Python matplotlib（相等的单位长度）：具有“相等”纵横比的 z 轴不等于 x- 和 y-
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matplotlib (equal unit length): with 'equal' aspect ratio z-axis is not equal to x- and y-
提问by
When I set up equal aspect ratio for 3d graph the z-axis does not change to 'equal'. So, this:
当我为 3d 图形设置相等的纵横比时，z 轴不会更改为“相等”。所以这：
fig = pylab.figure()
mesFig = fig.gca(projection='3d', adjustable='box')
mesFig.axis('equal')
mesFig.plot(xC, yC, zC, 'r.')
mesFig.plot(xO, yO, zO, 'b.')
pyplot.show()
gives me the following:
给我以下内容：
where obviously the unit length of z-axis is not equal to x- and y-units.
其中显然 z 轴的单位长度不等于 x 和 y 单位。
How can I make the unit length of all three axes equal? All the solutions I could find did not work. Thank you.
如何使所有三个轴的单位长度相等？我能找到的所有解决方案都不起作用。谢谢你。
采纳答案by Remy F
I believe matplotlib does not yet set correctly equal axis in 3D... But I found a trick some times ago (I don't remember where) that I've adapted using it. The concept is to create a fake cubic bounding box around your data. You can test it with the following code:
我相信 matplotlib 还没有在 3D 中正确设置相等的轴......但我前段时间发现了一个技巧（我不记得在哪里），我已经适应了它。这个概念是在你的数据周围创建一个假的三次边界框。您可以使用以下代码对其进行测试：
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect('equal')
X = np.random.rand(100)*10+5
Y = np.random.rand(100)*5+2.5
Z = np.random.rand(100)*50+25
scat = ax.scatter(X, Y, Z)
# Create cubic bounding box to simulate equal aspect ratio
max_range = np.array([X.max()-X.min(), Y.max()-Y.min(), Z.max()-Z.min()]).max()
Xb = 0.5*max_range*np.mgrid[-1:2:2,-1:2:2,-1:2:2][0].flatten() + 0.5*(X.max()+X.min())
Yb = 0.5*max_range*np.mgrid[-1:2:2,-1:2:2,-1:2:2][1].flatten() + 0.5*(Y.max()+Y.min())
Zb = 0.5*max_range*np.mgrid[-1:2:2,-1:2:2,-1:2:2][2].flatten() + 0.5*(Z.max()+Z.min())
# Comment or uncomment following both lines to test the fake bounding box:
for xb, yb, zb in zip(Xb, Yb, Zb):
ax.plot([xb], [yb], [zb], 'w')
plt.grid()
plt.show()
z data are about an order of magnitude larger than x and y, but even with equal axis option, matplotlib autoscale z axis:
z 数据大约比 x 和 y 大一个数量级，但即使使用相等轴选项，matplotlib 自动缩放 z 轴：
But if you add the bounding box, you obtain a correct scaling:
但是，如果添加边界框，则会获得正确的缩放比例：
回答by tauran
I simplified Remy F's solution by using the set_x/y/zlimfunctions.
我通过使用set_x/y/zlim函数简化了 Remy F 的解决方案。
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect('equal')
X = np.random.rand(100)*10+5
Y = np.random.rand(100)*5+2.5
Z = np.random.rand(100)*50+25
scat = ax.scatter(X, Y, Z)
max_range = np.array([X.max()-X.min(), Y.max()-Y.min(), Z.max()-Z.min()]).max() / 2.0
mid_x = (X.max()+X.min()) * 0.5
mid_y = (Y.max()+Y.min()) * 0.5
mid_z = (Z.max()+Z.min()) * 0.5
ax.set_xlim(mid_x - max_range, mid_x + max_range)
ax.set_ylim(mid_y - max_range, mid_y + max_range)
ax.set_zlim(mid_z - max_range, mid_z + max_range)
plt.show()
回答by karlo
I like the above solutions, but they do have the drawback that you need to keep track of the ranges and means over all your data. This could be cumbersome if you have multiple data sets that will be plotted together. To fix this, I made use of the ax.get_[xyz]lim3d() methods and put the whole thing into a standalone function that can be called just once before you call plt.show(). Here is the new version:
我喜欢上述解决方案，但它们确实有一个缺点，即您需要跟踪所有数据的范围和均值。如果您将多个数据集绘制在一起，这可能会很麻烦。为了解决这个问题，我使用了 ax.get_[xyz]lim3d() 方法并将整个内容放入一个独立的函数中，该函数可以在调用 plt.show() 之前调用一次。这是新版本：
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import matplotlib.pyplot as plt
import numpy as np
def set_axes_equal(ax):
'''Make axes of 3D plot have equal scale so that spheres appear as spheres,
cubes as cubes, etc.. This is one possible solution to Matplotlib's
ax.set_aspect('equal') and ax.axis('equal') not working for 3D.
Input
ax: a matplotlib axis, e.g., as output from plt.gca().
'''
x_limits = ax.get_xlim3d()
y_limits = ax.get_ylim3d()
z_limits = ax.get_zlim3d()
x_range = abs(x_limits[1] - x_limits[0])
x_middle = np.mean(x_limits)
y_range = abs(y_limits[1] - y_limits[0])
y_middle = np.mean(y_limits)
z_range = abs(z_limits[1] - z_limits[0])
z_middle = np.mean(z_limits)
# The plot bounding box is a sphere in the sense of the infinity
# norm, hence I call half the max range the plot radius.
plot_radius = 0.5*max([x_range, y_range, z_range])
ax.set_xlim3d([x_middle - plot_radius, x_middle + plot_radius])
ax.set_ylim3d([y_middle - plot_radius, y_middle + plot_radius])
ax.set_zlim3d([z_middle - plot_radius, z_middle + plot_radius])
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect('equal')
X = np.random.rand(100)*10+5
Y = np.random.rand(100)*5+2.5
Z = np.random.rand(100)*50+25
scat = ax.scatter(X, Y, Z)
set_axes_equal(ax)
plt.show()
回答by dalum
EDIT:user2525140's code should work perfectly fine, although this answer supposedly attempted to fix a non--existant error. The answer below is just a duplicate (alternative) implementation:
编辑：user2525140 的代码应该可以正常工作，尽管这个答案据说试图修复一个不存在的错误。下面的答案只是一个重复的（替代）实现：
def set_aspect_equal_3d(ax):
"""Fix equal aspect bug for 3D plots."""
xlim = ax.get_xlim3d()
ylim = ax.get_ylim3d()
zlim = ax.get_zlim3d()
from numpy import mean
xmean = mean(xlim)
ymean = mean(ylim)
zmean = mean(zlim)
plot_radius = max([abs(lim - mean_)
for lims, mean_ in ((xlim, xmean),
(ylim, ymean),
(zlim, zmean))
for lim in lims])
ax.set_xlim3d([xmean - plot_radius, xmean + plot_radius])
ax.set_ylim3d([ymean - plot_radius, ymean + plot_radius])
ax.set_zlim3d([zmean - plot_radius, zmean + plot_radius])
回答by Mateen Ulhaq
Adapted from @karlo's answer to make things even cleaner:
改编自@karlo 的回答，让事情变得更干净：
def set_axes_radius(ax, origin, radius):
ax.set_xlim3d([origin[0] - radius, origin[0] + radius])
ax.set_ylim3d([origin[1] - radius, origin[1] + radius])
ax.set_zlim3d([origin[2] - radius, origin[2] + radius])
def set_axes_equal(ax):
'''Make axes of 3D plot have equal scale so that spheres appear as spheres,
cubes as cubes, etc.. This is one possible solution to Matplotlib's
ax.set_aspect('equal') and ax.axis('equal') not working for 3D.
Input
ax: a matplotlib axis, e.g., as output from plt.gca().
'''
limits = np.array([
ax.get_xlim3d(),
ax.get_ylim3d(),
ax.get_zlim3d(),
])
origin = np.mean(limits, axis=1)
radius = 0.5 * np.max(np.abs(limits[:, 1] - limits[:, 0]))
set_axes_radius(ax, origin, radius)
Usage:
用法：
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect('equal') # important!
# ...draw here...
set_axes_equal(ax) # important!
plt.show()
