






'''simple docstring'''



from __future__ import annotations

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




      def __init__(  self ,   lowerCamelCase      )							->List[Any]:



         '''simple docstring'''
         __a				     =    list_of_points
         # Degree determines the flexibility of the curve.
         # Degree = 1 will produce a straight line.
         __a				     =    len(lowerCamelCase      ) - 1




      def  __UpperCamelCase							(  self ,   lowerCamelCase      )							->list[float]:



         '''simple docstring'''
         assert 0 <= t <= 1, "Time t must be between 0 and 1."
         __a				     =    []
         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  __UpperCamelCase							(  self ,   lowerCamelCase      )							->tuple[float, float]:



         '''simple docstring'''
         assert 0 <= t <= 1, "Time t must be between 0 and 1."

         __a				     =    self.basis_function(lowerCamelCase      )
         __a				     =    0.0
         __a				     =    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 ,   lowerCamelCase = 0.01      )							->Optional[int]:



         '''simple docstring'''
         from matplotlib import pyplot as plt  # type: ignore

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

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

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



import warnings

from .generation import TFGenerationMixin
class 							__SCREAMING_SNAKE_CASE       (							_lowerCAmelCase     ):
      # warning at import time
      warnings.warn(
          "Importing `TFGenerationMixin` from `src/transformers/generation_tf_utils.py` is deprecated and will "
          "be removed in Transformers v5. Import as `from transformers import TFGenerationMixin` instead."      ,      _lowerCAmelCase      ,      )