在Matplotlib中绘制一个以平面为中心的实心圆柱体

Question

我将一个平面拟合到3d中的一堆点并且最初使用np.meshgrid给它任意大小，但是现在我试图绘制一个以该平面为中心的圆柱并以相同的方式定向（这样的平面fit会将圆柱体的高度减半，但具有指定的半径和高度。在matplotlib中绘制的唯一圆柱示例我可以找到它是空心的，通常在顶部和底部开放。我希望我绘制的那个是坚实的，所以我可以清楚地看到它附带的内容。

这是一个随机生成平面的最小工作示例。由于我使用的平面总是由一个点和一个法向矢量给出，所以圆柱体也应该基于这些东西（加上提供的半径，以及在平面上方和下方延伸的高度）。

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

我修改了问题How to add colors to each individual face of a cylinder using matplotlib的解决方案，删除了花哨的阴影并添加了端盖。如果要显示所包含的点，可以使用alpha=0.5或其他一些来使圆柱体半透明。

圆柱体的方向由单位矢量v定义，长度为mag，可能是表面的法线。

#!/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()

结果：