





"""simple docstring"""



from __future__ import annotations

from scipy.special import comb  # type: ignore






class 		__snake_case					:





 """simple docstring"""


 def __init__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     __A    :						Dict						 =     list_of_points
     # Degree determines the flexibility of the curve.
     # Degree = 1 will produce a straight line.
     __A    :						List[str]						 =     len(__lowerCamelCase  ) - 1

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     assert 0 <= t <= 1, "Time t must be between 0 and 1."
     __A    :						list[float]						 =     []
     for i in range(len(self.list_of_points  )  ):
         # basis function for each i
         output_values.append(
             comb(self.degree					,						__lowerCamelCase  ) * ((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(__lowerCamelCase  )					,						5  ) == 1
     return output_values

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




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

     __A    :						List[Any]						 =     self.basis_function(__lowerCamelCase  )
     __A    :						Tuple						 =     0.0
     __A    :						Union[str, Any]						 =     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 					UpperCamelCase__(    self					,						__lowerCamelCase = 0.0_1  ):



     '''simple docstring'''




     from matplotlib import pyplot as plt  # type: ignore

     __A    :						list[float]						 =     []  # x coordinates of points to plot
     __A    :						list[float]						 =     []  # y coordinates of points to plot

     __A    :						int						 =     0.0
     while t <= 1:
         __A    :						List[str]						 =     self.bezier_curve_function(__lowerCamelCase  )
         to_plot_x.append(value[0]  )
         to_plot_y.append(value[1]  )
         t += step_size

     __A    :						List[Any]						 =     [i[0] for i in self.list_of_points]
     __A    :						Union[str, Any]						 =     [i[1] for i in self.list_of_points]

     plt.plot(
         __lowerCamelCase					,						__lowerCamelCase					,						color='''blue'''					,						label='''Curve of Degree ''' + str(self.degree  )					,						)
     plt.scatter(__lowerCamelCase					,						__lowerCamelCase					,						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











"""simple docstring"""



def 		__lowercase     (   snake_case_  :  int						)   ->int:



    '''simple docstring'''







    assert (
        isinstance(snake_case_				,snake_case_						) and number_of_steps > 0
    ), F"""number_of_steps needs to be positive integer, your input {number_of_steps}"""
    if number_of_steps == 1:
        return 1
    __A ,       __A    :						List[Any]						 =     1, 1
    for _ in range(number_of_steps - 1						):
        __A ,       __A    :						List[str]						 =     current + previous, current
    return current


if __name__ == "__main__":
       import doctest

       doctest.testmod()




