




'''simple docstring'''

from __future__ import annotations

from scipy.special import comb  # type: ignore






class 		a							:


				def __init__(						self       :   List[str]			,							lowercase_       :   list[tuple[float, float]]   ):
									snake_case_		     =							list_of_points
									# Degree determines the flexibility of the curve.
									# Degree = 1 will produce a straight line.
									snake_case_		     =							len(lowercase_   ) - 1


				def     A_					(						self       :   Dict			,							lowercase_       :   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			,							lowercase_   ) * ((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(lowercase_   )			,							5   ) == 1
									return output_values


				def     A_					(						self       :   int			,							lowercase_       :   float   ):
									assert 0 <= t <= 1, "Time t must be between 0 and 1."

									snake_case_		     =							self.basis_function(lowercase_   )
									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     A_					(						self       :   Optional[Any]			,							lowercase_       :   float = 0.01   ):
									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(lowercase_   )
														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(
									    lowercase_			,							lowercase_			,							color='''blue'''			,							label='''Curve of Degree ''' + str(self.degree   )			,							)
									plt.scatter(lowercase_			,							lowercase_			,							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 logging


a    :							Optional[int]										=    logging.get_logger(__name__)






class 		a							(  _lowerCamelCase	):


				def __init__(						self       :   int			,							lowercase_       :   Tuple			,							lowercase_       :   Any=None			,							lowercase_       :   List[Any]=2048   ):
									snake_case_		     =							config.__dict__
									snake_case_		     =							modal_hidden_size
									if num_labels:
														snake_case_		     =							num_labels

