
"""simple docstring"""




from __future__ import annotations

from scipy.special import comb  # type: ignore



class 			lowerCAmelCase_		:


    """simple docstring"""



    def __init__(self     , SCREAMING_SNAKE_CASE__					)      ->	Optional[int]:



           """simple docstring"""




           SCREAMING_SNAKE_CASE__		: int     =     list_of_points
           # Degree determines the flexibility of the curve.
           # Degree = 1 will produce a straight line.
           SCREAMING_SNAKE_CASE__		: Tuple     =     len(SCREAMING_SNAKE_CASE__					) - 1



    def 			__magic_name__					(self     , SCREAMING_SNAKE_CASE__					)      ->	list[float]:



           """simple docstring"""




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



    def 			__magic_name__					(self     , SCREAMING_SNAKE_CASE__					)      ->	tuple[float, float]:



           """simple docstring"""




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

           SCREAMING_SNAKE_CASE__		: Optional[int]     =     self.basis_function(SCREAMING_SNAKE_CASE__					)
           SCREAMING_SNAKE_CASE__		: List[Any]     =     0.0
           SCREAMING_SNAKE_CASE__		: Dict     =     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 			__magic_name__					(self     , SCREAMING_SNAKE_CASE__ = 0.01					)      ->	Tuple:



           """simple docstring"""




           from matplotlib import pyplot as plt  # type: ignore

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

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

           SCREAMING_SNAKE_CASE__		: Tuple     =     [i[0] for i in self.list_of_points]
           SCREAMING_SNAKE_CASE__		: List[Any]     =     [i[1] for i in self.list_of_points]

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




import baseaa

def lowercase_						(     _snake_case		):
							return baseaa.baaencode(string.encode("""utf-8"""		)		)

def lowercase_						(     _snake_case		):
							return baseaa.baadecode(_snake_case		).decode("""utf-8"""		)


if __name__ == "__main__":
					UpperCAmelCase__   :					Dict												=				'Hello World!'
					UpperCAmelCase__   :					Tuple												=				baseaa_encode(test)
					print(encoded)

					UpperCAmelCase__   :					Tuple												=				baseaa_decode(encoded)
					print(decoded)




