




'''simple docstring'''





from . import __version__

# Backward compatibility imports, to make sure all those objects can be found in file_utils
from .utils import (
    CLOUDFRONT_DISTRIB_PREFIX,
    CONFIG_NAME,
    DISABLE_TELEMETRY,
    DUMMY_INPUTS,
    DUMMY_MASK,
    ENV_VARS_TRUE_AND_AUTO_VALUES,
    ENV_VARS_TRUE_VALUES,
    FEATURE_EXTRACTOR_NAME,
    FLAX_WEIGHTS_NAME,
    HF_MODULES_CACHE,
    HUGGINGFACE_CO_PREFIX,
    HUGGINGFACE_CO_RESOLVE_ENDPOINT,
    MODEL_CARD_NAME,
    MULTIPLE_CHOICE_DUMMY_INPUTS,
    PYTORCH_PRETRAINED_BERT_CACHE,
    PYTORCH_TRANSFORMERS_CACHE,
    S3_BUCKET_PREFIX,
    SENTENCEPIECE_UNDERLINE,
    SPIECE_UNDERLINE,
    TF2_WEIGHTS_NAME,
    TF_WEIGHTS_NAME,
    TORCH_FX_REQUIRED_VERSION,
    TRANSFORMERS_CACHE,
    TRANSFORMERS_DYNAMIC_MODULE_NAME,
    USE_JAX,
    USE_TF,
    USE_TORCH,
    WEIGHTS_INDEX_NAME,
    WEIGHTS_NAME,
    ContextManagers,
    DummyObject,
    EntryNotFoundError,
    ExplicitEnum,
    ModelOutput,
    PaddingStrategy,
    PushToHubMixin,
    RepositoryNotFoundError,
    RevisionNotFoundError,
    TensorType,
    _LazyModule,
    add_code_sample_docstrings,
    add_end_docstrings,
    add_start_docstrings,
    add_start_docstrings_to_model_forward,
    cached_property,
    copy_func,
    default_cache_path,
    define_sagemaker_information,
    get_cached_models,
    get_file_from_repo,
    get_full_repo_name,
    get_torch_version,
    has_file,
    http_user_agent,
    is_apex_available,
    is_bsa_available,
    is_coloredlogs_available,
    is_datasets_available,
    is_detectrona_available,
    is_faiss_available,
    is_flax_available,
    is_ftfy_available,
    is_in_notebook,
    is_ipex_available,
    is_librosa_available,
    is_offline_mode,
    is_onnx_available,
    is_pandas_available,
    is_phonemizer_available,
    is_protobuf_available,
    is_psutil_available,
    is_pyanvml_available,
    is_pyctcdecode_available,
    is_pytesseract_available,
    is_pytorch_quantization_available,
    is_rjieba_available,
    is_sagemaker_dp_enabled,
    is_sagemaker_mp_enabled,
    is_scipy_available,
    is_sentencepiece_available,
    is_seqio_available,
    is_sklearn_available,
    is_soundfile_availble,
    is_spacy_available,
    is_speech_available,
    is_tensor,
    is_tensorflow_probability_available,
    is_tfaonnx_available,
    is_tf_available,
    is_timm_available,
    is_tokenizers_available,
    is_torch_available,
    is_torch_bfaa_available,
    is_torch_cuda_available,
    is_torch_fx_available,
    is_torch_fx_proxy,
    is_torch_mps_available,
    is_torch_tfaa_available,
    is_torch_tpu_available,
    is_torchaudio_available,
    is_training_run_on_sagemaker,
    is_vision_available,
    replace_return_docstrings,
    requires_backends,
    to_numpy,
    to_py_obj,
    torch_only_method,
)










'''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




