





'''simple docstring'''




from __future__ import annotations

from scipy.special import comb  # type: ignore







class   A_	:




 def __init__(					self       :    Any	,			snake_case_       :    Any    ):
      _UpperCAmelCase     							=   list_of_points
      # Degree determines the flexibility of the curve.
      # Degree = 1 will produce a straight line.
      _UpperCAmelCase     							=   len(__UpperCamelCase    ) - 1




 def      lowercase	(					self       :    List[Any]	,			snake_case_       :    Union[str, Any]    ):
      assert 0 <= t <= 1, "Time t must be between 0 and 1."
      _UpperCAmelCase     							=   []
      for i in range(len(self.list_of_points    )    ):
           # basis function for each i
           output_values.append(
               comb(self.degree	,			__UpperCamelCase    ) * ((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(__UpperCamelCase    )	,			5    ) == 1
      return output_values




 def      lowercase	(					self       :    Any	,			snake_case_       :    Optional[int]    ):
      assert 0 <= t <= 1, "Time t must be between 0 and 1."

      _UpperCAmelCase     							=   self.basis_function(__UpperCamelCase    )
      _UpperCAmelCase     							=   0.0
      _UpperCAmelCase     							=   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      lowercase	(					self       :    List[str]	,			snake_case_       :    Dict = 0.0_1    ):
      from matplotlib import pyplot as plt  # type: ignore

      _UpperCAmelCase     							=   []  # x coordinates of points to plot
      _UpperCAmelCase     							=   []  # y coordinates of points to plot

      _UpperCAmelCase     							=   0.0
      while t <= 1:
           _UpperCAmelCase     							=   self.bezier_curve_function(__UpperCamelCase    )
           to_plot_x.append(value[0]    )
           to_plot_y.append(value[1]    )
           t += step_size

      _UpperCAmelCase     							=   [i[0] for i in self.list_of_points]
      _UpperCAmelCase     							=   [i[1] for i in self.list_of_points]

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

from .dependency_versions_table import deps
from .utils.versions import require_version, require_version_core


# define which module versions we always want to check at run time
# (usually the ones defined in `install_requires` in setup.py)
#
# order specific notes:
# - tqdm must be checked before tokenizers

__SCREAMING_SNAKE_CASE    	="python tqdm regex requests packaging filelock numpy tokenizers".split()
if sys.version_info < (3, 7):
       pkgs_to_check_at_runtime.append("dataclasses")
if sys.version_info < (3, 8):
       pkgs_to_check_at_runtime.append("importlib_metadata")

for pkg in pkgs_to_check_at_runtime:
       if pkg in deps:
              if pkg == "tokenizers":
                     # must be loaded here, or else tqdm check may fail
                     from .utils import is_tokenizers_available

                     if not is_tokenizers_available():
                            continue  # not required, check version only if installed

              require_version_core(deps[pkg])
       else:
              raise ValueError(F"can't find {pkg} in {deps.keys()}, check dependency_versions_table.py")



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     int     ,			__SCREAMING_SNAKE_CASE							:     Union[str, Any]=None      ):
     require_version(deps[pkg]     ,			__SCREAMING_SNAKE_CASE      )

