


'''simple docstring'''



from __future__ import annotations

from scipy.special import comb  # type: ignore






class  UpperCamelCase__:




				def __init__(	self    :				Union[str, Any]   ,					lowerCAmelCase    :				list[tuple[float, float]]   )->  Any:

										"""simple docstring"""




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




				def   a__(	self    :				str   ,					lowerCAmelCase    :				float   )->  list[float]:

										"""simple docstring"""




										assert 0 <= t <= 1, "Time t must be between 0 and 1."
										UpperCAmelCase         =			[]
										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   a__(	self    :				Union[str, Any]   ,					lowerCAmelCase    :				float   )->  tuple[float, float]:

										"""simple docstring"""




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

										UpperCAmelCase         =			self.basis_function(lowerCAmelCase   )
										UpperCAmelCase         =			0.0
										UpperCAmelCase         =			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    :				List[str]   ,					lowerCAmelCase    :				float = 0.01   )->  Any:

										"""simple docstring"""




										from matplotlib import pyplot as plt  # type: ignore

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

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

										UpperCAmelCase         =			[i[0] for i in self.list_of_points]
										UpperCAmelCase         =			[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'''



from ..utils import DummyObject, requires_backends






class  UpperCamelCase__(     metaclass=lowerCAmelCase ):
				__magic_name__       :   List[str]							= ["note_seq"]




				def __init__(	self    :				Any   ,					*lowerCAmelCase    :				List[str]   ,					**lowerCAmelCase    :				int   )->  Optional[int]:

										"""simple docstring"""




										requires_backends(self   ,					['''note_seq''']   )




				@classmethod
				def   a__(	cls    :				Dict   ,					*lowerCAmelCase    :				int   ,					**lowerCAmelCase    :				Optional[int]   )->  Dict:

										"""simple docstring"""




										requires_backends(cls   ,					['''note_seq''']   )





				@classmethod
				def   a__(	cls    :				int   ,					*lowerCAmelCase    :				Tuple   ,					**lowerCAmelCase    :				Optional[Any]   )->  Union[str, Any]:

										"""simple docstring"""




										requires_backends(cls   ,					['''note_seq''']   )





