Vector Magnitude within a Domain

Animation control:

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

This example illustrates the magnitude of a vector field within a domain, as also shown in the static Vector Surfaces example for constant values.

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

# 0. Define animation control parameters ............................

totalTime, f_domain, numFrames = 10, (0.0,1.0), 101   # time in seconds
frames=np.linspace(*f_domain, numFrames, endpoint=True)
interval = int(1000.0*totalTime/numFrames)            # milliseconds

# 1. Define function to examine ....................................

def vector_mag(xyz) :
    x,y,z = xyz
    u =    np.sin(np.pi*x) * np.cos(np.pi*z)
    v = -2*np.sin(np.pi*y) * np.cos(2*np.pi*z)
    w = np.cos(np.pi*x)*np.sin(np.pi*z) + np.cos(np.pi*y)*np.sin(2*np.pi*z)
    vect = np.array([u,v,w]).T
    return np.linalg.norm(vect,axis=3).T

def frame_to_vals(f,cloud,zeta=0.85) :
    min_cldV, max_cldV = cloud.bounds['vlim']
    del_cldV = max_cldV - min_cldV
    mid_cldV = (max_cldV + min_cldV)/2
    frame_to_A = lambda t : 2*t if t<.5 else 2*(1-t)  # 0 <= A <= 1
    A = frame_to_A(f)
    A_to_Fo = lambda A : (A-.5)*zeta*del_cldV + mid_cldV
    A_to_cB = lambda A : zeta*A + (1-zeta)/2
    return A_to_cB(A), A_to_Fo(A)

def indicator_by_A(fig, A, vOld=None) :
    '''   0 <= A <= 1 '''
    symbol, blank = r'$\blacktriangleright$', r'$\blacksquare$'
    horz, vBot, vRng = 0.80, 0.22, 0.56
    horz, vBot, vRng = 0.825, 0.22, 0.56
    vert = vBot + vRng*A
    bkgrd = fig.get_facecolor()
    if vOld is not None: #.. cover current indicator with a blank symbol before showing indicator.
        fig.text(horz,vOld,blank, ha='right', va='center', fontsize='x-large', color=bkgrd)
    fig.text(horz,vert,symbol, ha='right', va='center', fontsize='large', color='k')
    return vert

# 2. Setup and map surfaces .........................................
domain = [ [0,1], [0,1], [0,1]  ]
xlim,ylim,zlim = domain
drez, cmap = 5, cmu.hue_cmap('b','r',2.0,name='BlRd')

cloudObj = ptc.Point3DCloud(drez, domain=domain)
cloudObj.map_vals_from_op(vector_mag)
cloudObj.map_cmap_from_cloudvals(cmap)

t=.25
vbar,Vo = frame_to_vals(t,cloudObj)
surface = cloudObj.valsurf(Vo)

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

fig = plt.figure(figsize=(5,4))
fig.text(.5,0.9,'Magnitude',ha='center')
ax = fig.add_subplot(111, projection='3d', aspect='equal', focal_length=0.25)
ax.view_init(0,-120)
ax.set(xlim=xlim, ylim=ylim, zlim=zlim, xlabel='x',ylabel='y',zlabel='z')

prevIndicator = indicator_by_A(fig, vbar)
surface = surface.shade(.4,ax=ax).hilite(.5,ax=ax)
ax.add_collection3d(surface)
s3d.add_boxCorner(ax,domain)

cbar =fig.colorbar(cloudObj.cBar_ScalarMappable, ax=ax,shrink=0.6, pad=.12)
cbar.set_label('cloud values', rotation=270, labelpad = 15)

fig.tight_layout(pad=1)
plt.show()
# 4. Animation ======================================================

def update_fig(frame):
    global surface,prevIndicator
    surface.remove()
    
    vbar,Vo = frame_to_vals(frame,cloudObj)
    surface = cloudObj.valsurf(Vo)
    prevIndicator = indicator_by_A(fig, vbar, prevIndicator)
    surface.shade(.4,ax=ax).hilite(.5,ax=ax)
    ax.add_collection3d(surface)

    return

anim = FuncAnimation(fig, update_fig, frames, interval=interval, repeat=True)
anim.save('anim_vmag.html',writer='html')

msg = "saved {} frames, values: [{:.3f} to {:.3f}] @ {} milliseconds/frane"
print(msg.format(numFrames,np.min(frames),np.max(frames),interval))

print('DONE')