




'''simple docstring'''





import warnings

from diffusers import StableDiffusionImgaImgPipeline  # noqa F401


warnings.warn(
    "The `image_to_image.py` script is outdated. Please use directly `from diffusers import"
    " StableDiffusionImg2ImgPipeline` instead."
)










'''simple docstring'''





from __future__ import annotations

from scipy.special import comb  # type: ignore




class 			_snake_case		:




			def __init__( self    ,							a__							)    ->    Union[str, Any]:

										'''simple docstring'''




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




			def        lowerCAmelCase__    ( self    ,							a__							)    ->    list[float]:

										'''simple docstring'''




										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    ,							a__							) * ((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(a__							)    ,							5							) == 1
										return output_values




			def        lowerCAmelCase__    ( self    ,							a__							)    ->    tuple[float, float]:

										'''simple docstring'''




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

										snake_case_      =				self.basis_function(a__							)
										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        lowerCAmelCase__    ( self    ,							a__ = 0.0_1							)    ->    Any:

										'''simple docstring'''




										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(a__							)
																	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(
										    a__    ,							a__    ,							color="blue"    ,							label="Curve of Degree " + str(self.degree							)    ,							)
										plt.scatter(a__    ,							a__    ,							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




