






"""simple docstring"""






from __future__ import annotations

from scipy.special import comb  # type: ignore





class       snake_case_       :



 """simple docstring"""

 def __init__(      self  ,					__a						):


     """simple docstring"""

     A__							 =       list_of_points
     # Degree determines the flexibility of the curve.
     # Degree = 1 will produce a straight line.
     A__							 =       len(__a						) - 1


 def       _UpperCAmelCase						(      self  ,					__a						):


     """simple docstring"""

     assert 0 <= t <= 1, "Time t must be between 0 and 1."
     A__							 =       []
     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       _UpperCAmelCase						(      self  ,					__a						):


     """simple docstring"""

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

     A__							 =       self.basis_function(__a						)
     A__							 =       0.0
     A__							 =       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  ,					__a = 0.01						):


     """simple docstring"""

     from matplotlib import pyplot as plt  # type: ignore

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

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

     A__							 =       [i[0] for i in self.list_of_points]
     A__							 =       [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










"""simple docstring"""






from math import factorial, pi



def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__ = 30				):

				if not isinstance(lowerCAmelCase__       ,(int, float)				):
								raise ValueError('maclaurin_sin() requires either an int or float for theta'				)

				if not isinstance(lowerCAmelCase__       ,lowerCAmelCase__				) or accuracy <= 0:
								raise ValueError('maclaurin_sin() requires a positive int for accuracy'				)

				A__							 =       float(lowerCAmelCase__				)
				A__							 =       theta // (2 * pi)
				theta -= 2 * div * pi
				return sum(
				    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1				) for r in range(lowerCAmelCase__				)				)



def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__ = 30				):

				if not isinstance(lowerCAmelCase__       ,(int, float)				):
								raise ValueError('maclaurin_cos() requires either an int or float for theta'				)

				if not isinstance(lowerCAmelCase__       ,lowerCAmelCase__				) or accuracy <= 0:
								raise ValueError('maclaurin_cos() requires a positive int for accuracy'				)

				A__							 =       float(lowerCAmelCase__				)
				A__							 =       theta // (2 * pi)
				theta -= 2 * div * pi
				return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r				) for r in range(lowerCAmelCase__				)				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					print(maclaurin_sin(10))
					print(maclaurin_sin(-10))
					print(maclaurin_sin(10, 15))
					print(maclaurin_sin(-10, 15))

					print(maclaurin_cos(5))
					print(maclaurin_cos(-5))
					print(maclaurin_cos(10, 15))
					print(maclaurin_cos(-10, 15))


