

import os
import string
import sys


lowercase_			=  1 << 8

lowercase_			=  {
    "tab": ord("\t"),
    "newline": ord("\r"),
    "esc": 27,
    "up": 65 + ARROW_KEY_FLAG,
    "down": 66 + ARROW_KEY_FLAG,
    "right": 67 + ARROW_KEY_FLAG,
    "left": 68 + ARROW_KEY_FLAG,
    "mod_int": 91,
    "undefined": sys.maxsize,
    "interrupt": 3,
    "insert": 50,
    "delete": 51,
    "pg_up": 53,
    "pg_down": 54,
}

lowercase_			=  KEYMAP["up"]
lowercase_			=  KEYMAP["left"]

if sys.platform == "win32":
     lowercase_			=  []
     lowercase_			=  {
         B"\xe0H": KEYMAP["up"] - ARROW_KEY_FLAG,
         B"\x00H": KEYMAP["up"] - ARROW_KEY_FLAG,
         B"\xe0P": KEYMAP["down"] - ARROW_KEY_FLAG,
         B"\x00P": KEYMAP["down"] - ARROW_KEY_FLAG,
         B"\xe0M": KEYMAP["right"] - ARROW_KEY_FLAG,
         B"\x00M": KEYMAP["right"] - ARROW_KEY_FLAG,
         B"\xe0K": KEYMAP["left"] - ARROW_KEY_FLAG,
         B"\x00K": KEYMAP["left"] - ARROW_KEY_FLAG,
     }

for i in range(10):
     lowercase_			=  ord(str(i))
def 						_snake_case(   )							->				List[Any]:





    '''simple docstring'''






    if os.name == "nt":
        import msvcrt

        A__   				=       'mbcs'
        # Flush the keyboard buffer
        while msvcrt.kbhit():
            msvcrt.getch()
        if len(SCREAMING_SNAKE_CASE__				) == 0:
            # Read the keystroke
            A__   				=       msvcrt.getch()

            # If it is a prefix char, get second part
            if ch in (b"\x00", b"\xe0"):
                A__   				=       ch + msvcrt.getch()
                # Translate actual Win chars to bullet char types
                try:
                    A__   				=       chr(WIN_KEYMAP[cha]				)
                    WIN_CH_BUFFER.append(chr(KEYMAP['mod_int']				)				)
                    WIN_CH_BUFFER.append(SCREAMING_SNAKE_CASE__				)
                    if ord(SCREAMING_SNAKE_CASE__				) in (
                        KEYMAP["insert"] - 1 << 9,
                        KEYMAP["delete"] - 1 << 9,
                        KEYMAP["pg_up"] - 1 << 9,
                        KEYMAP["pg_down"] - 1 << 9,
                    ):
                        WIN_CH_BUFFER.append(chr(126				)				)
                    A__   				=       chr(KEYMAP['esc']				)
                except KeyError:
                    A__   				=       cha[1]
            else:
                A__   				=       ch.decode(SCREAMING_SNAKE_CASE__				)
        else:
            A__   				=       WIN_CH_BUFFER.pop(0				)
    elif os.name == "posix":
        import termios
        import tty

        A__   				=       sys.stdin.fileno()
        A__   				=       termios.tcgetattr(SCREAMING_SNAKE_CASE__				)
        try:
            tty.setraw(SCREAMING_SNAKE_CASE__				)
            A__   				=       sys.stdin.read(1				)
        finally:
            termios.tcsetattr(SCREAMING_SNAKE_CASE__   ,      termios.TCSADRAIN   ,      SCREAMING_SNAKE_CASE__				)
    return ch

def 						_snake_case(   )							->				Dict:





    '''simple docstring'''






    A__   				=       get_raw_chars()
    if ord(SCREAMING_SNAKE_CASE__				) in [KEYMAP["interrupt"], KEYMAP["newline"]]:
        return char

    elif ord(SCREAMING_SNAKE_CASE__				) == KEYMAP["esc"]:
        A__   				=       get_raw_chars()
        if ord(SCREAMING_SNAKE_CASE__				) == KEYMAP["mod_int"]:
            A__   				=       get_raw_chars()
            if ord(SCREAMING_SNAKE_CASE__				) >= KEYMAP["arrow_begin"] - ARROW_KEY_FLAG and ord(SCREAMING_SNAKE_CASE__				) <= KEYMAP["arrow_end"] - ARROW_KEY_FLAG:
                return chr(ord(SCREAMING_SNAKE_CASE__				) + ARROW_KEY_FLAG				)
            else:
                return KEYMAP["undefined"]
        else:
            return get_raw_chars()

    else:
        if char in string.printable:
            return char
        else:
            return KEYMAP["undefined"]




from __future__ import annotations

from scipy.special import comb  # type: ignore


class 			A						:







    """simple docstring"""





    def __init__(				self			:	Any,lowercase_			:	list[tuple[float, float]]		)->   Optional[int]:





        '''simple docstring'''







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


    def 						snake_case__					(				self			:	List[Any],lowercase_			:	float		)->   list[float]:





        '''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,lowercase_		) * ((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(lowercase_		),5		) == 1
        return output_values


    def 						snake_case__					(				self			:	str,lowercase_			:	float		)->   tuple[float, float]:





        '''simple docstring'''







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

        A__   				=       self.basis_function(lowercase_		)
        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 						snake_case__					(				self			:	str,lowercase_			:	float = 0.01		)->   str:





        '''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(lowercase_		)
            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(
            lowercase_,lowercase_,color='blue',label='Curve of Degree ' + str(self.degree		),)
        plt.scatter(lowercase_,lowercase_,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

