
from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray




def  lowerCamelCase__ (  a__     :     float		,					a__     :     float		,					a__     :     bool = False   )						->		list[float]:
       if radian_mode:
              return [magnitude * cos(_lowerCAmelCase   ), magnitude * sin(_lowerCAmelCase   )]
       return [magnitude * cos(radians(_lowerCAmelCase   )   ), magnitude * sin(radians(_lowerCAmelCase   )   )]




def  lowerCamelCase__ (  a__     :     NDArray[floataa]		,					a__     :     NDArray[floataa]		,					a__     :     float = 10**-1   )						->		bool:
       UpperCamelCase_											=				cross(_lowerCAmelCase		,					_lowerCAmelCase   )
       UpperCamelCase_											=				sum(_lowerCAmelCase   )
       return abs(_lowerCAmelCase   ) < eps


if __name__ == "__main__":
      # Test to check if it works
      _A		     =    array(
          [
              polar_force(7_1_8.4, 180 - 30),
              polar_force(8_7_9.5_4, 45),
              polar_force(100, -90),
          ]
      )

      _A		     =    array([[0, 0], [0, 0], [0, 0]])

      assert in_static_equilibrium(forces, location)

      # Problem 1 in image_data/2D_problems.jpg
      _A		     =    array(
          [
              polar_force(30 * 9.8_1, 15),
              polar_force(215, 180 - 45),
              polar_force(264, 90 - 30),
          ]
      )

      _A		     =    array([[0, 0], [0, 0], [0, 0]])

      assert in_static_equilibrium(forces, location)

      # Problem in image_data/2D_problems_1.jpg
      _A		     =    array([[0, -2_000], [0, -1_200], [0, 15_600], [0, -12_400]])

      _A		     =    array([[0, 0], [6, 0], [10, 0], [12, 0]])

      assert in_static_equilibrium(forces, location)

      import doctest

      doctest.testmod()








'''simple docstring'''






from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
UpperCamelCase__:   Tuple								=			numpy.array([0, 0])
UpperCamelCase__:   Union[str, Any]								=			numpy.array([0.5, 0.8660254])
UpperCamelCase__:   Dict								=			numpy.array([1, 0])
UpperCamelCase__:   int								=			[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]


def  snake_case_     (					_lowerCAmelCase  :						list[numpy.ndarray]   ,      _lowerCAmelCase  :						int  )      ->   list[numpy.ndarray]:
							UpperCAmelCase :       Union[str, Any] 							=		initial_vectors
							for _ in range(_lowerCAmelCase  ):
														UpperCAmelCase :       Union[str, Any] 							=		iteration_step(_lowerCAmelCase  )
							return vectors


def  snake_case_     (					_lowerCAmelCase  :						list[numpy.ndarray]  )      ->   list[numpy.ndarray]:
							UpperCAmelCase :       Tuple 							=		[]
							for i, start_vector in enumerate(vectors[:-1]  ):
														UpperCAmelCase :       List[str] 							=		vectors[i + 1]
														new_vectors.append(_lowerCAmelCase  )
														UpperCAmelCase :       Optional[Any] 							=		end_vector - start_vector
														new_vectors.append(start_vector + difference_vector / 3  )
														new_vectors.append(
														    start_vector + difference_vector / 3 + rotate(difference_vector / 3   ,      60  )  )
														new_vectors.append(start_vector + difference_vector * 2 / 3  )
							new_vectors.append(vectors[-1]  )
							return new_vectors


def  snake_case_     (					_lowerCAmelCase  :						numpy.ndarray   ,      _lowerCAmelCase  :						float  )      ->   numpy.ndarray:
							UpperCAmelCase :       List[str] 							=		numpy.radians(_lowerCAmelCase  )
							UpperCAmelCase							,		UpperCAmelCase :       Tuple 							=		numpy.cos(_lowerCAmelCase  ), numpy.sin(_lowerCAmelCase  )
							UpperCAmelCase :       Union[str, Any] 							=		numpy.array(((c, -s), (s, c))  )
							return numpy.dot(_lowerCAmelCase   ,      _lowerCAmelCase  )


def  snake_case_     (					_lowerCAmelCase  :						list[numpy.ndarray]  )      ->   None:
							UpperCAmelCase :       List[Any] 							=		plt.gca()
							axes.set_aspect('''equal'''  )

							# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
							# y-coordinates as inputs, which are constructed from the vector-list using
							# zip()
							UpperCAmelCase							,		UpperCAmelCase :       str 							=		zip(*_lowerCAmelCase  )
							plt.plot(_lowerCAmelCase   ,      _lowerCAmelCase  )
							plt.show()


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						UpperCamelCase__:   List[Any]								=			iterate(INITIAL_VECTORS, 5)
						plot(processed_vectors)





