



"""simple docstring"""





from __future__ import annotations

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



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


             '''simple docstring'''




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



       def 					lowercase__    (							self      :  Optional[Any]		,    _UpperCAmelCase      :  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		,    _UpperCAmelCase   ) * ((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(_UpperCAmelCase   )		,    5   ) == 1
             return output_values



       def 					lowercase__    (							self      :  Tuple		,    _UpperCAmelCase      :  float   )			->						tuple[float, float]:


             '''simple docstring'''




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

             UpperCAmelCase_      			=							self.basis_function(_UpperCAmelCase   )
             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 					lowercase__    (							self      :  int		,    _UpperCAmelCase      :  float = 0.01   )			->						str:


             '''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(_UpperCAmelCase   )
                   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(
                 _UpperCAmelCase		,    _UpperCAmelCase		,    color="blue"		,    label="Curve of Degree " + str(self.degree   )		,    )
             plt.scatter(_UpperCAmelCase		,    _UpperCAmelCase		,    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 .configuration_bert_masked import MaskedBertConfig
from .modeling_bert_masked import (
    MaskedBertForMultipleChoice,
    MaskedBertForQuestionAnswering,
    MaskedBertForSequenceClassification,
    MaskedBertForTokenClassification,
    MaskedBertModel,
)
from .modules import *




