在 Matplotlib 绘制一个3 d 立方体、一个球体和一个矢量

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最佳答案

It is a little complicated, but you can draw all the objects by the following code:

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
from itertools import product, combinations




fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect("equal")


# draw cube
r = [-1, 1]
for s, e in combinations(np.array(list(product(r, r, r))), 2):
if np.sum(np.abs(s-e)) == r[1]-r[0]:
ax.plot3D(*zip(s, e), color="b")


# draw sphere
u, v = np.mgrid[0:2*np.pi:20j, 0:np.pi:10j]
x = np.cos(u)*np.sin(v)
y = np.sin(u)*np.sin(v)
z = np.cos(v)
ax.plot_wireframe(x, y, z, color="r")


# draw a point
ax.scatter([0], [0], [0], color="g", s=100)


# draw a vector
from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d




class Arrow3D(FancyArrowPatch):


def __init__(self, xs, ys, zs, *args, **kwargs):
FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)
self._verts3d = xs, ys, zs


def draw(self, renderer):
xs3d, ys3d, zs3d = self._verts3d
xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
FancyArrowPatch.draw(self, renderer)


a = Arrow3D([0, 1], [0, 1], [0, 1], mutation_scale=20,
lw=1, arrowstyle="-|>", color="k")
ax.add_artist(a)
plt.show()

output_figure

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For drawing just the arrow, there is an easier method:-

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect("equal")


#draw the arrow
ax.quiver(0,0,0,1,1,1,length=1.0)


plt.show()

quiver can actually be used to plot multiple vectors at one go. The usage is as follows:- [ from http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html?highlight=quiver#mpl_toolkits.mplot3d.Axes3D.quiver]

quiver(X, Y, Z, U, V, W, **kwargs)

Arguments:

The x, y and z coordinates of the arrow locations

The x, y and z components of the arrow vectors

The arguments could be array-like or scalars.

Keyword arguments:

length: [1.0 | float] The length of each quiver, default to 1.0, the unit is the same with the axes

arrow_length_ratio: [0.3 | float] The ratio of the arrow head with respect to the quiver, default to 0.3

pivot: [ ‘tail’ | ‘middle’ | ‘tip’ ] The part of the arrow that is at the grid point; the arrow rotates about this point, hence the name pivot. Default is ‘tail’

normalize: [False | True] When True, all of the arrows will be the same length. This defaults to False, where the arrows will be different lengths depending on the values of u,v,w.

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My answer is an amalgamation of the above two with extension to drawing sphere of user-defined opacity and some annotation. It finds application in b-vector visualization on a sphere for magnetic resonance image (MRI). Hope you find it useful:

from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt import numpy as np fig = plt.figure() ax = fig.gca(projection='3d') # draw sphere u, v = np.mgrid[0:2*np.pi:50j, 0:np.pi:50j] x = np.cos(u)*np.sin(v) y = np.sin(u)*np.sin(v) z = np.cos(v) # alpha controls opacity ax.plot_surface(x, y, z, color="g", alpha=0.3) # a random array of 3D coordinates in [-1,1] bvecs= np.random.randn(20,3) # tails of the arrows tails= np.zeros(len(bvecs)) # heads of the arrows with adjusted arrow head length ax.quiver(tails,tails,tails,bvecs[:,0], bvecs[:,1], bvecs[:,2], length=1.0, normalize=True, color='r', arrow_length_ratio=0.15) ax.set_xlabel('X-axis') ax.set_ylabel('Y-axis') ax.set_zlabel('Z-axis') ax.set_title('b-vectors on unit sphere') plt.show()