Manim (optional)¶

import math

from manim import *

%reload_ext mytutor

Manim Community v0.7.0

Manim is a powerful animation engine for mathemetics developed by 3Blue1Brown. We will use manim to domenstrate how object-oriented programming uses classes and objects to make it create complex animation.

Creating a scene¶

How to create an animation with manim?

In jupyter notebook, we can use %%manim cell magic:

%%manim -qm --progress_bar=none --disable_caching --flush_cache -v ERROR HelloWorld
class HelloWorld(Scene):
    def construct(self):
        self.play(Write(Text("Hello, World!")))

In the line starting with %%:

-qm is the alias for --quality=m, which means the video is rendered in medium quality. Change it to -ql (-qh) for low (high) quality.
--progress_bar=none --disable_caching --flush_cache -v ERROR are additional configurations to turn off some features.

HelloWorld is the class to render, which is defined in the body:

class HelloWorld(Scene):
    def construct(self):
        ...

How to define a class?

As a toy example, the following defines a class Pet and its subclasses Cat and Dog:

%%mytutor -h 700
class Pet:
    kind = "Pet"

    def __init__(self, name):
        self.name = name

    def __str__(self):
        return f"{self.kind} {self.name}"


class Cat(Pet):
    kind = "Cat"


class Dog(Pet):
    kind = "Dog"


p1 = Pet("Alfie")
p2 = Dog("Bobbie")
p3, p4 = Cat("Bella"), Cat("Kelly")
print(p1, p2, p3, p4, sep=", ")

Each pet has its own name but they share kind from their class without duplicating it.
Subclasses can reuse (inherit) code from their superclass but produce different results:
- Line 19-21 calls Pet.__init__ implicitly to create pets with different names.
- Line 22 calls Pet.__str__ implicitly to return a string containing pets’ specific kind in addition to its name.

Animating an Object¶

How to add objects to a Scene?

We can create a square and add it to the scene as follows:

%%manim -qm --progress_bar=none --disable_caching --flush_cache -v ERROR BlueSquare1
class BlueSquare1(Scene):
    def construct(self):
        s = Square(fill_color=BLUE, color=WHITE)
        self.add(s)

The square object is create using Square, BLUE and WHITE imported from manim.
It is then placed to to the scene using self.add inherited from Scene.

How to animate an object?

The following shows the creation of a square:

%%manim -qm --progress_bar=none --disable_caching --flush_cache -v ERROR BlueSquare2
class BlueSquare2(Scene):
    def construct(self):
        s = Square(color=WHITE, fill_color=BLUE, fill_opacity=0.8)
        self.play(Create(s))
        self.wait()

self.play plays the animation Create(s).
self.wait() creates a pause “animation”.

How to transform an object?

To scale, move, or rotate the shape:

%%manim -qm --progress_bar=none --disable_caching --flush_cache -v ERROR BlueSquare3
class BlueSquare3(Scene):
    def construct(self):
        s = Square(color=WHITE, fill_color=BLUE, fill_opacity=0.8)
        self.play(Create(s))
        self.play(s.animate.scale(1.5).rotate(PI / 4))
        self.play(s.animate.move_to([-3, 0, 0]))
        self.play(s.animate.move_to([3, 0, 0]))
        self.play(s.animate.scale(0.5).move_to(ORIGIN).rotate(-PI / 4))
        self.wait()

Exercise (Optional) The attribute s.animate is an object that provides the methods scale, move_to, and rotate. Note that the methods can be called successively as in s.animate.scale(0.5).move_to(ORIGIN).rotate(-PI/4). Why?

Animating multiple objects¶

Tessellation with regular polygons

Consider tiling a 12-by-6 plane using squares:

%%manim -qm --progress_bar=none --disable_caching --flush_cache -v ERROR SquareTiling1
class SquareTiling1(Scene):
    WIDTH = 12
    HEIGHT = 6
    EDGE = 1

    def construct(self):
        plane = Rectangle(width=self.WIDTH, height=self.HEIGHT)
        unit = Square(color=WHITE, fill_color=BLUE, fill_opacity=0.8).scale(
            self.EDGE / 2
        )
        self.add(plane, unit)

The first line of squares can be animated as follows:

%%manim -qm --progress_bar=none --disable_caching --flush_cache -v ERROR SquareTiling2
class SquareTiling2(Scene):
    WIDTH = 12
    HEIGHT = 6
    EDGE = 1

    def construct(self):

        plane = Rectangle(width=self.WIDTH, height=self.HEIGHT)
        self.add(plane)

        unit = Square(color=WHITE, fill_color=BLUE, fill_opacity=0.8).scale(
            self.EDGE / 2
        )
        self.play(Create(unit))
        self.play(
            unit.animate.move_to(
                [-self.WIDTH / 2 + self.EDGE / 2, self.HEIGHT / 2 - self.EDGE / 2, 0]
            )
        )

        for i in range(1, self.WIDTH // self.EDGE):
            self.play(unit.copy().animate.shift([i, 0, 0]), run_time=1 / i)
        self.wait()

We can use VGroup method to create a group of shapes.

%%manim -qm --progress_bar=none --disable_caching --flush_cache -v ERROR SquareTiling3
class SquareTiling3(Scene):
    WIDTH = 12
    HEIGHT = 6
    EDGE = 1

    def construct(self):

        plane = Rectangle(width=self.WIDTH, height=self.HEIGHT)
        self.add(plane)

        unit = Square(color=WHITE, fill_color=BLUE, fill_opacity=0.8).scale(
            self.EDGE / 2
        )
        self.play(Create(unit))
        self.play(
            unit.animate.move_to(
                [-self.WIDTH / 2 + self.EDGE / 2, self.HEIGHT / 2 - self.EDGE / 2, 0]
            )
        )

        for i in range(1, math.floor(self.WIDTH / self.EDGE)):
            self.play(unit.copy().animate.shift([i * self.EDGE, 0, 0]), run_time=1 / i)

        line = VGroup(
            *[
                unit.copy().shift([i * self.EDGE, 0, 0])
                for i in range(math.floor(self.WIDTH / self.EDGE))
            ]
        )
        for i in range(1, math.floor(self.HEIGHT / self.EDGE)):
            self.play(line.copy().animate.shift([0, -i * self.EDGE, 0]), run_time=1 / i)

        self.wait()

Exercise (Optional) Use manim to show the other two ways of tiling with regular polygons (triangle and hexagon). (see tiling with regular polygons)

CS1302

Manim (optional)¶

Creating a scene¶

Animating an Object¶

Animating multiple objects¶