绘制锥体时断开连接的曲面

Question

我想用python绘制曲面（z + 1）²=x²+y²和4z =x²+y²。

我写了这段代码：

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')
X= np.arange(-2,3,.1)
Z=np.arange(0,2,.1)
X,Z = np.meshgrid(X,Z)
Y=np.sqrt((Z+1)**2-X**2)
Y2=np.sqrt(4*Z-X**2)
ax.plot_wireframe(X, Y, Z, rstride = 1, cstride =1)
ax.plot_wireframe(X, -Y, Z, rstride = 1, cstride =1)
ax.plot_surface(X,Y2,Z,rstride=1,cstride=1,color='red')
ax.plot_surface(X,-Y2,Z,rstride=1,cstride=1,color='red')
ax.set_zlim(0,2)

plt.show()

这必须显示两个锥体。但是，每个锥体都不是连续的，即有一些面缺失，我不知道为什么。非常感谢任何帮助。

Answer 1

你定义X和Y的方式在这些连接上引起了一些惊愕。通过在将半径和角度转换为X和Y之前定义锥体，可以获得更平滑的连接，这样就可以保持以旧方式生成的漂亮的Z轮廓。

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')

# Set up the grid in polar
theta = np.linspace(0,2*np.pi,90)
r = np.linspace(0,3,50)
T, R = np.meshgrid(theta, r)

# Then calculate X, Y, and Z
X = R * np.cos(T)
Y = R * np.sin(T)
Z = np.sqrt(X**2 + Y**2) - 1

# Set the Z values outside your range to NaNs so they aren't plotted
Z[Z < 0] = np.nan
Z[Z > 2.1] = np.nan
ax.plot_wireframe(X, Y, Z)

ax.set_zlim(0,2)

plt.show()

这会给你一个非常好的锥形：

Answer 2

您的曲面已损坏，因为您正在为每个圆锥绘制两个单独的曲面。使每个圆锥体成为完整，连续的表面而不中断的一种方法是制作x和y的网格，然后为每个圆锥体仅绘制单个表面：

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
xvec = np.arange(-2, 3, 0.1)
yvec = np.arange(-3, 3, 0.1)
X, Y = np.meshgrid(xvec, yvec)
Z1 = np.sqrt(X**2 + Y**2) - 1 
Z2 = (X**2 + Y**2)/4.
ax.plot_wireframe(X, Y, Z1, rstride=1, cstride=1)
ax.plot_surface(X, Y, Z2, rstride=1, cstride=1, color='red')
ax.set_zlim(0,2)
plt.show()

Answer 3

这太神秘了... 一般情况是

import numpy as np
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')


#xyz position of tip of cone, radius of the end of the cone, and height of the cone
radi = 4
height = 2
a=1 #x
b=1 #y
c=0 #z
choose=max(radi,height)


# Set up the grid in polar
theta = np.linspace(0,2*np.pi,90)
r = np.linspace(0,choose,50)
T, R = np.meshgrid(theta, r)

# Then calculate X, Y, and Z
X = R * np.cos(T) + a
Y = R * np.sin(T) + b
Z = (np.sqrt((X-a)**2 + (Y-b)**2)/(radi/height)) + c

ax.plot_wireframe(X, Y, Z)

ax.set_zlim(-1.2,2.2)

plt.show()