By Vincent

2012-06-21 14:15:43 8 Comments

I search how to plot something with less instruction as possible with Matplotlib but I don't find any help for this in the documentation.

I want to plot the following things:

  • a wireframe cube centered in 0 with a side length of 2
  • a "wireframe" sphere centered in 0 with a radius of 1
  • a point at coordinates [0, 0, 0]
  • a vector that starts at this point and goes to [1, 1, 1]

How to do that?


@tash 2020-09-02 15:16:33

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_title('b-vectors on unit sphere')

@HYRY 2012-06-22 12:39:26

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')

# 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")


@Aritra 2017-01-26 13:44:19

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')

#draw the arrow

quiver can actually be used to plot multiple vectors at one go. The usage is as follows:- [ from]

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


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.

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