# Time Sequence AnimationΒΆ

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])

# 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()

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])