





'''simple docstring'''







from __future__ import annotations

from scipy.special import comb  # type: ignore


class 					__a      :

							def __init__(							self							:     Tuple       ,     __magic_name__							:     list[tuple[float, float]]   )					->       Optional[Any]:







													"""simple docstring"""
													UpperCAmelCase_			:      Dict     						=  list_of_points
													# Degree determines the flexibility of the curve.
													# Degree = 1 will produce a straight line.
													UpperCAmelCase_			:      List[str]     						=  len(__magic_name__   ) - 1

							def     UpperCAmelCase__	(							self							:     Tuple       ,     __magic_name__							:     float   )					->       list[float]:







													"""simple docstring"""
													assert 0 <= t <= 1, "Time t must be between 0 and 1."
													UpperCAmelCase_			:      list[float]     						=  []
													for i in range(len(self.list_of_points   )   ):
																			# basis function for each i
																			output_values.append(
																			    comb(self.degree       ,     __magic_name__   ) * ((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(__magic_name__   )       ,     5   ) == 1
													return output_values

							def     UpperCAmelCase__	(							self							:     Optional[Any]       ,     __magic_name__							:     float   )					->       tuple[float, float]:







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

													UpperCAmelCase_			:      Any     						=  self.basis_function(__magic_name__   )
													UpperCAmelCase_			:      Union[str, Any]     						=  0.0
													UpperCAmelCase_			:      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     UpperCAmelCase__	(							self							:     Optional[Any]       ,     __magic_name__							:     float = 0.0_1   )					->       List[str]:







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

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

													UpperCAmelCase_			:      int     						=  0.0
													while t <= 1:
																			UpperCAmelCase_			:      str     						=  self.bezier_curve_function(__magic_name__   )
																			to_plot_x.append(value[0]   )
																			to_plot_y.append(value[1]   )
																			t += step_size

													UpperCAmelCase_			:      Any     						=  [i[0] for i in self.list_of_points]
													UpperCAmelCase_			:      Union[str, Any]     						=  [i[1] for i in self.list_of_points]

													plt.plot(
													    __magic_name__       ,     __magic_name__       ,     color='''blue'''       ,     label='''Curve of Degree ''' + str(self.degree   )       ,     )
													plt.scatter(__magic_name__       ,     __magic_name__       ,     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'''







snake_case_     :       int						=  {
    "Pillow": "Pillow",
    "accelerate": "accelerate>=0.11.0",
    "compel": "compel==0.1.8",
    "black": "black~=23.1",
    "datasets": "datasets",
    "filelock": "filelock",
    "flax": "flax>=0.4.1",
    "hf-doc-builder": "hf-doc-builder>=0.3.0",
    "huggingface-hub": "huggingface-hub>=0.13.2",
    "requests-mock": "requests-mock==1.10.0",
    "importlib_metadata": "importlib_metadata",
    "invisible-watermark": "invisible-watermark",
    "isort": "isort>=5.5.4",
    "jax": "jax>=0.2.8,!=0.3.2",
    "jaxlib": "jaxlib>=0.1.65",
    "Jinja2": "Jinja2",
    "k-diffusion": "k-diffusion>=0.0.12",
    "torchsde": "torchsde",
    "note_seq": "note_seq",
    "librosa": "librosa",
    "numpy": "numpy",
    "omegaconf": "omegaconf",
    "parameterized": "parameterized",
    "protobuf": "protobuf>=3.20.3,<4",
    "pytest": "pytest",
    "pytest-timeout": "pytest-timeout",
    "pytest-xdist": "pytest-xdist",
    "ruff": "ruff>=0.0.241",
    "safetensors": "safetensors",
    "sentencepiece": "sentencepiece>=0.1.91,!=0.1.92",
    "scipy": "scipy",
    "onnx": "onnx",
    "regex": "regex!=2019.12.17",
    "requests": "requests",
    "tensorboard": "tensorboard",
    "torch": "torch>=1.4",
    "torchvision": "torchvision",
    "transformers": "transformers>=4.25.1",
    "urllib3": "urllib3<=2.0.0",
}





