Time Sequence Animation

Animation control:

Visualization	Frame Value
Surface geometry	displacement parameter per frame
Surface position	fixed to the coordinate axis
Surface color	constant
Shading and highlighting	fixed to the coordinate axis
Axis coordinate	constant

Based on the static plot from the Surface Displacements in Cylindrical Coordinates example.

import numpy as np
from matplotlib import pyplot as plt
from matplotlib.animation import FuncAnimation
import matplotlib.animation as animation
import s3dlib.surface as s3d
import s3dlib.cmap_utilities as cmu

#.. Cylindrical Vibration Animation

# 1. Define functions to examine ....................................

n,m = 3,3
Um, Vm, Wm = 0.2, 0.1, 0.1
cyLen = 2.5

def displacements(rtz,time) :
    r,t,z = rtz
    eit = np.cos(2*np.pi*time)
    Z = np.pi*z/2
    u = Um*np.cos(n*t)*np.cos(m*Z)*eit
    v = Vm*np.sin(n*t)*np.sin(m*Z)*eit
    w = Wm*np.cos(n*t)*np.sin(m*Z)*eit
    return [u, v, w] 

def newCoor(rtz,time) :
    r,t,z = rtz
    u, v, w = displacements(rtz,time)
    R = r + u  
    T = t + v/r  # small angle displacements:  v ~ r*dt
    Z = z + w
    return R,T,Z

# 2. Setup and map surfaces .........................................
start_time = 0
rez = 5
cboard = cmu.rgb_cmap_gradient([0.25,0.15,0], [1,.9,.75], 'cardboard' )

cylinder = s3d.CylindricalSurface(rez,basetype='tri')
cylinder.map_geom_from_op(lambda rtz : newCoor(rtz, start_time ) )
cylinder.transform(s3d.eulerRot(0,40), scale=[1,1,cyLen])
cylinder.map_cmap_from_normals( 'cardboard' ).shade(0.8)

# 3. Construct figure, add surfaces, and plot .....................

fig = plt.figure(figsize=plt.figaspect(1))
ax = plt.axes(projection='3d')
mnmx = [-1.8,1.8]
ax.set(xlim=mnmx, ylim=mnmx, zlim=mnmx )
ax.view_init(elev=10)
ax.set_axis_off()

ax.add_collection3d(cylinder)

fig.tight_layout()

# 4. Animation ......................................................

def init_fig():
    return cylinder,

def update_fig(frame):
    global cylinder
    ax.collections.remove(cylinder)

    cylinder = s3d.CylindricalSurface(rez,basetype='tri')
    cylinder.map_geom_from_op(lambda rtz : newCoor(rtz,frame ) )
    cylinder.transform(s3d.eulerRot(0,40), scale=[1,1,cyLen])
    cylinder.map_cmap_from_normals( 'cardboard' ).shade(0.8)

    ax.add_collection3d(cylinder)
    return cylinder,

ani = FuncAnimation(fig, update_fig, frames=np.linspace(0, 1, 40),
                    init_func=init_fig, blit=False, repeat=True, interval=100)

print(">>>>>>>>>>>>>>> Animation completed, file save proceeds")
#ani.save('ZZZ.mp4')                                   # use for movie file.
ani.save(None,writer=animation.FFMpegFileWriter())    # use for temp files.
print(">>>>>>>>>>>>>>> Save completed, screen display proceeds")
#plt.show()
print(">>>>>>>>>>>>>>> process completed")