我怎样才能将这些注释添加到这个二次贝塞尔曲线中？

简单地遍历你的控制点坐标并使用 annotate 来写注释：for i, p in enumerate(control_points):             ax.annotate(f'P{i:d}', xy=p, xytext=(0,5), textcoords='offset points', ha='center')完整代码：import matplotlib.pyplot as pltimport numpy as npimport scipy.specialshow_animation = Truedef calc_4points_bezier_path(sx, sy, syaw, ex, ey, eyaw, offset):    """    Compute control points and path given start and end position.    :param sx: (float) x-coordinate of the starting point    :param sy: (float) y-coordinate of the starting point    :param syaw: (float) yaw angle at start    :param ex: (float) x-coordinate of the ending point    :param ey: (float) y-coordinate of the ending point    :param eyaw: (float) yaw angle at the end    :param offset: (float)    :return: (numpy array, numpy array)    """    dist = np.sqrt((sx - ex) ** 2 + (sy - ey) ** 2) / offset    control_points = np.array(        [[sx, sy],         [sx + dist * np.cos(syaw), sy + dist * np.sin(syaw)],         [ex - dist * np.cos(eyaw), ey - dist * np.sin(eyaw)],         [ex, ey]])    path = calc_bezier_path(control_points, n_points=100)    return path, control_pointsdef calc_bezier_path(control_points, n_points=100):    """    Compute bezier path (trajectory) given control points.    :param control_points: (numpy array)    :param n_points: (int) number of points in the trajectory    :return: (numpy array)    """    traj = []    for t in np.linspace(0, 1, n_points):        traj.append(bezier(t, control_points))    return np.array(traj)def bernstein_poly(n, i, t):    """    Bernstein polynom.    :param n: (int) polynom degree    :param i: (int)    :param t: (float)    :return: (float)    """    return scipy.special.comb(n, i) * t ** i * (1 - t) ** (n - i)def bezier(t, control_points):    """    Return one point on the bezier curve.    :param t: (float) number in [0, 1]    :param control_points: (numpy array)    :return: (numpy array) Coordinates of the point    """    n = len(control_points) - 1    return np.sum([bernstein_poly(n, i, t) * control_points[i] for i in range(n + 1)], axis=0)def bezier_derivatives_control_points(control_points, n_derivatives):    """    Compute control points of the successive derivatives of a given bezier curve.    A derivative of a bezier curve is a bezier curve.    See https://pomax.github.io/bezierinfo/#derivatives    for detailed explanations    :param control_points: (numpy array)    :param n_derivatives: (int)    e.g., n_derivatives=2 -> compute control points for first and second derivatives    :return: ([numpy array])    """    w = {0: control_points}    for i in range(n_derivatives):        n = len(w[i])        w[i + 1] = np.array([(n - 1) * (w[i][j + 1] - w[i][j])                             for j in range(n - 1)])    return wdef curvature(dx, dy, ddx, ddy):    """    Compute curvature at one point given first and second derivatives.    :param dx: (float) First derivative along x axis    :param dy: (float)    :param ddx: (float) Second derivative along x axis    :param ddy: (float)    :return: (float)    """    return (dx * ddy - dy * ddx) / (dx ** 2 + dy ** 2) ** (3 / 2)def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):  # pragma: no cover    """Plot arrow."""    if not isinstance(x, float):        for (ix, iy, iyaw) in zip(x, y, yaw):            plot_arrow(ix, iy, iyaw)    else:        plt.arrow(x, y, length * np.cos(yaw), length * np.sin(yaw),                  fc=fc, ec=ec, head_width=width, head_length=width)        plt.plot(x, y)def main():    """Plot an example bezier curve."""    start_x = 10.0  # [m]    start_y = 1.0  # [m]    start_yaw = np.radians(180.0)  # [rad]    end_x = -0.0  # [m]    end_y = -3.0  # [m]    end_yaw = np.radians(-45.0)  # [rad]    offset = 3.0    path, control_points = calc_4points_bezier_path(        start_x, start_y, start_yaw, end_x, end_y, end_yaw, offset)    # Note: alternatively, instead of specifying start and end position    # you can directly define n control points and compute the path:    #control_points = np.array([[5., 1.], [-2.78, 1.], [-11.5, -4.5], [-6., -8.]])    #path = calc_bezier_path(control_points, n_points=100)    # Display the tangent, normal and radius of cruvature at a given point    t = 0.86  # Number in [0, 1]    x_target, y_target = bezier(t, control_points)    derivatives_cp = bezier_derivatives_control_points(control_points, 2)    point = bezier(t, control_points)    dt = bezier(t, derivatives_cp[1])    ddt = bezier(t, derivatives_cp[2])    # Radius of curvature    radius = 1 / curvature(dt[0], dt[1], ddt[0], ddt[1])    # Normalize derivative    dt /= np.linalg.norm(dt, 2)    tangent = np.array([point, point + dt])    normal = np.array([point, point + [- dt[1], dt[0]]])    curvature_center = point + np.array([- dt[1], dt[0]]) * radius    circle = plt.Circle(tuple(curvature_center), radius,                        color=(0, 0.8, 0.8), fill=False, linewidth=1)    assert path.T[0][0] == start_x, "path is invalid"    assert path.T[1][0] == start_y, "path is invalid"    assert path.T[0][-1] == end_x, "path is invalid"    assert path.T[1][-1] == end_y, "path is invalid"    if show_animation:  # pragma: no cover        fig, ax = plt.subplots()        ax.plot(path.T[0], path.T[1], label="Cubic Bezier Path")        ax.plot(control_points.T[0], control_points.T[1],                '--o', label="Control Points")        ax.plot(x_target, y_target)        ax.plot(tangent[:, 0], tangent[:, 1], label="Tangent")        ax.plot(normal[:, 0], normal[:, 1], label="Normal")        ax.add_artist(circle)        plot_arrow(start_x, start_y, start_yaw)        plot_arrow(end_x, end_y, end_yaw)        plt.xlabel('X')        plt.ylabel('Y')        ax.legend()        ax.axis("equal")        ax.grid(True)        for i, p in enumerate(control_points):            ax.annotate(f'P{i:d}', xy=p, xytext=(0,5), textcoords='offset points', ha='center')        plt.show()if __name__ == '__main__':    main()

我怎样才能将这些注释添加到这个二次贝塞尔曲线中？

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