在Matplotlib中繪製一個以飛機爲中心的實心圓柱體

Question

我在3d中將一個平面擬合到一束點上，並且最初使用np.meshgrid給它一個任意大小，但是現在我試圖繪製一個以該平面爲中心的圓柱體並以相同的方式定向（使平面擬合將圓柱體的高度減半），但是具有指定的半徑和高度。在matplotlib中繪製的圓柱體的唯一例子是空心的，通常在頂部和底部打開。我想要一個我打算堅實的人，這樣我就可以清楚地看到它所包含的點。

下面是隨機生成的飛機的最小工作示例。由於我使用的飛機總是由一個點和一個法線矢量給出，所以圓柱體應該基於這些東西（加上提供的半徑，以及在飛機上下延伸的高度）。

from __future__ import division #Enables new-style division 
import matplotlib.pyplot as plt 
from mpl_toolkits.mplot3d import Axes3D 
import seaborn as sns 
import numpy as np 

cen_x = 0 
cen_y = 0 
cen_z = 0 

origin = np.array([cen_x,cen_y,cen_z]) 

normal = np.array([np.random.uniform(-1,1),np.random.uniform(-1,1),np.random.uniform(0,1)]) 

a = normal[0] 
b = normal[1] 
c = normal[2] 

#equation for a plane is a*x+b*y+c*z+d=0 where [a,b,c] is the normal 
#so calculate d from the normal 
d = -origin.dot(normal) 

# create x,y meshgrid 
xx, yy = np.meshgrid(np.arange(cen_x-1,cen_x+1,0.01),np.arange(cen_y-1,cen_y+1,0.01)) 

# calculate corresponding z 
zz = (-a * xx - b * yy - d) * 1./c 

halo_x = [-0.3, -0.9, 0.8, 1.3, -0.1, 0.5] 
halo_y = [0.8, 1.1, -0.5, -0.7, -1.2, 0.1] 
halo_z = [1.0, -0.4, 0.3, -1.2, 0.9, 1.2] 

fig = plt.figure(figsize=(9,9)) 
plt3d = fig.gca(projection='3d') 
plt3d.plot_surface(xx, yy, zz, color='r', alpha=0.4) 
plt3d.set_xlim3d(cen_x-3,cen_x+3) 
plt3d.set_ylim3d(cen_y-3,cen_y+3) 
plt3d.set_zlim3d(cen_z-3,cen_z+3) 
plt3d.set_xlabel('X') 
plt3d.set_ylabel('Y') 
plt3d.set_zlabel('Z') 
plt.show() 

Answer 1

我已經修改解決一個問題How to add colors to each individual face of a cylinder using matplotlib，除去花式陰影和添加端蓋。如果您想要顯示封閉點，則可以使用alpha=0.5或其他類似的方法使圓柱半透明。

圓柱體的方向由長度爲mag的單位矢量v定義，該單位矢量v可以是表面的法線。

#!/usr/bin/env python2 
# -*- coding: utf-8 -*- 
""" 
Created on Sun Oct 2 18:33:10 2016 

Modified from https://stackoverflow.com/questions/38076682/how-to-add-colors-to-each-individual-face-of-a-cylinder-using-matplotlib 
to add "end caps" and to undo fancy coloring. 

@author: astrokeat 
""" 

import numpy as np 
from matplotlib import pyplot as plt 
from scipy.linalg import norm 

#axis and radius 
p0 = np.array([1, 3, 2]) #point at one end 
p1 = np.array([8, 5, 9]) #point at other end 
R = 5 

#vector in direction of axis 
v = p1 - p0 

#find magnitude of vector 
mag = norm(v) 

#unit vector in direction of axis 
v = v/mag 

#make some vector not in the same direction as v 
not_v = np.array([1, 0, 0]) 
if (v == not_v).all(): 
    not_v = np.array([0, 1, 0]) 

#make vector perpendicular to v 
n1 = np.cross(v, not_v) 
#normalize n1 
n1 /= norm(n1) 

#make unit vector perpendicular to v and n1 
n2 = np.cross(v, n1) 

#surface ranges over t from 0 to length of axis and 0 to 2*pi 
t = np.linspace(0, mag, 2) 
theta = np.linspace(0, 2 * np.pi, 100) 
rsample = np.linspace(0, R, 2) 

#use meshgrid to make 2d arrays 
t, theta2 = np.meshgrid(t, theta) 

rsample,theta = np.meshgrid(rsample, theta) 

#generate coordinates for surface 
# "Tube" 
X, Y, Z = [p0[i] + v[i] * t + R * np.sin(theta2) * n1[i] + R * np.cos(theta2) *  n2[i] for i in [0, 1, 2]] 
# "Bottom" 
X2, Y2, Z2 = [p0[i] + rsample[i] * np.sin(theta) * n1[i] + rsample[i] * np.cos(theta) * n2[i] for i in [0, 1, 2]] 
# "Top" 
X3, Y3, Z3 = [p0[i] + v[i]*mag + rsample[i] * np.sin(theta) * n1[i] + rsample[i] * np.cos(theta) * n2[i] for i in [0, 1, 2]] 


ax=plt.subplot(111, projection='3d') 
ax.plot_surface(X, Y, Z, color='blue') 
ax.plot_surface(X2, Y2, Z2, color='blue') 
ax.plot_surface(X3, Y3, Z3, color='blue') 

plt.show() 

其結果是：