manim/docs/source/examples.rst
2021-01-01 17:59:12 +01:00

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###############
Example Gallery
###############
This gallery contains a collection of best practice code snippets
together with their corresponding video/image output, illustrating
different functionalities all across the library.
These are all under the MIT licence, so feel free to copy & paste them to your projects.
Enjoy this taste of Manim!
.. tip::
This gallery is not the only place in our documentation where you can see explicit
code and video examples: there are many more in our
:doc:`reference manual </reference>` -- see, for example, our documentation for
the modules :mod:`~.tex_mobject`, :mod:`~.geometry`, :mod:`~.moving_camera_scene`,
and many more.
Also, visit our `Twitter <https://twitter.com/manim_community/>`_ for more
*manimations*!
.. contents:: Overview of thematic video categories
:backlinks: none
:local:
Basic Concepts
==============
.. manim:: ManimCELogo
:save_last_frame:
:ref_classes: MathTex Circle Square Triangle
class ManimCELogo(Scene):
def construct(self):
self.camera.background_color = "#ece6e2"
logo_green = "#87c2a5"
logo_blue = "#525893"
logo_red = "#e07a5f"
logo_black = "#343434"
ds_m = MathTex(r"\mathbb{M}", fill_color=logo_black).scale(7)
ds_m.shift(2.25 * LEFT + 1.5 * UP)
circle = Circle(color=logo_green, fill_opacity=1).shift(LEFT)
square = Square(color=logo_blue, fill_opacity=1).shift(UP)
triangle = Triangle(color=logo_red, fill_opacity=1).shift(RIGHT)
logo = VGroup(triangle, square, circle, ds_m) # order matters
logo.move_to(ORIGIN)
self.add(logo)
.. manim:: BraceAnnotation
:save_last_frame:
:ref_classes: Brace
:ref_functions: Brace.get_text Brace.get_tex
class BraceAnnotation(Scene):
def construct(self):
dot = Dot([-2, -1, 0])
dot2 = Dot([2, 1, 0])
line = Line(dot.get_center(), dot2.get_center()).set_color(ORANGE)
b1 = Brace(line)
b1text = b1.get_text("Horizontal distance")
b2 = Brace(line, direction=line.copy().rotate(PI / 2).get_unit_vector())
b2text = b2.get_tex("x-x_1")
self.add(line, dot, dot2, b1, b2, b1text, b2text)
.. manim:: VectorArrow
:save_last_frame:
:ref_classes: Dot Arrow NumberPlane Text
class VectorArrow(Scene):
def construct(self):
dot = Dot(ORIGIN)
arrow = Arrow(ORIGIN, [2, 2, 0], buff=0)
numberplane = NumberPlane()
origin_text = Text('(0, 0)').next_to(dot, DOWN)
tip_text = Text('(2, 2)').next_to(arrow.get_end(), RIGHT)
self.add(numberplane, dot, arrow, origin_text, tip_text)
.. manim:: GradientImageFromArray
:save_last_frame:
:ref_classes: ImageMobject
class GradientImageFromArray(Scene):
def construct(self):
n = 256
imageArray = np.uint8(
[[i * 256 / n for i in range(0, n)] for _ in range(0, n)]
)
image = ImageMobject(imageArray).scale(2)
self.add(image)
.. manim:: BezierSpline
:save_last_frame:
:ref_classes: Line VGroup
:ref_functions: VMobject.add_cubic_bezier_curve
class BezierSpline(Scene):
def construct(self):
np.random.seed(42)
area = 4
x1 = np.random.randint(-area, area)
y1 = np.random.randint(-area, area)
p1 = np.array([x1, y1, 0])
destination_dot1 = Dot(point=p1).set_color(BLUE)
x2 = np.random.randint(-area, area)
y2 = np.random.randint(-area, area)
p2 = np.array([x2, y2, 0])
destination_dot2 = Dot(p2).set_color(RED)
deltaP = p1 - p2
deltaPNormalized = deltaP / get_norm(deltaP)
theta = np.radians(90)
r = np.array(
(
(np.cos(theta), -np.sin(theta), 0),
(np.sin(theta), np.cos(theta), 0),
(0, 0, 0),
)
)
senk = r.dot(deltaPNormalized)
offset = 0.1
offset_along = 0.5
offset_connect = 0.25
dest_line1_point1 = p1 + senk * offset - deltaPNormalized * offset_along
dest_line1_point2 = p2 + senk * offset + deltaPNormalized * offset_along
dest_line2_point1 = p1 - senk * offset - deltaPNormalized * offset_along
dest_line2_point2 = p2 - senk * offset + deltaPNormalized * offset_along
s1 = p1 - offset_connect * deltaPNormalized
s2 = p2 + offset_connect * deltaPNormalized
dest_line1 = Line(dest_line1_point1, dest_line1_point2)
dest_line2 = Line(dest_line2_point1, dest_line2_point2)
Lp1s1 = Line(p1, s1)
Lp1s1.add_cubic_bezier_curve(
s1,
s1 - deltaPNormalized * 0.1,
dest_line2_point1 + deltaPNormalized * 0.1,
dest_line2_point1 - deltaPNormalized * 0.01,
)
Lp1s1.add_cubic_bezier_curve(
s1,
s1 - deltaPNormalized * 0.1,
dest_line1_point1 + deltaPNormalized * 0.1,
dest_line1_point1,
)
Lp2s2 = Line(p2, s2)
Lp2s2.add_cubic_bezier_curve(
s2,
s2 + deltaPNormalized * 0.1,
dest_line2_point2 - deltaPNormalized * 0.1,
dest_line2_point2,
)
Lp2s2.add_cubic_bezier_curve(
s2,
s2 + deltaPNormalized * 0.1,
dest_line1_point2 - deltaPNormalized * 0.1,
dest_line1_point2,
)
mobjects = VGroup(
Lp1s1, Lp2s2, dest_line1, dest_line2, destination_dot1, destination_dot2
)
mobjects.scale(2)
self.add(mobjects)
Animations
==========
.. manim:: PointMovingOnShapes
:ref_classes: Circle Dot Line GrowFromCenter Transform MoveAlongPath Rotating
class PointMovingOnShapes(Scene):
def construct(self):
circle = Circle(radius=1, color=BLUE)
dot = Dot()
dot2 = dot.copy().shift(RIGHT)
self.add(dot)
line = Line([3, 0, 0], [5, 0, 0])
self.add(line)
self.play(GrowFromCenter(circle))
self.play(Transform(dot, dot2))
self.play(MoveAlongPath(dot, circle), run_time=2, rate_func=linear)
self.play(Rotating(dot, about_point=[2, 0, 0]), run_time=1.5)
self.wait()
.. manim:: MovingAround
:ref_functions: Mobject.shift VMobject.set_fill Mobject.scale Mobject.rotate
class MovingAround(Scene):
def construct(self):
square = Square(color=BLUE, fill_opacity=1)
self.play(square.animate.shift(LEFT))
self.play(square.animate.set_fill(ORANGE))
self.play(square.animate.scale(0.3))
self.play(square.animate.rotate(0.4))
.. manim:: MovingFrameBox
:ref_modules: manim.mobject.svg.tex_mobject
:ref_classes: MathTex SurroundingRectangle
class MovingFrameBox(Scene):
def construct(self):
text=MathTex(
"\\frac{d}{dx}f(x)g(x)=","f(x)\\frac{d}{dx}g(x)","+",
"g(x)\\frac{d}{dx}f(x)"
)
self.play(Write(text))
framebox1 = SurroundingRectangle(text[1], buff = .1)
framebox2 = SurroundingRectangle(text[3], buff = .1)
self.play(
ShowCreation(framebox1),
)
self.wait()
self.play(
ReplacementTransform(framebox1,framebox2),
)
self.wait()
.. manim:: RotationUpdater
:ref_functions: Mobject.add_updater Mobject.remove_updater
class RotationUpdater(Scene):
def construct(self):
def updater_forth(mobj, dt):
mobj.rotate_about_origin(dt)
def updater_back(mobj, dt):
mobj.rotate_about_origin(-dt)
line_reference = Line(ORIGIN, LEFT).set_color(WHITE)
line_moving = Line(ORIGIN, LEFT).set_color(YELLOW)
line_moving.add_updater(updater_forth)
self.add(line_reference, line_moving)
self.wait(2)
line_moving.remove_updater(updater_forth)
line_moving.add_updater(updater_back)
self.wait(2)
line_moving.remove_updater(updater_back)
self.wait(0.5)
.. manim:: PointWithTrace
:ref_classes: Rotating
:ref_functions: VMobject.set_points_as_corners Mobject.add_updater
class PointWithTrace(Scene):
def construct(self):
path = VMobject()
dot = Dot()
path.set_points_as_corners([dot.get_center(), dot.get_center()])
def update_path(path):
previous_path = path.copy()
previous_path.add_points_as_corners([dot.get_center()])
path.become(previous_path)
path.add_updater(update_path)
self.add(path, dot)
self.play(Rotating(dot, radians=PI, about_point=RIGHT, run_time=2))
self.wait()
self.play(dot.animate.shift(UP))
self.play(dot.animate.shift(LEFT))
self.wait()
Plotting with Manim
===================
.. manim:: SinAndCosFunctionPlot
:save_last_frame:
:ref_modules: manim.scene.graph_scene
:ref_classes: MathTex
:ref_functions: GraphScene.setup_axes GraphScene.get_graph GraphScene.get_vertical_line_to_graph GraphScene.input_to_graph_point
class SinAndCosFunctionPlot(GraphScene):
def __init__(self, **kwargs):
GraphScene.__init__(
self,
x_min=-10,
x_max=10.3,
num_graph_anchor_points=100,
y_min=-1.5,
y_max=1.5,
graph_origin=ORIGIN,
axes_color=GREEN,
x_labeled_nums=range(-10, 12, 2),
**kwargs
)
self.function_color = RED
def construct(self):
self.setup_axes(animate=False)
func_graph = self.get_graph(np.cos, self.function_color)
func_graph2 = self.get_graph(np.sin)
vert_line = self.get_vertical_line_to_graph(TAU, func_graph, color=YELLOW)
graph_lab = self.get_graph_label(func_graph, label="\\cos(x)")
graph_lab2 = self.get_graph_label(func_graph2, label="\\sin(x)",
x_val=-10, direction=UP / 2)
two_pi = MathTex(r"x = 2 \pi")
label_coord = self.input_to_graph_point(TAU, func_graph)
two_pi.next_to(label_coord, RIGHT + UP)
self.add(func_graph, func_graph2, vert_line, graph_lab, graph_lab2, two_pi)
.. manim:: GraphAreaPlot
:save_last_frame:
:ref_modules: manim.scenes.graph_scene
:ref_functions: GraphScene.setup_axes GraphScene.get_graph GraphScene.get_vertical_line_to_graph GraphScene.get_area
class GraphAreaPlot(GraphScene):
def __init__(self, **kwargs):
GraphScene.__init__(
self,
x_min=0,
x_max=5,
y_min=0,
y_max=6,
x_labeled_nums=[0,2,3],
**kwargs)
def construct(self):
self.setup_axes()
curve1 = self.get_graph(lambda x: 4 * x - x ** 2, x_min=0, x_max=4)
curve2 = self.get_graph(lambda x: 0.8 * x ** 2 - 3 * x + 4, x_min=0, x_max=4)
line1 = self.get_vertical_line_to_graph(2, curve1, DashedLine, color=YELLOW)
line2 = self.get_vertical_line_to_graph(3, curve1, DashedLine, color=YELLOW)
area1 = self.get_area(curve1, 0.3, 0.6, dx_scaling=10, area_color=BLUE)
area2 = self.get_area(curve2, 2, 3, bounded=curve1)
self.add(curve1, curve2, line1, line2, area1, area2)
.. manim:: HeatDiagramPlot
:save_last_frame:
:ref_modules: manim.scenes.graph_scene
:ref_functions: GraphScene.setup_axes GraphScene.coords_to_point
class HeatDiagramPlot(GraphScene):
def __init__(self, **kwargs):
GraphScene.__init__(
self,
y_axis_label=r"T[$^\circ C$]",
x_axis_label=r"$\Delta Q$",
y_min=-8,
y_max=30,
x_min=0,
x_max=40,
y_labeled_nums=np.arange(-5, 34, 5),
x_labeled_nums=np.arange(0, 40, 5),
**kwargs)
def construct(self):
data = [20, 0, 0, -5]
x = [0, 8, 38, 39]
self.setup_axes()
dot_collection = VGroup()
for time, val in enumerate(data):
dot = Dot().move_to(self.coords_to_point(x[time], val))
self.add(dot)
dot_collection.add(dot)
l1 = Line(dot_collection[0].get_center(), dot_collection[1].get_center())
l2 = Line(dot_collection[1].get_center(), dot_collection[2].get_center())
l3 = Line(dot_collection[2].get_center(), dot_collection[3].get_center())
self.add(l1, l2, l3)
Special Camera Settings
=======================
.. manim:: FollowingGraphCamera
:ref_modules: manim.scene.moving_camera_scene
:ref_classes: GraphScene MovingCameraScene MoveAlongPath Restore
:ref_functions: Mobject.add_updater
class FollowingGraphCamera(GraphScene, MovingCameraScene):
def setup(self):
GraphScene.setup(self)
MovingCameraScene.setup(self)
def construct(self):
self.camera_frame.save_state()
self.setup_axes(animate=False)
graph = self.get_graph(lambda x: np.sin(x),
color=BLUE,
x_min=0,
x_max=3 * PI
)
moving_dot = Dot().move_to(graph.points[0]).set_color(ORANGE)
dot_at_start_graph = Dot().move_to(graph.points[0])
dot_at_end_graph = Dot().move_to(graph.points[-1])
self.add(graph, dot_at_end_graph, dot_at_start_graph, moving_dot)
self.play(self.camera_frame.animate.scale(0.5).move_to(moving_dot))
def update_curve(mob):
mob.move_to(moving_dot.get_center())
self.camera_frame.add_updater(update_curve)
self.play(MoveAlongPath(moving_dot, graph, rate_func=linear))
self.camera_frame.remove_updater(update_curve)
self.play(Restore(self.camera_frame))
.. manim:: MovingZoomedSceneAround
:ref_modules: manim.scene.zoomed_scene
:ref_classes: ZoomedScene BackgroundRectangle UpdateFromFunc
:ref_functions: Mobject.add_updater ZoomedScene.get_zoomed_display_pop_out_animation
class MovingZoomedSceneAround(ZoomedScene):
# contributed by TheoremofBeethoven, www.youtube.com/c/TheoremofBeethoven
def __init__(self, **kwargs):
ZoomedScene.__init__(
self,
zoom_factor=0.3,
zoomed_display_height=1,
zoomed_display_width=6,
image_frame_stroke_width=20,
zoomed_camera_config={
"default_frame_stroke_width": 3,
},
**kwargs
)
def construct(self):
dot = Dot().shift(UL * 2)
image = ImageMobject(np.uint8([[0, 100, 30, 200],
[255, 0, 5, 33]]))
image.set_height(7)
frame_text = Text("Frame", color=PURPLE).scale(1.4)
zoomed_camera_text = Text("Zoomed camera", color=RED).scale(1.4)
self.add(image, dot)
zoomed_camera = self.zoomed_camera
zoomed_display = self.zoomed_display
frame = zoomed_camera.frame
zoomed_display_frame = zoomed_display.display_frame
frame.move_to(dot)
frame.set_color(PURPLE)
zoomed_display_frame.set_color(RED)
zoomed_display.shift(DOWN)
zd_rect = BackgroundRectangle(zoomed_display, fill_opacity=0, buff=MED_SMALL_BUFF)
self.add_foreground_mobject(zd_rect)
unfold_camera = UpdateFromFunc(zd_rect, lambda rect: rect.replace(zoomed_display))
frame_text.next_to(frame, DOWN)
self.play(ShowCreation(frame), FadeInFrom(frame_text, direction=DOWN))
self.activate_zooming()
self.play(self.get_zoomed_display_pop_out_animation(), unfold_camera)
zoomed_camera_text.next_to(zoomed_display_frame, DOWN)
self.play(FadeInFrom(zoomed_camera_text, direction=DOWN))
# Scale in x y z
scale_factor = [0.5, 1.5, 0]
self.play(
frame.animate.scale(scale_factor),
zoomed_display.animate.scale(scale_factor),
FadeOut(zoomed_camera_text),
FadeOut(frame_text)
)
self.wait()
self.play(ScaleInPlace(zoomed_display, 2))
self.wait()
self.play(frame.animate.shift(2.5 * DOWN))
self.wait()
self.play(self.get_zoomed_display_pop_out_animation(), unfold_camera, rate_func=lambda t: smooth(1 - t))
self.play(Uncreate(zoomed_display_frame), FadeOut(frame))
self.wait()
.. manim:: FixedInFrameMObjectTest
:save_last_frame:
:ref_classes: ThreeDScene
:ref_functions: ThreeDScene.set_camera_orientation ThreeDScene.add_fixed_in_frame_mobjects
class FixedInFrameMObjectTest(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
self.set_camera_orientation(phi=75 * DEGREES, theta=-45 * DEGREES)
text3d = Text("This is a 3D text")
self.add_fixed_in_frame_mobjects(text3d)
text3d.to_corner(UL)
self.add(axes)
self.wait()
.. manim:: ThreeDLightSourcePosition
:save_last_frame:
:ref_classes: ThreeDScene ThreeDAxes ParametricSurface
:ref_functions: ThreeDScene.set_camera_orientation
class ThreeDLightSourcePosition(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
sphere = ParametricSurface(
lambda u, v: np.array([
1.5 * np.cos(u) * np.cos(v),
1.5 * np.cos(u) * np.sin(v),
1.5 * np.sin(u)
]), v_min=0, v_max=TAU, u_min=-PI / 2, u_max=PI / 2,
checkerboard_colors=[RED_D, RED_E], resolution=(15, 32)
)
self.renderer.camera.light_source.move_to(3*IN) # changes the source of the light
self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
self.add(axes, sphere)
.. manim:: ThreeDCameraRotation
:ref_classes: ThreeDScene ThreeDAxes
:ref_functions: ThreeDScene.begin_ambient_camera_rotation ThreeDScene.stop_ambient_camera_rotation
class ThreeDCameraRotation(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
circle=Circle()
self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
self.add(circle,axes)
self.begin_ambient_camera_rotation(rate=0.1)
self.wait(3)
self.stop_ambient_camera_rotation()
self.move_camera(phi=75 * DEGREES, theta=30 * DEGREES)
self.wait()
.. manim:: ThreeDCameraIllusionRotation
:ref_classes: ThreeDScene ThreeDAxes
:ref_functions: ThreeDScene.begin_3dillusion_camera_rotation ThreeDScene.stop_3dillusion_camera_rotation
class ThreeDCameraIllusionRotation(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
circle=Circle()
self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
self.add(circle,axes)
self.begin_3dillusion_camera_rotation(rate=2)
self.wait(PI)
self.stop_3dillusion_camera_rotation()
.. manim:: ThreeDFunctionPlot
:ref_classes: ThreeDScene ParametricSurface
class ThreeDFunctionPlot(ThreeDScene):
def construct(self):
resolution_fa = 22
self.set_camera_orientation(phi=75 * DEGREES, theta=-30 * DEGREES)
def param_plane(u, v):
x = u
y = v
z = 0
return np.array([x, y, z])
plane = ParametricSurface(
param_plane,
resolution=(resolution_fa, resolution_fa),
v_min=-2,
v_max=+2,
u_min=-2,
u_max=+2,
)
plane.scale_about_point(2, ORIGIN)
def param_gauss(u, v):
x = u
y = v
d = np.sqrt(x * x + y * y)
sigma, mu = 0.4, 0.0
z = np.exp(-((d - mu) ** 2 / (2.0 * sigma ** 2)))
return np.array([x, y, z])
gauss_plane = ParametricSurface(
param_gauss,
resolution=(resolution_fa, resolution_fa),
v_min=-2,
v_max=+2,
u_min=-2,
u_max=+2,
)
gauss_plane.scale_about_point(2, ORIGIN)
gauss_plane.set_style(fill_opacity=1)
gauss_plane.set_style(stroke_color=GREEN)
gauss_plane.set_fill_by_checkerboard(GREEN, BLUE, opacity=0.1)
axes = ThreeDAxes()
self.add(axes)
self.play(Write(plane))
self.play(Transform(plane, gauss_plane))
self.wait()
Advanced Projects
=================
.. manim:: OpeningManim
:ref_classes: Tex MathTex Write FadeInFrom LaggedStart NumberPlane ShowCreation
:ref_functions: NumberPlane.prepare_for_nonlinear_transform
class OpeningManim(Scene):
def construct(self):
title = Tex(r"This is some \LaTeX")
basel = MathTex(r"\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}")
VGroup(title, basel).arrange(DOWN)
self.play(
Write(title),
FadeInFrom(basel, UP),
)
self.wait()
transform_title = Tex("That was a transform")
transform_title.to_corner(UP + LEFT)
self.play(
Transform(title, transform_title),
LaggedStart(*[FadeOutAndShift(obj, direction=DOWN) for obj in basel]),
)
self.wait()
grid = NumberPlane()
grid_title = Tex("This is a grid")
grid_title.scale(1.5)
grid_title.move_to(transform_title)
self.add(grid, grid_title) # Make sure title is on top of grid
self.play(
FadeOut(title),
FadeInFrom(grid_title, direction=DOWN),
ShowCreation(grid, run_time=3, lag_ratio=0.1),
)
self.wait()
grid_transform_title = Tex(
r"That was a non-linear function \\ applied to the grid"
)
grid_transform_title.move_to(grid_title, UL)
grid.prepare_for_nonlinear_transform()
self.play(
grid.animate.apply_function(
lambda p: p
+ np.array(
[
np.sin(p[1]),
np.sin(p[0]),
0,
]
)
),
run_time=3,
)
self.wait()
self.play(Transform(grid_title, grid_transform_title))
self.wait()
.. manim:: SineCurveUnitCircle
:ref_classes: MathTex Circle Dot Line VGroup
:ref_functions: Mobject.add_updater Mobject.remove_updater always_redraw
class SineCurveUnitCircle(Scene):
# contributed by heejin_park, https://infograph.tistory.com/230
def construct(self):
self.show_axis()
self.show_circle()
self.move_dot_and_draw_curve()
self.wait()
def show_axis(self):
x_start = np.array([-6,0,0])
x_end = np.array([6,0,0])
y_start = np.array([-4,-2,0])
y_end = np.array([-4,2,0])
x_axis = Line(x_start, x_end)
y_axis = Line(y_start, y_end)
self.add(x_axis, y_axis)
self.add_x_labels()
self.origin_point = np.array([-4,0,0])
self.curve_start = np.array([-3,0,0])
def add_x_labels(self):
x_labels = [
MathTex("\pi"), MathTex("2 \pi"),
MathTex("3 \pi"), MathTex("4 \pi"),
]
for i in range(len(x_labels)):
x_labels[i].next_to(np.array([-1 + 2*i, 0, 0]), DOWN)
self.add(x_labels[i])
def show_circle(self):
circle = Circle(radius=1)
circle.move_to(self.origin_point)
self.add(circle)
self.circle = circle
def move_dot_and_draw_curve(self):
orbit = self.circle
origin_point = self.origin_point
dot = Dot(radius=0.08, color=YELLOW)
dot.move_to(orbit.point_from_proportion(0))
self.t_offset = 0
rate = 0.25
def go_around_circle(mob, dt):
self.t_offset += (dt * rate)
# print(self.t_offset)
mob.move_to(orbit.point_from_proportion(self.t_offset % 1))
def get_line_to_circle():
return Line(origin_point, dot.get_center(), color=BLUE)
def get_line_to_curve():
x = self.curve_start[0] + self.t_offset * 4
y = dot.get_center()[1]
return Line(dot.get_center(), np.array([x,y,0]), color=YELLOW_A, stroke_width=2 )
self.curve = VGroup()
self.curve.add(Line(self.curve_start,self.curve_start))
def get_curve():
last_line = self.curve[-1]
x = self.curve_start[0] + self.t_offset * 4
y = dot.get_center()[1]
new_line = Line(last_line.get_end(),np.array([x,y,0]), color=YELLOW_D)
self.curve.add(new_line)
return self.curve
dot.add_updater(go_around_circle)
origin_to_circle_line = always_redraw(get_line_to_circle)
dot_to_curve_line = always_redraw(get_line_to_curve)
sine_curve_line = always_redraw(get_curve)
self.add(dot)
self.add(orbit, origin_to_circle_line, dot_to_curve_line, sine_curve_line)
self.wait(8.5)
dot.remove_updater(go_around_circle)