Bezier curve surface

Question

I have Bezier curve and I need to make surface of revolution based on this curve. Bezier curve should be rotating around an axis of rotation. How it can be done? Maybe some examples? Dots can be fixed, but only 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

And main part

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: I do something on this task. But this is not exactly what I need.Now its many lines, not surface. I tried to make a surface, but failed

Upd2: This is my attempt to make surface of revolution, but its failed too

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

Copy-rotate your coordinates about whatever axis vector you want, and then construct your surface as a quad surface using the vertices that generates? — Mike 'Pomax' Kamermans, Nov 20 '18 at 18:19
@mike-pomax-kamermans, yeah)) I know it too, but i cant do it — Ильшат Мурзурбеков, Nov 25 '18 at 12:13
What do you mean you know it but you can't do it? Either you know it, and then you know how to do it (or you know how to look up how to do it, there's even wikipedia articles about 3D rotations), or you don't know it, in which case step one is look up how to do it and then as last resort when you absolutely can't find anything, ask on SO. If you have no idea how to get started, then read through https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle and the article around it, but finding a python package to do this for you is probably less work. — Mike 'Pomax' Kamermans, Nov 25 '18 at 16:25
@mike-pomax-kamermans I updated my post. I have some problems with surface based on this curve — Ильшат Мурзурбеков, Nov 25 '18 at 17:41
If you have all the coordinates, surely SO always has the answer for you over on https://stackoverflow.com/a/38946791/740553, which you can easily find by searching for something like "python define 3d bezier surface"? — Mike 'Pomax' Kamermans, Nov 25 '18 at 17:58
@mike-pomax-kamermans sorry but I cant see surface there. Only 2d plots — Ильшат Мурзурбеков, Nov 26 '18 at 16:22
Okay but at this point you have all the data, you need to plot them in 3d: this is _definitely_ a solved problem on SO and Google. Take your data, generate any missing vertices if they make the difference, and throw that at https://plot.ly/python/3d-surface-plots, and you're on your way (after reading its documentation of course). Or any other 3d plotting library for Python? — Mike 'Pomax' Kamermans, Nov 26 '18 at 16:52
Thank you for your time, but i have google, and i saw all this things — Ильшат Мурзурбеков, Nov 26 '18 at 17:17
Then you need to update your post: did you try it? Because if you did, it should have worked, and if it didn't work, [you need to tell people what you already tried](/help/how-to-ask) because no one wants to keep asking questions in a comment thread just to get the information necessary to help you piece by piece. — Mike 'Pomax' Kamermans, Nov 27 '18 at 00:15
Thanks. I notice that doesn't use pandas in any way, so: did you try https://plot.ly/python/3d-surface-plots? — Mike 'Pomax' Kamermans, Nov 28 '18 at 15:55
@mike-pomax-kamermans, To be honest I could not understand how I can use it — Ильшат Мурзурбеков, Nov 28 '18 at 16:21

Bezier curve surface

0 Answers0