在Matplotlib中以平面为中心绘制实心圆柱 [英] Plotting a solid cylinder centered on a plane in Matplotlib
问题描述
我在3d中将平面拟合到一堆点上，并最初使用np.meshgrid为其赋予了任意大小，但是现在我试图绘制以该平面为中心并以相同方式定向的圆柱体（以使该平面fit会将圆柱体的高度减半），但具有指定的半径和高度。我可以找到在matplotlib中绘制的圆柱体的唯一示例是中空的，通常在顶部和底部都是敞开的。我希望绘制的图是实心的，这样我才能清楚地看到它所包围的点。
这是一个随机生成的平面的最小工作示例。由于我正在使用的平面始终由一个点和一个法线向量给定，因此圆柱体也应基于这些东西（加上提供的半径和高度，以在该平面的上方和下方延伸）。
__future__进口部门的 ＃启用新型部门
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
来源= 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 =普通[0]
b =普通[1]
c =普通[2]
＃一个平面的等式为a * x + b * y + c * z + d = 0，其中[a，b，c]是法线
＃因此请根据法线
d计算d = -origin.dot（正常）
＃创建x，y网格
xx，yy = np.meshgrid（np.arange（cen_x-1，cen_x + 1,0.01），np .arange（cen_y-1，cen_y + 1,0.01））
＃计算对应的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（）
我已修改问题的解决方案
I fit a plane to a bunch of points in 3d and initially gave it an arbitrary size using np.meshgrid, but now I'm trying to plot a cylinder centered on that plane and oriented the same way (such that the plane fit would cut the height of the cylinder in half), but with a specified radius and height. The only examples of cylinders plotted in matplotlib I can find are hollow and usually open at the top and bottom. I want the one I plot to be solid so I can clearly see what points it's enclosing.
Here's a minimum working example with a randomly generated plane. Since the plane I'm using is always given by a point and a normal vector, the cylinder should be based off of those things as well (plus a provided radius, and height to extend above and below the plane).
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()
I have modified a solution to a question How to add colors to each individual face of a cylinder using matplotlib, removing the fancy shading and adding end caps. If you want to show the enclosed points, you can use alpha=0.5 or some such to make the cylinder semi-transparent.
The orientation of the cylinder is defined by a unit vector v with length mag, which could be the normal to your surface.
#!/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()
The result:
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