


'''simple docstring'''

from __future__ import annotations

from scipy.special import comb  # type: ignore





class      snake_case    :





  """simple docstring"""




  def __init__(    self			,  UpperCamelCase     ):







   """simple docstring"""
   lowerCamelCase_      =  list_of_points
   # Degree determines the flexibility of the curve.
   # Degree = 1 will produce a straight line.
   lowerCamelCase_      =  len(UpperCamelCase     ) - 1






  def   snake_case		(    self			,  UpperCamelCase     ):







   """simple docstring"""
   assert 0 <= t <= 1, "Time t must be between 0 and 1."
   lowerCamelCase_      =  []
   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   snake_case		(    self			,  UpperCamelCase     ):







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

   lowerCamelCase_      =  self.basis_function(UpperCamelCase     )
   lowerCamelCase_      =  0.0
   lowerCamelCase_      =  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   snake_case		(    self			,  UpperCamelCase = 0.01     ):







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

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

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

   lowerCamelCase_      =  [i[0] for i in self.list_of_points]
   lowerCamelCase_      =  [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'''


def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase      ):

		if density <= 0:
				raise ValueError("Impossible fluid density"      )
		if bulk_modulus <= 0:
				raise ValueError("Impossible bulk modulus"      )

		return (bulk_modulus / density) ** 0.5


if __name__ == "__main__":
						import doctest

						doctest.testmod()



