





'''simple docstring'''







from __future__ import annotations

from scipy.special import comb  # type: ignore
class 			_lowercase						:







     def __init__( self    ,   A__    ) ->	List[Any]:
      snake_case				=			list_of_points
      # Degree determines the flexibility of the curve.
      # Degree = 1 will produce a straight line.
      snake_case				=			len(A__    ) - 1







     def     UpperCamelCase			( self    ,   A__    ) ->	list[float]:
      assert 0 <= t <= 1, "Time t must be between 0 and 1."
      snake_case				=			[]
      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     UpperCamelCase			( self    ,   A__    ) ->	tuple[float, float]:
      assert 0 <= t <= 1, "Time t must be between 0 and 1."

      snake_case				=			self.basis_function(A__    )
      snake_case				=			0.0
      snake_case				=			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    ,   A__ = 0.0_1    ) ->	str:
      from matplotlib import pyplot as plt  # type: ignore

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

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

      snake_case				=			[i[0] for i in self.list_of_points]
      snake_case				=			[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








'''simple docstring'''







from ..utils import DummyObject, requires_backends
class 			_lowercase						(       metaclass=__a					):
     _UpperCAmelCase										=					['''transformers''', '''torch''', '''note_seq''']







     def __init__( self    ,   *A__    ,   **A__    ) ->	Union[str, Any]:
      requires_backends(self    ,   ['''transformers''', '''torch''', '''note_seq''']    )







     @classmethod
     def     UpperCamelCase			( cls    ,   *A__    ,   **A__    ) ->	Optional[Any]:
      requires_backends(cls    ,   ['''transformers''', '''torch''', '''note_seq''']    )







     @classmethod
     def     UpperCamelCase			( cls    ,   *A__    ,   **A__    ) ->	Any:
      requires_backends(cls    ,   ['''transformers''', '''torch''', '''note_seq''']    )

