Pandas Read CSV and animate the data

Introduction

Use Python and Pandas.

Read CSV data, filter, interpolate and smooth it, and the animate the plotting. The file is File:Convergence dataOnly.csv.

Size			10	15	20	40	50	100	500	1000	1500	3000	3000
Nodes	n		560842	240807	172644	110324	103903	101052	100919	138706	100919	77741	69092
Triangles	n		140118	70994	48044	28684	26868	26024	25948	29970	25948	23230	22232
Tetrahedrons	n		313370	126061	92463	60451	57002	55513	55480	80746	55480	40067	34291
Displacement magnitude	max	mm	0	0	0	0	0	0	0	0	0	0	0
Displacement magnitude	min	mm	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2
Displacement X	max	um	-31.59	-31.59	-31.59	-31.59	-31.56	-31.46	-31.47	-31.32	-31.47	-31.33	-30.91
Displacement X	min	um	1.45	1.45	1.45	1.45	1.44	1.43	1.42	1.46	1.42	1.37	1.28
Displacement Y	max	um	-12.69	-12.69	-12.69	-12.69	-12.68	-12.67	-12.67	-12.69	-12.67	-12.64	-12.57
Displacement Y	min	um	16.03	16.03	16.03	16.03	16.03	16.01	16	15.98	16	16.01	16.1
Displacement Z	max	mm	-0.2	-0.2	-0.2	-0.2	-0.2	-0.2	-0.2	-0.2	-0.2	-0.2	-0.2
Displacement Z	min	um	1.8	1.8	1.8	1.8	1.8	1.81	1.81	1.81	1.81	1.77	1.71
von Mises Stress	max	kPa	0	0	0	0	0	0	0	0	0	0	0
von Mises Stress	min	kPa	1281.81	1281.81	1281.81	1281.81	1297.14	1311.81	1286.65	1250	1286.65	1273.95	1282.35
Max Principal Stress	max	kPa	-176.22	-176.22	-176.22	-176.22	-172.74	-172.69	-171.95	-184.54	-171.95	-169.48	-180.97
Max Principal Stress	min	kPa	967.43	967.43	967.43	967.43	1014.52	955.45	1085.01	1140.49	1085.01	798.06	754.78
Min Principal Stress	max	kPa	-1345.87	-1345.87	-1345.87	-1345.87	-1358.44	-1343.18	-1306.44	-1295.94	-1306.44	-1325.73	-1359.73
Min Principal Stress	min	kPa	109.99	109.99	109.99	109.99	108.23	114.84	115.2	126.83	115.2	106.69	119.98
Max Shear Stress	max	kPa	0	0	0	0	0	0	0	0	0	0	0
Max Shear Stress	min	kPa	648.93	648.93	648.93	648.93	658.46	663.91	654.4	628.53	654.4	647.25	647.95

Read and Interpolate

• 

  Interpolated data

• 

  Original, non-interpolated data

import matplotlib.pyplot as plt
import pandas  as pd
import numpy as np

#Read, transpose, sort, drop and set the index to be the number of tetrahedrons
#and drop the columns with zero values and some parameters
df = pd.read_csv("convergence_dataOnly.csv" ).T
df.columns = ( df.iloc[0] + " " + df.iloc[1] )
df = df[3:].sort_values("Tetrahedrons n")
df.set_index("Tetrahedrons n", inplace=True)
df = df.drop('Displacement magnitude max', axis=1)
df = df.drop('von Mises Stress max', axis=1)
df = df.drop('Max Shear Stress max', axis=1)
df = df.drop('Nodes n', axis=1)
df = df.drop('Triangles n', axis=1)

#Convert values and index to numeric
df= df.apply(pd.to_numeric)
df.index = pd.to_numeric( df.index, errors='coerce' )

# Interpolate # Need to drop the one with the same number of tetrahedrons
mask = np.ones( len(df), dtype=bool)
mask[2] = False
df = df[mask]

#Get the percentage
df = df.divide( df.iloc[9] )
print(df)

df_i = df.reindex(df.index.union(np.linspace(df.index.min(),df.index.max(), df.index.shape[0]*10)))  # insert 10 NaN points between existing ones
df_i = df_i.interpolate('pchip', order=2)  # fill the gaps with values
df_i.plot( legend=False)  # draw new Dataframe

Animate the data

Images to GIF

Reverse the layers: From the main menu through Layers → Stack → Reverse Layer Order.

Animate 1 line updating

Click the image to see the animation

This tutorial was found on https://docs.kanaries.net/topics/Matplotlib/matplotlib-animation.

from matplotlib.animation import FuncAnimation

x = df_i.index.to_numpy()
y = df_i["Max Shear Stress min"].to_numpy()
xdata, ydata = [], []

fig, ax = plt.subplots()
fig.set_size_inches( 10/2.54, 20/2.54  )
ax.set(xlim=(0, max(x)), ylim=(.8, 1.2))
line = ax.plot( [], [], color='r', lw=2)[0]

def animate(i):
    xdata.append( x[i] )
    ydata.append( y[i] )
    line.set_data( xdata, ydata )
    plt.savefig("image{i}.png".format(i=i), dpi=300 )
    return line

anim = FuncAnimation(fig, animate, frames=x.size, interval=100, repeat=False)
plt.show()

Animate N lines updating

Click the image to see the animation.

Animation is easy, once you find the correct tutorial.

from matplotlib.animation import FuncAnimation

x = df_i.index.to_numpy()
y = df_i.to_numpy()

fig, ax = plt.subplots()
ax.set(xlim=(0, max(x)), ylim=(.7, 1.3))
lines = ax.plot(np.empty((0, y.shape[1])), np.empty((0, y.shape[1])), lw=2)

def animate(i):
    for line_k, y_k in zip(lines, y.T):
        line_k.set_data(x[:i], y_k[:i])
    plt.savefig("image{i}.png".format(i=1), dpi=50 )
    return lines

anim = FuncAnimation(fig, animate, frames=x.size, interval=100, repeat=False)
plt.show()

Animate x + t dimensional

Brushing Up Science demonstrates many beautiful animation procedures. This is one (https://brushingupscience.com/2016/06/21/matplotlib-animations-the-easy-way/):

fig, ax = plt.subplots(figsize=(5, 3))
ax.set(xlim=(-3, 3), ylim=(-1, 1))

x = np.linspace(-3, 3, 91)
t = np.linspace(1, 25, 30)
X2, T2 = np.meshgrid(x, t)

sinT2 = np.sin(2*np.pi*T2/T2.max())
F = 0.9*sinT2*np.sinc(X2*(1 + sinT2))

line = ax.plot(x, F[0, :], color='k', lw=2)[0]

def animate(i):
    line.set_ydata(F[i, :])

anim = FuncAnimation( fig, animate, interval=100, frames=len(t)-1 )

plt.draw()
plt.show()

Animate 2

Add the new points in the update function. The clear command clears everything, so this in not very neat.

from random import randint

import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

# create empty lists for the x and y data
x = []
y = []

# create the figure and axes objects
fig, ax = plt.subplots()


def animate(i):
    pt = randint(1,9) # grab a random integer to be the next y-value in the animation
    x.append(i)
    y.append(pt)
    ax.clear()
    ax.set_xlim([0,20])
    ax.set_ylim([0,10])
    ax.plot(x,y)

# run the animation
ani = FuncAnimation(fig, animate, frames=20, interval=100, repeat=False)

plt.show()

Animate Bar Graphs

Try easings functions to get a nice bounce or elastic effect; https://gist.github.com/robweychert/7efa6a5f762207245646b16f29dd6671 ; https://easings.net/ https://robertpenner.com/easing/ or pypi Easings (https://pypi.org/project/easing-functions/).

Use virtual engine

The virtual engine is used because of the easing functions. However, it requires installing the other packages too.

python -m venv .
source bin/activate
pip install easing-functions
pip install numpy
pip install pandas
pip install matplotlib

Read the data and set variables

Import the packages. The data is csv ( File:FEM results.csv, from [1]), but a slightly modified (the two top rows are combined compared to the original at FEM and Blender page). The index is set, and title depicts which column is used.

the names depict which columns are to be plotted. Equally, the idxs variable contains the corresponding indexes. Setting those could be automated, but I didn't do that.

from matplotlib import pyplot as plt
from matplotlib import animation
from easing_functions import *
import numpy as np
import pandas  as pd

fig, ax = plt.subplots()

df = pd.read_csv("FEM_results.csv" )
df.set_index( df["Design"], inplace=True  )
df.drop( ["Design"], axis=1, inplace=True )
title = "Max Shear Stress Max [kPa]"
dmax = df[title]

colors = ['#442b48', '#726e60', '#98b06f', '#b6dc76', '#dbff67']
idxs = [5, 6, 7, 8, 9]
names = ['No Rafters\n + Roof', '22.5° rafter \n+ Roof', '22.5° × 2 \nrafters + Roof', '45° rafter\n short + Roof', '45° rafter \nlong + Roof']

Dps = 100

Make the bouncing scheme

The X matrix (array) will contain the animation steps for all idxs. The easing functions are designed such that the input of the functions is $[0,1]$, and thus x is a variable containing the corresponding floating point numbers. The easing functions input the beginning and the end position of the y values. The duration is set to one, 1.

X = np.zeros( (len(names), Dps)  )
x = np.linspace(0, 1, Dps)
for i,j in enumerate(idxs):
    a = BounceEaseOut(start=0, end=dmax.iloc[j], duration=1)
    X[i] = list( map( a,x ) )

Animate the data

The animation is simple and follows directly the manual given at https://matplotlib.org/stable/users/explain/animations/animations.html. We use the artist which will contain all the animation data at all timesteps. Thus, we will have a precomputed list of images.

artists = []
for i in range( Dps ):
    container = ax.bar( names, X[:,i], color=colors )
    artists.append( container )

ani = animation.ArtistAnimation(fig=fig, artists=artists, interval=10, repeat=False)
plt.title( title )
plt.show()

Save the animation

The animation can be saved. GIF (and mp4) format is easy:

f = (title+".gif").replace(" ", "")
writergif = animation.PillowWriter(fps=30)
ani.save(f, writer=writergif)

but png is giving some troubles. Thus, save it in gif and convert using Imagemagick's converto to pngs

magick convert -coalesce image.gif image.png