





from __future__ import annotations

from scipy.special import comb  # type: ignore

class  __A:

     def __init__(      self,       A      ):





            """simple docstring"""

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

     def 	_UpperCamelCase     (      self,       A      ):





            """simple docstring"""

            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,       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."

            _UpperCamelCase              =						self.basis_function(A      )
            _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 	_UpperCamelCase     (      self,       A = 0.01      ):





            """simple docstring"""

            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(A      )
                   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(
                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













def     SCREAMING_SNAKE_CASE			(      lowerCAmelCase    ,       lowerCAmelCase    ,       lowerCAmelCase = 0    ,       lowerCAmelCase = 0					):
       _UpperCamelCase              =						right or len(lowerCAmelCase					) - 1
       if left > right:
              return -1
       elif list_data[left] == key:
              return left
       elif list_data[right] == key:
              return right
       else:
              return search(lowerCAmelCase    ,       lowerCAmelCase    ,       left + 1    ,       right - 1					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()






