我使用了一个技巧，使绘图过程更容易。
与绕x轴旋转不同，使用球坐标绕z轴旋转要容易得多。matplotlib具有利用球坐标绘制球的intuitive example。因此，我们可以交换轴（e）。例如，将2D图中的x轴视为3D图中的z轴），从给定的两个函数计算所需的球坐标，然后转换回笛卡尔用于绘图。
由于我们交换了坐标，最终我们必须旋转图并手动分配轴标签。

import matplotlib.pyplot as plt
import numpy as np
from typing import Tuple, Callable

fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(projection='3d')

# Define the function to rotate
def f(x):
    return x**2
def g(x):
    return (x-2)**2

def get_p(phi: np.ndarray, f: Callable, x0: float = 0) -> np.ndarray:
    """Get the distance p
    
    Let the origin be O and a line starting from O with its angle relative to
    x-axis being phi intersect with the curve y = f(x) at point Q, the distance
    p is the length of the line segment OQ.

    :param phi: the angle relative to x-axis
    :type phi: np.ndarray
    :param f: the curve to be rotated around its x-axis
    :type f: Callable
    :param x0: starting estimate of x-coord of intersection Q. Use this to
        control which intersection is desired. default to 0
    :type x0: optional, float
    :return: an array of distance, corresponding to each given phi
    :rtype: np.ndarray
    """
    ks = np.tan(phi)
    x = []
    for k in ks:
        func = lambda x : f(x) - k * x
        # we only look for one root
        x.append(scipy.optimize.fsolve(func, x0)[0])
    x = np.array(x)
    y = x * ks
    return np.sqrt(x**2 + y**2)

def get_xyz(
    theta: np.ndarray, phi: np.ndarray, p: np.ndarray,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """Produce the Cartesian coordinates from the given spherical coordinates.

    For reference, see: https://mathinsight.org/spherical_coordinates#:~:text=In%20summary%2C%20the%20formulas%20for,%CE%B8z%3D%CF%81cos%CF%95.

    :param theta: in the 3D coordinate, given its origin O, a point P and its
        projection Q on the XY plane, theta is the angle between line segment
        OQ and positive x-axis.
    :type theta: np.ndarray
    :param phi: using the same setup as described above, phi is the angle
        between line segment OP and positive z-axis
    :type phi: np.ndarray
    :param p: using the same setup as described above, p is the length of line
        segment OP.
    :type p: np.ndarray
    :return: the Cartesian coordinates converted from the spherical coordinates
        in the form of (x, y, z)
    :rtype: Tuple[np.ndarray, np.ndarray, np.ndarray]
    """
    return (
        np.outer(np.cos(theta), np.sin(phi) * p),
        np.outer(np.sin(theta), np.sin(phi) * p),
        np.outer(np.ones(np.size(theta)), np.cos(phi) * p),
    )

# Make data
theta = np.linspace(0, 2 * np.pi, 100)
phi_intercept = np.pi / 4  # the angle relative to x-axis when the two curves meet

# Plot y = x^2 half
phi2 = np.linspace(0, phi_intercept, 50)
p2 = get_p(phi2, f, x0=1)
ax.plot_surface(*get_xyz(theta, phi2, p2))

# Plot y = (x - 2)^2 half
phi1 = np.linspace(0, phi_intercept, 50)
p1 = get_p(phi1, g, x0=1)
ax.plot_surface(*get_xyz(theta, phi1, p1))

# Set plot properties
ax.set_box_aspect([1,1,1])
# x axis in the 2D plot becomes z here
ax.set_zlim(0, 2)
ax.set_zlabel('X')
# y axis in the 2D plot is still y here
ax.set_ylim(-1, 1)
ax.set_ylabel('Y')
# the new z axis after rotation becomes x here
ax.set_xlim(-1, 1)
ax.set_xlabel('Z')

# rotate the plot
ax.view_init(10, 0, -90)
plt.savefig('demo.png', dpi=100)