Scene Building With Plots

One can distingish between two kinds of plots:

• Quantitative scientific plots with numbers and dimensions to describe data (e.g. made with matplotlib).

• Qualitative explanatory plots that convey a message in the clearest way possible (e.g. made with manim)

In this tutorial, I will take you on a journey from choosing a topic to making a scientific plot to then transforming it into an explanatory plot with manim:

Formulating a Quantitative Concept

First, we do research on our topic of choice and then look up the formulas that we need. Alternatively, one can search for existing implementations.

I chose the carnot process where I want to see how the pressure pressure p is altering, when volume V or temperature T are changing.

In order to see how this works, the only think we need to know is that the Carnot Cycle obeys these formulas:

• $pV = RT $ ideal gas equation

• $pV = const $ upper and lower curve (also called “isotherm”)

• $pV^k = const $ with $ k = 5/3$ for the left and right curve (also called “adiabatic”)

You don’t have to understand these formulas in detail in order to understand this tutorial.

As we need reference points in the diagram, we first define some default values.

For temperatures, we choose $ 20 °$C and \(300°\)C. For volumes we choose \(v_1= 1 \, \text{m}^3\), and \(v_2 = 2 \, \text{m}^3\).

import numpy as np
import matplotlib.pyplot as plt
from scipy.constants import zero_Celsius
plt.rcParams['figure.dpi'] = 150

Tmax = zero_Celsius +300
Tmin = zero_Celsius +20
R = 8.314
kappa = 5/3
V1= 1
V2= 2

Matplotlib is building the font cache; this may take a moment.

Now, let’s have a look on the plot via matplotlib. As of now, implementing and debugging formulas is important, design is not.

p1 = R*Tmax/V1 # ideal gas equation
p2 = p1*V1/V2

V3 = (Tmax/Tmin * V2**(kappa-1))**(1/(kappa-1))
p3 = p2* V2**kappa / V3**kappa

V4 = (Tmax/Tmin * V1**(kappa-1))**(1/(kappa-1))
p4 = p3*V3/V4

V12 = np.linspace(V1,V2,100)
V23 = np.linspace(V2,V3,100)
V34 = np.linspace(V3,V4,100)
V41 = np.linspace(V4,V1,100)

def p_isotherm(V,T):
    return (R*T)/V

def p_adiabatisch(V,p_start,v_start):
    return (p_start*v_start**kappa)/V**kappa

plt.plot(V12, p_isotherm(V12,Tmax),label = "T$_{max}$" +f"= {Tmax-zero_Celsius:.0f}°C")
plt.plot(V23, p_adiabatisch(V23, p2,V2),label = f"adiabatic expansion")
plt.plot(V34, p_isotherm(V34,Tmin),label = "T$_{min}$" +f"= {Tmin-zero_Celsius:.0f}°C")
plt.plot(V41, p_adiabatisch(V41, p4,V4),label = f"adiabatic contraction")

plt.legend()
plt.scatter(V1,p1)
plt.scatter(V2,p2)
plt.scatter(V3,p3)
plt.scatter(V4,p4)

plt.ylabel("Pressure [Pa]")
plt.xlabel("Volume [m$^3$]")
plt.ticklabel_format(axis="x", style="sci", scilimits=(0,5))

Good! Now comes the second part:

Building the explanatory plot!

Extending to The Qualitiative Concept

Now we have a good basis to convert this idea into a visually appealing and explanatory graph that will make it easy for everyone to understand complex problems.

from manim import *
config.media_embed = True
param   = "-v WARNING -s -ql --disable_caching --progress_bar None Example"

Manim Community v0.17.3

%%manim $param
class Example(Scene):
    def construct(self):
        my_ax = Axes()
        labels = my_ax.get_axis_labels(x_label="V", y_label="p")
        self.add(my_ax,labels)

# making some styling here
Axes.set_default(axis_config={"color": BLACK}, tips= False)
MathTex.set_default(color = BLACK)
config.background_color = WHITE

%%manim $param
ax = Axes(x_range=[0.9, 5.8, 4.9], y_range=[0, 5000, 5000],x_length=8, y_length=5,stroke_color=BLACK)
labels = ax.get_axis_labels(x_label="V", y_label="p")
labels[0].shift(.6*DOWN)
labels[1].shift(.6*LEFT)
isotherm12_graph = ax.plot(
    lambda x: p_isotherm(x, Tmax), x_range=[V1, V2,0.01], color=BLACK
)
adiabatisch23_graph = ax.plot(
    lambda x: p_adiabatisch(x, p2, V2) , x_range=[V2, V3,0.01], color=BLACK
)
isotherm34_graph = ax.plot(
    lambda x: p_isotherm(x, Tmin), x_range=[V3, V4,-0.01], color=BLACK
)
adiabatisch41_graph = ax.plot(
    lambda x: p_adiabatisch(x, p4, V4), x_range=[V4, V1,-0.01], color=BLACK
)
lines = VGroup(
    isotherm12_graph, adiabatisch23_graph, isotherm34_graph, adiabatisch41_graph
)

ax.add(labels)

class Example(Scene):
    def construct(self):
        self.add(ax,lines)

%%manim $param

Dot.set_default(color=BLACK)
dots = VGroup()
dots += Dot().move_to(isotherm12_graph.get_start())
dots += Dot().move_to(isotherm12_graph.get_end())
dots += Dot().move_to(isotherm34_graph.get_start())
dots += Dot().move_to(isotherm34_graph.get_end())

class Example(Scene):
    def construct(self):
        self.add(ax,lines,dots)

%%manim $param

nums= VGroup()
nums+= MathTex(r"{\large \textcircled{\small 1}} ").scale(0.7).next_to(dots[0],RIGHT,buff=0.4*SMALL_BUFF)
nums+= MathTex(r"{\large \textcircled{\small 2}} ").scale(0.7).next_to(dots[1],UP, buff=0.4 * SMALL_BUFF)
nums+= MathTex(r"{\large \textcircled{\small 3}} ").scale(0.7).next_to(dots[2],UP,buff=0.4*SMALL_BUFF)
nums+= MathTex(r"{\large \textcircled{\small 4}} ").scale(0.7).next_to(dots[3],DL ,buff=0.4*SMALL_BUFF)

class Example(Scene):
    def construct(self):
        self.add(ax,lines, dots,nums)

%%manim $param

background_strokes = VGroup()
background_strokes += ax.plot(lambda x: p_isotherm(x, Tmax),x_range=[V1 - 0.1, V2 + 0.5, 0.01], color=RED, stroke_opacity=0.5)
background_strokes += ax.plot(lambda x: p_isotherm(x, Tmin), x_range=[V3 + 0.3,V4 - 0.5,-0.01], color=BLUE, stroke_opacity=0.5)
background_strokes.set_z_index(-1);
label = VGroup()
label += MathTex(r"\text{T}_{\text{min}}").scale(0.7).next_to(background_strokes[1],RIGHT,aligned_edge=DOWN, buff=0)
label += MathTex(r"\text{T}_{\text{max}}").scale(0.7).next_to(background_strokes[0],RIGHT,aligned_edge=DOWN, buff=0)
background_strokes += label

class Example(Scene):
    def construct(self):
        self.add(ax,lines, dots,nums,background_strokes)

%%manim $param

downstrokes = VGroup()
downstrokes += ax.get_vertical_line(ax.i2gp(V1, isotherm12_graph), color=BLACK).set_z_index(-2)
downstrokes += ax.get_vertical_line(ax.i2gp(V2, isotherm12_graph), color=BLACK).set_z_index(-2)
downstrokes += ax.get_vertical_line(ax.i2gp(V3, isotherm34_graph), color=BLACK).set_z_index(-2)
downstrokes += ax.get_vertical_line(ax.i2gp(V4, isotherm34_graph), color=BLACK).set_z_index(-2)
down_labels= VGroup()
down_labels += MathTex("{ V }_{ 1 }").next_to(downstrokes[0], DOWN)
down_labels += MathTex("{ V }_{ 2 }").next_to(downstrokes[1], DOWN)
down_labels += MathTex("{ V }_{ 3 }").next_to(downstrokes[2], DOWN)
down_labels += MathTex("{ V }_{ 4 }").next_to(downstrokes[3], DOWN)

class Example(Scene):
    def construct(self):
        self.add(ax,lines, dots,nums,background_strokes, downstrokes,down_labels)

%%manim $param

heat_annotation = VGroup()
deltaW = MathTex(r"\Delta W").next_to(dots[3], UL).scale(0.65).shift(0.15 * UP)
bg = deltaW.add_background_rectangle(color=WHITE)
heat_annotation += deltaW

point = isotherm12_graph.point_from_proportion(0.5)
arrow = Arrow(point + UR * 0.5, point, buff=0).set_color(BLACK)
deltaQa = MathTex(r"\Delta Q_a").scale(0.7).next_to(arrow, UR, buff=0)
heat_annotation += arrow
heat_annotation += deltaQa

point = isotherm34_graph.point_from_proportion(0.4)
arrow = Arrow(point, point + DL * 0.5, buff=0).set_color(BLACK)
deltaQb = MathTex(r"\Delta Q_b").scale(0.7).next_to(arrow, LEFT, buff=0.1).shift(0.1 * DOWN)
heat_annotation += arrow
heat_annotation += deltaQb

class Example(Scene):
    def construct(self):
        self.add(ax,lines, dots,nums,background_strokes, downstrokes,down_labels,heat_annotation)

%%manim $param

c1 = Cutout(lines[0].copy().reverse_points(),lines[3]).set_opacity(1).set_color(GREEN)
c2 = Cutout(lines[1],lines[2])
bg_grey = Union(c1,c2, color=GREY_A).set_opacity(1)
bg_grey.z_index=-1

class Example(Scene):
    def construct(self):
        #self.add(c1,c2)
        self.add(ax,lines, dots,nums,background_strokes)
        self.add(downstrokes,down_labels,heat_annotation,bg_grey)

carnot_graph= VGroup(ax,lines, dots,nums,background_strokes,downstrokes,down_labels,heat_annotation,bg_grey)

And here is the final plot:

%%manim $param

sourunding_dot = Dot().scale(1.3).set_fill(color=BLACK).set_z_index(-1)
innerdot = Dot().set_color(WHITE).scale(1)
moving_dot = VGroup(sourunding_dot, innerdot)
moving_dot.move_to(isotherm12_graph.point_from_proportion(0.3))

class Example(Scene):
    def construct(self):
        self.add(carnot_graph)
        self.add(moving_dot)

Outlook

After having this foundation of an explanory plot, one can go on and animtate it as can be seen here.

(A tutorial for this animation will follow!)

from IPython.display import YouTubeVideo
YouTubeVideo('_8RkZaiXP0E', width=800, height=600)