How to update 3D arrow animation in matplotlib

Question

I am trying to reproduce the left plot of this animation in python using matplotlib.

I am able to generate the vector arrows using the 3D quiver function, but as I read here, it does not seem possible to set the lengths of the arrows. So, my plot does not look quite right:

So, the question is: how do I generate a number of 3D arrows with different lengths? Importantly, can I generate them in such a way so that I can easily modify for each frame of the animation?

Here's my code so far, with the not-so-promising 3D quiver approach:

import numpy as np
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d.axes3d

ax1 = plt.subplot(111,projection='3d')

t = np.linspace(0,10,40)

y = np.sin(t)
z = np.sin(t)
line, = ax1.plot(t,y,z,color='r',lw=2)

ax1.quiver(t,y,z, t*0,y,z)
plt.show() 

Answer 1

Another solution is to call ax.quiever on each arrow, individually - with each call having an own length attribute. This is not very efficient but it will get you going.

And there's no need to change MPL-code

Answer 2

As Azad suggests, an inelegant, but effective, solution is to simply edit the mpl_toolkits/mplot3d/axes3d.py to remove the normalization. Since I didn't want to mess with my actual matplotlib installation, I simply copied the axes3d.py file to the same directory as my other script and modified the line

norm = math.sqrt(u ** 2 + v ** 2 + w ** 2)

to

norm = 1

(Be sure to change the correct line. There is another use of "norm" a few lines higher.) Also, to get axes3d.py to function correctly when it's outside of the mpl directory, I changed

from . import art3d
from . import proj3d
from . import axis3d

to

from mpl_toolkits.mplot3d import art3d
from mpl_toolkits.mplot3d import proj3d
from mpl_toolkits.mplot3d import axis3d

And here is the nice animation that I was able to generate (not sure what's going wrong with the colors, it looks fine before I uploaded to SO).

And the code to generate the animation:

import numpy as np
import matplotlib.pyplot as plt
import axes3d_hacked

ax1 = plt.subplot(111,projection='3d')
plt.ion()
plt.show()

t = np.linspace(0,10,40)

for index,delay in enumerate(np.linspace(0,1,20)):
    y = np.sin(t+delay)
    z = np.sin(t+delay)

    if delay > 0:
        line.remove()
        ax1.collections.remove(linecol)

    line, = ax1.plot(t,y,z,color='r',lw=2)
    linecol = ax1.quiver(t,y,z, t*0,y,z)

    plt.savefig('images/Frame%03i.gif'%index)
    plt.draw()

plt.ioff()
plt.show()

Now, if I could only get those arrows to look prettier, with nice filled heads. But that's a separate question...

EDIT: In the future, matplotlib will not automatically normalize the arrow lengths in the 3D quiver per this pull request.