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3b1b-manim/docs/source/getting_started/example_scenes.rst

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Example Scenes
==============
After understanding the previous knowledge, we can understand more scenes.
Many example scenes are given in ``example_scenes.py``, let's start with
the simplest and one by one.
SquareToCircle
--------------
.. manim-example:: SquareToCircle
:media: ../_static/example_scenes/SquareToCircle.mp4
from manimlib.imports import *
class SquareToCircle(Scene):
def construct(self):
circle = Circle()
circle.set_fill(BLUE, opacity=0.5)
circle.set_stroke(BLUE_E, width=4)
square = Square()
self.play(ShowCreation(square))
self.wait()
self.play(ReplacementTransform(square, circle))
self.wait()
This scene is what we wrote in :doc:`quickstart`.
No more explanation here
AnimatingMethods
----------------
.. manim-example:: AnimatingMethods
:media: ../_static/example_scenes/AnimatingMethods.mp4
class AnimatingMethods(Scene):
def construct(self):
grid = Tex(r"\pi").get_grid(10, 10, height=4)
self.add(grid)
# You can animate the application of mobject methods with the
# ".animate" syntax:
self.play(grid.animate.shift(LEFT))
# Alternatively, you can use the older syntax by passing the
# method and then the arguments to the scene's "play" function:
self.play(grid.shift, LEFT)
# Both of those will interpolate between the mobject's initial
# state and whatever happens when you apply that method.
# For this example, calling grid.shift(LEFT) would shift the
# grid one unit to the left, but both of the previous calls to
# "self.play" animate that motion.
# The same applies for any method, including those setting colors.
self.play(grid.animate.set_color(YELLOW))
self.wait()
self.play(grid.animate.set_submobject_colors_by_gradient(BLUE, GREEN))
self.wait()
self.play(grid.animate.set_height(TAU - MED_SMALL_BUFF))
self.wait()
# The method Mobject.apply_complex_function lets you apply arbitrary
# complex functions, treating the points defining the mobject as
# complex numbers.
self.play(grid.animate.apply_complex_function(np.exp), run_time=5)
self.wait()
# Even more generally, you could apply Mobject.apply_function,
# which takes in functions form R^3 to R^3
self.play(
grid.animate.apply_function(
lambda p: [
p[0] + 0.5 * math.sin(p[1]),
p[1] + 0.5 * math.sin(p[0]),
p[2]
]
),
run_time=5,
)
self.wait()
The new usage in this scene is ``.get_grid()`` and ``self.play(mob.animate.method(args))``.
- ``.get_grid()`` method will return a new mobject containing multiple copies of this one arranged in a grid.
- ``self.play(mob.animate.method(args))`` animates the method, and the details are in the comments above.
TextExample
-----------
.. manim-example:: TextExample
:media: ../_static/example_scenes/TextExample.mp4
class TextExample(Scene):
def construct(self):
text = Text("Here is a text", font="Consolas", font_size=90)
difference = Text(
"""
The most important difference between Text and TexText is that\n
you can change the font more easily, but can't use the LaTeX grammar
""",
font="Arial", font_size=24,
t2c={"Text": BLUE, "TexText": BLUE, "LaTeX": ORANGE}
)
VGroup(text, difference).arrange(DOWN, buff=1)
self.play(Write(text))
self.play(FadeIn(difference, UP))
self.wait(3)
fonts = Text(
"And you can also set the font according to different words",
font="Arial",
t2f={"font": "Consolas", "words": "Consolas"},
t2c={"font": BLUE, "words": GREEN}
)
slant = Text(
"And the same as slant and weight",
font="Consolas",
t2s={"slant": ITALIC},
t2w={"weight": BOLD},
t2c={"slant": ORANGE, "weight": RED}
)
VGroup(fonts, slant).arrange(DOWN, buff=0.8)
self.play(FadeOut(text), FadeOut(difference, shift=DOWN))
self.play(Write(fonts))
self.wait()
self.play(Write(slant))
self.wait()
The new classes in this scene are ``Text``, ``VGroup``, ``Write``, ``FadeIn`` and ``FadeOut``.
- ``Text`` can create text, define fonts, etc. The usage ais clearly reflected in the above examples.
- ``VGroup`` can put multiple ``VMobject`` together as a whole. In the example, the ``.arrange()`` method is called to arrange the sub-mobjects in sequence downward (``DOWN``), and the spacing is ``buff``.
- ``Write`` is an animation that shows similar writing effects.
- ``FadeIn`` fades the object in, the second parameter indicates the direction of the fade in.
- ``FadeOut`` fades out the object, the second parameter indicates the direction of the fade out.
TexTransformExample
-------------------
.. manim-example:: TexTransformExample
:media: ../_static/example_scenes/TexTransformExample.mp4
class TexTransformExample(Scene):
def construct(self):
to_isolate = ["B", "C", "=", "(", ")"]
lines = VGroup(
# Surrounding substrings with double braces
# will ensure that those parts are separated
# out in the Tex. For example, here the
# Tex will have 5 submobjects, corresponding
# to the strings [A^2, +, B^2, =, C^2]
Tex("{{A^2}} + {{B^2}} = {{C^2}}"),
Tex("{{A^2}} = {{C^2}} - {{B^2}}"),
# Alternatively, you can pass in the keyword argument
# "isolate" with a list of strings that should be out as
# their own submobject. So both lines below are equivalent
# to what you'd get by wrapping every instance of "B", "C"
# "=", "(" and ")" with double braces
Tex("{{A^2}} = (C + B)(C - B)", isolate=to_isolate),
Tex("A = \\sqrt{(C + B)(C - B)}", isolate=to_isolate)
)
lines.arrange(DOWN, buff=LARGE_BUFF)
for line in lines:
line.set_color_by_tex_to_color_map({
"A": BLUE,
"B": TEAL,
"C": GREEN,
})
play_kw = {"run_time": 2}
self.add(lines[0])
# The animation TransformMatchingTex will line up parts
# of the source and target which have matching tex strings.
# Here, giving it a little path_arc makes each part sort of
# rotate into their final positions, which feels appropriate
# for the idea of rearranging an equation
self.play(
TransformMatchingTex(
lines[0].copy(), lines[1],
path_arc=90 * DEGREES,
),
**play_kw
)
self.wait()
# Now, we could try this again on the next line...
self.play(
TransformMatchingTex(lines[1].copy(), lines[2]),
**play_kw
)
self.wait()
# ...and this looks nice enough, but since there's no tex
# in lines[2] which matches "C^2" or "B^2", those terms fade
# out to nothing while the C and B terms fade in from nothing.
# If, however, we want the C^2 to go to C, and B^2 to go to B,
# we can specify that with a key map.
self.play(FadeOut(lines[2]))
self.play(
TransformMatchingTex(
lines[1].copy(), lines[2],
key_map={
"C^2": "C",
"B^2": "B",
}
),
**play_kw
)
self.wait()
# And to finish off, a simple TransformMatchingShapes would work
# just fine. But perhaps we want that exponent on A^2 to transform into
# the square root symbol. At the moment, lines[2] treats the expression
# A^2 as a unit, so we might create a new version of the same line which
# separates out just the A. This way, when TransformMatchingTex lines up
# all matching parts, the only mismatch will be between the "^2" from
# new_line2 and the "\sqrt" from the final line. By passing in,
# transform_mismatches=True, it will transform this "^2" part into
# the "\sqrt" part.
new_line2 = Tex("{{A}}^2 = (C + B)(C - B)", isolate=to_isolate)
new_line2.replace(lines[2])
new_line2.match_style(lines[2])
self.play(
TransformMatchingTex(
new_line2, lines[3],
transform_mismatches=True,
),
**play_kw
)
self.wait(3)
self.play(FadeOut(lines, RIGHT))
# Alternatively, if you don't want to think about breaking up
# the tex strings deliberately, you can TransformMatchingShapes,
# which will try to line up all pieces of a source mobject with
# those of a target, regardless of the submobject hierarchy in
# each one, according to whether those pieces have the same
# shape (as best it can).
source = Text("the morse code", height=1)
target = Text("here come dots", height=1)
self.play(Write(source))
self.wait()
kw = {"run_time": 3, "path_arc": PI / 2}
self.play(TransformMatchingShapes(source, target, **kw))
self.wait()
self.play(TransformMatchingShapes(target, source, **kw))
self.wait()
The new classes in this scene are ``Tex``, ``TexText``, ``TransformMatchingTex``
and ``TransformMatchingShapes``.
- ``Tex`` uses LaTeX to create mathematical formulas.
- ``TexText`` uses LaTeX to create text.
- ``TransformMatchingTeX`` automatically transforms sub-objects according to the similarities and differences of tex in ``Tex``.
- ``TransformMatchingShapes`` automatically transform sub-objects directly based on the similarities and differences of the object point sets.
UpdatersExample
---------------
.. manim-example:: UpdatersExample
:media: ../_static/example_scenes/UpdatersExample.mp4
class UpdatersExample(Scene):
def construct(self):
square = Square()
square.set_fill(BLUE_E, 1)
# On all all frames, the constructor Brace(square, UP) will
# be called, and the mobject brace will set its data to match
# that of the newly constructed object
brace = always_redraw(Brace, square, UP)
text, number = label = VGroup(
Text("Width = "),
DecimalNumber(
0,
show_ellipsis=True,
num_decimal_places=2,
include_sign=True,
)
)
label.arrange(RIGHT)
# This ensures that the method deicmal.next_to(square)
# is called on every frame
always(label.next_to, brace, UP)
# You could also write the following equivalent line
# label.add_updater(lambda m: m.next_to(brace, UP))
# If the argument itself might change, you can use f_always,
# for which the arguments following the initial Mobject method
# should be functions returning arguments to that method.
# The following line ensures thst decimal.set_value(square.get_y())
# is called every frame
f_always(number.set_value, square.get_width)
# You could also write the following equivalent line
# number.add_updater(lambda m: m.set_value(square.get_width()))
self.add(square, brace, label)
# Notice that the brace and label track with the square
self.play(
square.animate.scale(2),
rate_func=there_and_back,
run_time=2,
)
self.wait()
self.play(
square.set_width(5, stretch=True),
run_time=3,
)
self.wait()
self.play(
square.animate.set_width(2),
run_time=3
)
self.wait()
# In general, you can alway call Mobject.add_updater, and pass in
# a function that you want to be called on every frame. The function
# should take in either one argument, the mobject, or two arguments,
# the mobject and the amount of time since the last frame.
now = self.time
w0 = square.get_width()
square.add_updater(
lambda m: m.set_width(w0 * math.cos(self.time - now))
)
self.wait(4 * PI)
The new classes and usage in this scene are ``always_redraw()``, ``DecimalNumber``, ``.to_edge()``,
``.center()``, ``always()``, ``f_always()``, ``.set_y()`` and ``.add_updater()``.
- ``always_redraw()`` function create a new mobject every frame.
- ``DecimalNumber`` is a variable number, speed it up by breaking it into ``Text`` characters.
- ``.to_edge()`` means to place the object on the edge of the screen.
- ``.center()`` means to place the object in the center of the screen.
- ``always(f, x)`` means that a certain function (``f(x)``) is executed every frame.
- ``f_always(f, g)`` is similar to ``always``, executed ``f(g())`` every frame.
- ``.set_y()`` means to set the ordinate of the object on the screen.
- ``.add_updater()`` sets an update function for the object. For example: ``mob1.add_updater(lambda mob: mob.next_to(mob2))`` means ``mob1.next_to(mob2)`` is executed every frame.
SurfaceExample
--------------
.. manim-example:: SurfaceExample
:media: ../_static/example_scenes/SurfaceExample.mp4
class SurfaceExample(Scene):
CONFIG = {
"camera_class": ThreeDCamera,
}
def construct(self):
surface_text = Text("For 3d scenes, try using surfaces")
surface_text.fix_in_frame()
surface_text.to_edge(UP)
self.add(surface_text)
self.wait(0.1)
torus1 = Torus(r1=1, r2=1)
torus2 = Torus(r1=3, r2=1)
sphere = Sphere(radius=3, resolution=torus1.resolution)
# You can texture a surface with up to two images, which will
# be interpreted as the side towards the light, and away from
# the light. These can be either urls, or paths to a local file
# in whatever you've set as the image directory in
# the custom_defaults.yml file
# day_texture = "EarthTextureMap"
# night_texture = "NightEarthTextureMap"
day_texture = "https://upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Whole_world_-_land_and_oceans.jpg/1280px-Whole_world_-_land_and_oceans.jpg"
night_texture = "https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/The_earth_at_night.jpg/1280px-The_earth_at_night.jpg"
surfaces = [
TexturedSurface(surface, day_texture, night_texture)
for surface in [sphere, torus1, torus2]
]
for mob in surfaces:
mob.shift(IN)
mob.mesh = SurfaceMesh(mob)
mob.mesh.set_stroke(BLUE, 1, opacity=0.5)
# Set perspective
frame = self.camera.frame
frame.set_euler_angles(
theta=-30 * DEGREES,
phi=70 * DEGREES,
)
surface = surfaces[0]
self.play(
FadeIn(surface),
ShowCreation(surface.mesh, lag_ratio=0.01, run_time=3),
)
for mob in surfaces:
mob.add(mob.mesh)
surface.save_state()
self.play(Rotate(surface, PI / 2), run_time=2)
for mob in surfaces[1:]:
mob.rotate(PI / 2)
self.play(
Transform(surface, surfaces[1]),
run_time=3
)
self.play(
Transform(surface, surfaces[2]),
# Move camera frame during the transition
frame.animate.increment_phi(-10 * DEGREES),
frame.animate.increment_theta(-20 * DEGREES),
run_time=3
)
# Add ambient rotation
frame.add_updater(lambda m, dt: m.increment_theta(-0.1 * dt))
# Play around with where the light is
light_text = Text("You can move around the light source")
light_text.move_to(surface_text)
light_text.fix_in_frame()
self.play(FadeTransform(surface_text, light_text))
light = self.camera.light_source
self.add(light)
light.save_state()
self.play(light.animate.move_to(3 * IN), run_time=5)
self.play(light.animate.shift(10 * OUT), run_time=5)
drag_text = Text("Try moving the mouse while pressing d or s")
drag_text.move_to(light_text)
drag_text.fix_in_frame()
self.play(FadeTransform(light_text, drag_text))
self.wait()
This scene shows an example of using a three-dimensional surface, and
the related usage has been briefly described in the notes.
- ``.fix_in_frame()`` makes the object not change with the view angle of the screen, and is always displayed at a fixed position on the screen.
OpeningManimExample
-------------------
.. manim-example:: OpeningManimExample
:media: ../_static/example_scenes/OpeningManimExample.mp4
class OpeningManimExample(Scene):
def construct(self):
intro_words = Text("""
The original motivation for manim was to
better illustrate mathematical functions
as transformations.
""")
intro_words.to_edge(UP)
self.play(Write(intro_words))
self.wait(2)
# Linear transform
grid = NumberPlane((-10, 10), (-5, 5))
matrix = [[1, 1], [0, 1]]
linear_transform_words = VGroup(
Text("This is what the matrix"),
IntegerMatrix(matrix, include_background_rectangle=True),
Text("looks like")
)
linear_transform_words.arrange(RIGHT)
linear_transform_words.to_edge(UP)
linear_transform_words.set_stroke(BLACK, 10, background=True)
self.play(
ShowCreation(grid),
FadeTransform(intro_words, linear_transform_words)
)
self.wait()
self.play(grid.animate.apply_matrix(matrix), run_time=3)
self.wait()
# Complex map
c_grid = ComplexPlane()
moving_c_grid = c_grid.copy()
moving_c_grid.prepare_for_nonlinear_transform()
c_grid.set_stroke(BLUE_E, 1)
c_grid.add_coordinate_labels(font_size=24)
complex_map_words = TexText("""
Or thinking of the plane as $\\mathds{C}$,\\\\
this is the map $z \\rightarrow z^2$
""")
complex_map_words.to_corner(UR)
complex_map_words.set_stroke(BLACK, 5, background=True)
self.play(
FadeOut(grid),
Write(c_grid, run_time=3),
FadeIn(moving_c_grid),
FadeTransform(linear_transform_words, complex_map_words),
)
self.wait()
self.play(
moving_c_grid.animate.apply_complex_function(lambda z: z**2),
run_time=6,
)
self.wait(2)
This scene is a comprehensive application of a two-dimensional scene.
After seeing these scenes, you have already understood part of the
usage of manim. For more examples, see `the video code of 3b1b <https://github.com/3b1b/videos>`_.
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