Plotting a 3d cube, a sphere and a vector in Matplotlib
Solution 1:
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()
Solution 2:
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:
X, Y, Z: The x, y and z coordinates of the arrow locations
U, V, W: 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.
Solution 3:
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()