"""simple docstring"""






from ..utils import DummyObject, requires_backends





class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   Optional[int]							  =	['torch', 'torchsde']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """torchsde"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """torchsde"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """torchsde"""]						)




"""simple docstring"""






from __future__ import annotations

from scipy.special import comb  # type: ignore





class  _A						:

      def __init__(						self		,       __lowerCAmelCase						):







            """simple docstring"""



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

      def 				A__       (						self		,       __lowerCAmelCase						):







            """simple docstring"""



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

      def 				A__       (						self		,       __lowerCAmelCase						):







            """simple docstring"""



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

            lowercase														=	self.basis_function(__lowerCAmelCase						)
            lowercase														=	0.0
            lowercase														=	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 				A__       (						self		,       __lowerCAmelCase = 0.0_1						):







            """simple docstring"""



            from matplotlib import pyplot as plt  # type: ignore

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

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

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

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



