python matplotlib：用圆周绘制3D球体

Question

我正在尝试使用matplotlib绘制一个像这样的球体：

但我找不到背面有虚线的方法，垂直圆周看起来有点奇怪

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure(figsize=(12,12), dpi=300)
ax = fig.add_subplot(111, projection='3d')
ax.set_aspect('equal')

u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)

x = 1 * np.outer(np.cos(u), np.sin(v))
y = 1 * np.outer(np.sin(u), np.sin(v))
z = 1 * np.outer(np.ones(np.size(u)), np.cos(v))
#for i in range(2):
#    ax.plot_surface(x+random.randint(-5,5), y+random.randint(-5,5), z+random.randint(-5,5),  rstride=4, cstride=4, color='b', linewidth=0, alpha=0.5)

ax.plot_surface(x, y, z,  rstride=4, cstride=4, color='b', linewidth=0, alpha=0.5)
ax.plot(np.sin(theta),np.cos(u),0,color='k')
ax.plot([0]*100,np.sin(theta),np.cos(u),color='k')

Answer 1

在你展示的例子中，我不认为圆圈可以彼此垂直（即一个是赤道，一个穿过北极和南极）。如果水平圆是赤道，则北极必须位于通过代表球体的黄色圆圈中心绘制的垂直线上的某个位置。否则，赤道右侧看起来比左侧更高或更低。但是，表示极坐标圆的椭圆仅穿过黄色圆圈顶部和底部的中心线。因此，北极位于球体的顶部，这意味着我们必须直视赤道，这意味着它应该看起来像一条线，而不是一条椭圆。

这里有一些代码可以重现与您发布的图形类似的内容：

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_aspect('equal')

u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)

x = 1 * np.outer(np.cos(u), np.sin(v))
y = 1 * np.outer(np.sin(u), np.sin(v))
z = 1 * np.outer(np.ones(np.size(u)), np.cos(v))
#for i in range(2):
#    ax.plot_surface(x+random.randint(-5,5), y+random.randint(-5,5), z+random.randint(-5,5),  rstride=4, cstride=4, color='b', linewidth=0, alpha=0.5)
elev = 10.0
rot = 80.0 / 180 * np.pi
ax.plot_surface(x, y, z,  rstride=4, cstride=4, color='b', linewidth=0, alpha=0.5)
#calculate vectors for "vertical" circle
a = np.array([-np.sin(elev / 180 * np.pi), 0, np.cos(elev / 180 * np.pi)])
b = np.array([0, 1, 0])
b = b * np.cos(rot) + np.cross(a, b) * np.sin(rot) + a * np.dot(a, b) * (1 - np.cos(rot))
ax.plot(np.sin(u),np.cos(u),0,color='k', linestyle = 'dashed')
horiz_front = np.linspace(0, np.pi, 100)
ax.plot(np.sin(horiz_front),np.cos(horiz_front),0,color='k')
vert_front = np.linspace(np.pi / 2, 3 * np.pi / 2, 100)
ax.plot(a[0] * np.sin(u) + b[0] * np.cos(u), b[1] * np.cos(u), a[2] * np.sin(u) + b[2] * np.cos(u),color='k', linestyle = 'dashed')
ax.plot(a[0] * np.sin(vert_front) + b[0] * np.cos(vert_front), b[1] * np.cos(vert_front), a[2] * np.sin(vert_front) + b[2] * np.cos(vert_front),color='k')

ax.view_init(elev = elev, azim = 0)


plt.show()