在Matplotlib中绘制一个以飞机为中心的实心圆柱体

Question

我在3d中将一个平面拟合到一束点上，并且最初使用np.meshgrid给它一个任意大小，但是现在我试图绘制一个以该平面为中心的圆柱体并以相同的方式定向（使平面拟合将圆柱体的高度减半），但是具有指定的半径和高度。在matplotlib中绘制的圆柱体的唯一例子是空心的，通常在顶部和底部打开。我想要一个我打算坚实的人，这样我就可以清楚地看到它所包含的点。

下面是随机生成的飞机的最小工作示例。由于我使用的飞机总是由一个点和一个法线矢量给出，所以圆柱体应该基于这些东西（加上提供的半径，以及在飞机上下延伸的高度）。

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

我已经修改解决一个问题How to add colors to each individual face of a cylinder using matplotlib，除去花式阴影和添加端盖。如果您想要显示封闭点，则可以使用alpha=0.5或其他类似的方法使圆柱半透明。

圆柱体的方向由长度为mag的单位矢量v定义，该单位矢量v可以是表面的法线。

#!/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() 

其结果是：