Question

我有贝塞尔曲线，我需要根据该曲线制作旋转曲面。贝塞尔曲线应围绕旋转轴旋转。怎么做？也许有一些例子？点可以固定，但只能固定3

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

主要部分

if __name__ == "__main__":
nPoints = 3
points = [[0,0,0],[0,1,2],[0,2,1]]#3 points of curve
xvals, yvals, zvals = bezier_curve(points, nTimes=1000)
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot(xvals, yvals, zvals, label='bezier')

p1=[0,0,0]#axis of rotation
p2=[0,0,1]#axis of rotation

angle = pi/12

while angle <= 2*pi:
    pp1 = Rotate(points[0], p1, p2, angle)
    pp2 = Rotate(points[1], p1, p2, angle)
    pp3 = Rotate(points[2], p1, p2, angle)
    npoints=[pp1,pp2,pp3]
    xnvals, ynvals, znvals = bezier_curve(npoints, nTimes=1000)
    ax.plot(xnvals, ynvals, znvals, label='bezier')
    angle= angle + pi/24

plt.show()

upd：我在这项任务上做了一些事情。但这并不是我真正需要的，现在有很多行，而不是表面。我试图做一个表面，但是失败了

Upd2：这是我尝试进行革命的尝试，但也失败了

x = np.arange (0, 0.1, 0.005)
y = np.arange (0, 0.1, 0.005)
xgrid, ygrid = np.meshgrid(x, y)
points = [[0,0,0],[0,1,2],[0,2,1]] #Bezier curve points

p1=[0,0,0]#axis of rotation
p2=[0,0,1]#axis of rotation

angle = pi/12

xval, yval, zval = bezier_curve(points, nTimes=20)

x=xgrid
y=ygrid
z=zval

fig = pylab.figure()
axes = Axes3D(fig)

axes.plot_surface(x, y, z)


while angle <= 2*pi:
    pp1 = Rotate(points[0], p1, p2, angle)
        pp2 = Rotate(points[1], p1, p2, angle)
        pp3 = Rotate(points[2], p1, p2, angle)
        npoints=[pp1,pp2,pp3]

    x = np.arange (0, 0.1, 0.005)
    y = np.arange (0, 0.1, 0.005)
    xgrid, ygrid = np.meshgrid(x, y)

    xval, yval, zval = bezier_curve(npoints, nTimes=20)
    zgrid= zval
    x=xgrid
    y=ygrid
    z=zgrid
    axes.plot_surface(x, y, z)
    angle= angle + pi/24

贝塞尔曲线曲面

0 个答案: