



"""simple docstring"""






from __future__ import annotations

from scipy.special import comb  # type: ignore






class 	__snake_case	:




  def __init__(			self					:						str						, __lowerCAmelCase					:						list[tuple[float, float]]		):






         """simple docstring"""






         _lowerCamelCase						:    Union[str, Any]         =			list_of_points
         # Degree determines the flexibility of the curve.
         # Degree = 1 will produce a straight line.
         _lowerCamelCase						:    Dict         =			len(__lowerCAmelCase		) - 1




  def 						SCREAMING_SNAKE_CASE    (			self					:						str						, __lowerCAmelCase					:						float		):






         """simple docstring"""






         assert 0 <= t <= 1, "Time t must be between 0 and 1."
         _lowerCamelCase						:    list[float]         =			[]
         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 						SCREAMING_SNAKE_CASE    (			self					:						Optional[int]						, __lowerCAmelCase					:						float		):






         """simple docstring"""






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

         _lowerCamelCase						:    Tuple         =			self.basis_function(__lowerCAmelCase		)
         _lowerCamelCase						:    Any         =			0.0
         _lowerCamelCase						:    Tuple         =			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 						SCREAMING_SNAKE_CASE    (			self					:						Optional[int]						, __lowerCAmelCase					:						float = 0.01		):






         """simple docstring"""






         from matplotlib import pyplot as plt  # type: ignore

         _lowerCamelCase						:    list[float]         =			[]  # x coordinates of points to plot
         _lowerCamelCase						:    list[float]         =			[]  # y coordinates of points to plot

         _lowerCamelCase						:    Tuple         =			0.0
         while t <= 1:
                _lowerCamelCase						:    Dict         =			self.bezier_curve_function(__lowerCAmelCase		)
                to_plot_x.append(value[0]		)
                to_plot_y.append(value[1]		)
                t += step_size

         _lowerCamelCase						:    Any         =			[i[0] for i in self.list_of_points]
         _lowerCamelCase						:    List[str]         =			[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 math






def 	snake_case_  (				A_ :		int						):


       '''simple docstring'''





       return math.sqrt(A_						) * math.sqrt(A_						) == num






def 	snake_case_  (				A_ :		int						):


       '''simple docstring'''





       _lowerCamelCase						:    Dict         =			0
       _lowerCamelCase						:    Tuple         =			n
       while left <= right:
              _lowerCamelCase						:    List[str]         =			(left + right) // 2
              if mid**2 == n:
                     return True
              elif mid**2 > n:
                     _lowerCamelCase						:    int         =			mid - 1
              else:
                     _lowerCamelCase						:    Optional[Any]         =			mid + 1
       return False


if __name__ == "__main__":
   import doctest

   doctest.testmod()


