贝塞尔曲线

Question

我有贝塞尔曲线，我需要根据这条曲线做旋转曲面。贝塞尔曲线应该绕着旋转轴旋转。怎么做？也许有些例子？点可以固定，但只有3个

import matplotlib as mpl
import numpy as np
from scipy.misc import comb
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import math
import pylab
def bernstein_poly(i, n, t):
    return comb(n, i) * (t**(n - i)) * (1 - t)**i


def bezier_curve(points, nTimes=1000):
    nPoints = len(points)
    xPoints = np.array([p[0] for p in points])
    yPoints = np.array([p[1] for p in points])
    zPoints = np.array([p[2] for p in points])

    t = np.linspace(0.0, 1.0, nTimes)

    polynomial_array = np.array(
        [bernstein_poly(i, nPoints - 1, t) for i in range(0, nPoints)])

    xvals = np.dot(xPoints, polynomial_array)
    yvals = np.dot(yPoints, polynomial_array)
    zvals = np.dot(zPoints, polynomial_array)

    return xvals, yvals, zvals

from math import pi ,sin, cos

def R(theta, u):


    return [[cos(theta) + u[0]**2 * (1-cos(theta)), 
             u[0] * u[1] * (1-cos(theta)) - u[2] * sin(theta), 
             u[0] * u[2] * (1 - cos(theta)) + u[1] * sin(theta)],
            [u[0] * u[1] * (1-cos(theta)) + u[2] * sin(theta),
             cos(theta) + u[1]**2 * (1-cos(theta)),
             u[1] * u[2] * (1 - cos(theta)) - u[0] * sin(theta)],
            [u[0] * u[2] * (1-cos(theta)) - u[1] * sin(theta),
             u[1] * u[2] * (1-cos(theta)) + u[0] * sin(theta),
             cos(theta) + u[2]**2 * (1-cos(theta))]]

def Rotate(pointToRotate, point1, point2, theta):


    u= []
    squaredSum = 0
    for i,f in zip(point1, point2):
        u.append(f-i)
        squaredSum += (f-i) **2

    u = [i/squaredSum for i in u]

    r = R(theta, u)
    rotated = []

    for i in range(3):
        rotated.append(round(sum([r[j][i] * pointToRotate[j] for j in range(3)])))

    return rotated

和主体部分

^{pr2}$

upd：我在这项任务上做了些什么。但这不是我想要的需要。现在它有很多线条，而不是表面。我想做个表面，但失败了

升级2： 这是我试图使革命浮出水面的尝试，但也失败了

^{3}$