCase      )				->np.array:






       '''simple docstring'''




       return (gray > 127) & (gray <= 255)




def 		a_( lowerCamelCase   ,				lowerCamelCase      )				->np.array:






       '''simple docstring'''




       lowercase  :		Optional[Any]						=      np.zeros_like(lowerCamelCase      )
       lowercase  :		Any						=      np.zeros(
           (image.shape[0] + kernel.shape[0] - 1, image.shape[1] + kernel.shape[1] - 1)      )

       # Copy image to padded image
       lowercase  :		List[str]						=      image

       # Iterate over image & apply kernel
       for x in range(image.shape[1]      ):
              for y in range(image.shape[0]      ):
                     lowercase  :		Union[str, Any]						=      (
                         kernel * image_padded[y : y + kernel.shape[0], x : x + kernel.shape[1]]
                     ).sum()
                     lowercase  :		Any						=      int(summation == 5      )
       return output


# kernel to be applied
lowercase	:      List[Any]				=       np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])

if __name__ == "__main__":
      # read original image
      lowercase	:      Dict				=       np.array(Image.open(r'''..\image_data\lena.jpg'''))
      # Apply erosion operation to a binary image
      lowercase	:      List[str]				=       erosion(grayabinary(rgbagray(image)), structuring_element)
      # Save the output image
      lowercase	:      Optional[Any]				=       Image.fromarray(output).convert('''RGB''')
      pil_img.save('''result_erosion.png''')




