



from __future__ import annotations

from scipy.special import comb  # type: ignore

class        snake_case__    :







						"""simple docstring"""




						def __init__(       self ,       __lowercase  ) ->				Union[str, Any]:
									"""simple docstring"""




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

						def 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase  ) ->				list[float]:
									"""simple docstring"""




									assert 0 <= t <= 1, "Time t must be between 0 and 1."
									a__       :						list[float]							=  []
									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 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase  ) ->				tuple[float, float]:
									"""simple docstring"""




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

									a__       :						Any							=  self.basis_function(__lowercase  )
									a__       :						List[Any]							=  0.0
									a__       :						Any							=  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 ,       __lowercase = 0.0_1  ) ->				Any:
									"""simple docstring"""




									from matplotlib import pyplot as plt  # type: ignore

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

									a__       :						Optional[Any]							=  0.0
									while t <= 1:
												a__       :						List[str]							=  self.bezier_curve_function(__lowercase  )
												to_plot_x.append(value[0]  )
												to_plot_y.append(value[1]  )
												t += step_size

									a__       :						Any							=  [i[0] for i in self.list_of_points]
									a__       :						str							=  [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









import os
import sys
from contextlib import contextmanager


# Windows only
if os.name == "nt":
		import ctypes
		import msvcrt  # noqa

		class        snake_case__    (ctypes.Structure		):







								"""simple docstring"""




								__lowerCAmelCase					:Dict      =					[("size", ctypes.c_int), ("visible", ctypes.c_byte)]

def      lowerCAmelCase_					(  )							->	List[Any]:







			"""simple docstring"""
			if os.name == "nt":
						a__       :						int							=  CursorInfo()
						a__       :						Union[str, Any]							=  ctypes.windll.kernelaa.GetStdHandle(-11)
						ctypes.windll.kernelaa.GetConsoleCursorInfo(_lowercase						,       ctypes.byref(_lowercase))
						a__       :						List[str]							=  False
						ctypes.windll.kernelaa.SetConsoleCursorInfo(_lowercase						,       ctypes.byref(_lowercase))
			elif os.name == "posix":
						sys.stdout.write("""\033[?25l""")
						sys.stdout.flush()

def      lowerCAmelCase_					(  )							->	Optional[Any]:







			"""simple docstring"""
			if os.name == "nt":
						a__       :						List[Any]							=  CursorInfo()
						a__       :						Optional[int]							=  ctypes.windll.kernelaa.GetStdHandle(-11)
						ctypes.windll.kernelaa.GetConsoleCursorInfo(_lowercase						,       ctypes.byref(_lowercase))
						a__       :						Dict							=  True
						ctypes.windll.kernelaa.SetConsoleCursorInfo(_lowercase						,       ctypes.byref(_lowercase))
			elif os.name == "posix":
						sys.stdout.write("""\033[?25h""")
						sys.stdout.flush()





@contextmanager
def      lowerCAmelCase_					(  )							->	Any:







			"""simple docstring"""
			try:
						hide_cursor()
						yield
			finally:
						show_cursor()




