




from __future__ import annotations

from scipy.special import comb  # type: ignore







class   A:



 '''simple docstring'''


 def __init__(    self :  Optional[int]						,							A_ :  list[tuple[float, float]]  )       ->     Optional[int]:

       """simple docstring"""






       lowerCamelCase_							=   list_of_points
       # Degree determines the flexibility of the curve.
       # Degree = 1 will produce a straight line.
       lowerCamelCase_							=   len(A_  ) - 1

 def     a__			(    self :  int						,							A_ :  float  )       ->     list[float]:

       """simple docstring"""






       assert 0 <= t <= 1, "Time t must be between 0 and 1."
       lowerCamelCase_							=   []
       for i in range(len(self.list_of_points  )  ):
             # basis function for each i
             output_values.append(
                 comb(self.degree						,							A_  ) * ((1 - t) ** (self.degree - i)) * (t**i)  )
       # the basis must sum up to 1 for it to produce a valid Bezier curve.
       assert round(sum(A_  )						,							5  ) == 1
       return output_values

 def     a__			(    self :  Any						,							A_ :  float  )       ->     tuple[float, float]:

       """simple docstring"""






       assert 0 <= t <= 1, "Time t must be between 0 and 1."

       lowerCamelCase_							=   self.basis_function(A_  )
       lowerCamelCase_							=   0.0
       lowerCamelCase_							=   0.0
       for i in range(len(self.list_of_points  )  ):
             # For all points, sum up the product of i-th basis function and i-th point.
             x += basis_function[i] * self.list_of_points[i][0]
             y += basis_function[i] * self.list_of_points[i][1]
       return (x, y)





 def     a__			(    self :  int						,							A_ :  float = 0.01  )       ->     Any:

       """simple docstring"""






       from matplotlib import pyplot as plt  # type: ignore

       lowerCamelCase_							=   []  # x coordinates of points to plot
       lowerCamelCase_							=   []  # y coordinates of points to plot

       lowerCamelCase_							=   0.0
       while t <= 1:
             lowerCamelCase_							=   self.bezier_curve_function(A_  )
             to_plot_x.append(value[0]  )
             to_plot_y.append(value[1]  )
             t += step_size

       lowerCamelCase_							=   [i[0] for i in self.list_of_points]
       lowerCamelCase_							=   [i[1] for i in self.list_of_points]

       plt.plot(
           A_						,							A_						,							color='blue'						,							label='Curve of Degree ' + str(self.degree  )						,							)
       plt.scatter(A_						,							A_						,							color='red'						,							label='Control Points'  )
       plt.legend()
       plt.show()


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
  BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
  BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3









def       _SCREAMING_SNAKE_CASE      (							lowercase     :	Tuple     ,							lowercase     :	Dict     ,							lowercase     :	List[str]     ,							lowercase     :	Dict     ,							lowercase     :	Dict     ,							lowercase     :	List[str]					):


      '''simple docstring'''



      if index == r:
            for j in range(lowercase					):
                  print(data[j]     ,							end=' '					)
            print(' '					)
            return
      #  When no more elements are there to put in data[]
      if i >= n:
            return
      # current is included, put next at next location
      lowerCamelCase_							=   arr[i]
      combination_util(lowercase     ,							lowercase     ,							lowercase     ,							index + 1     ,							lowercase     ,							i + 1					)
      # current is excluded, replace it with
      # next (Note that i+1 is passed, but
      # index is not changed)
      combination_util(lowercase     ,							lowercase     ,							lowercase     ,							lowercase     ,							lowercase     ,							i + 1					)
      # The main function that prints all combinations
      # of size r in arr[] of size n. This function
      # mainly uses combinationUtil()

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	int     ,							lowercase     :	Any     ,							lowercase     :	Tuple					):


      '''simple docstring'''



      lowerCamelCase_							=   [0] * r
      # Print all combination using temporary array 'data[]'
      combination_util(lowercase     ,							lowercase     ,							lowercase     ,							0     ,							lowercase     ,							0					)


if __name__ == "__main__":
 # Driver code to check the function above
 lowerCamelCase    :		int			   =       [10, 20, 30, 40, 50]
 print_combination(arr, len(arr), 3)
 # This code is contributed by Ambuj sahu



