Let’s look at the animation first:
The above animation shows pretty graph of r=2 sin( 3 theta). The manim scene class rendering the above video is following (download codes and raw videos used above ):
from manim import *
class sin_graph(Scene):
def construct(self):
value_tracker = ValueTracker(0.01) #Tracks the end value of both functions
a_color = PINK
b_color = BLUE_D
th_color = RED_D
r_color = YELLOW
text_scaleUp=1.2
text_scaleDown=1.0/text_scaleUp
a=2
b=3
if b%2==0:
period=2*PI
else:
period=PI
sin_g=a_sin_b_theta(value_tracker,r_color,a,b) #a=2,b=3
moving_line=MovingLine(value_tracker,sin_g.radius,th_color)
self.play(Create(sin_g.plane))
self.wait()
self.play(Create(sin_g.title))
self.wait()
self.play(Create(sin_g.title[2].set_color(a_color)),
sin_g.title[2].animate.scale(text_scaleUp))
self.wait()
self.play(Create(sin_g.circle.set_color(a_color)),run_time=2)
self.wait()
self.play(sin_g.title[2].animate.scale(text_scaleDown))
self.wait()
self.play(sin_g.title[4].animate.set_color(b_color))
self.play(sin_g.title[4].animate.scale(text_scaleUp))
self.wait()
self.play(Create(sin_g.leaf_lines.set_color(b_color)),run_time=3)
self.wait()
self.play(sin_g.title[4].animate.scale(text_scaleDown))
self.wait()
self.play(Create(sin_g.title[5].set_color(th_color)),
sin_g.title[5].animate.scale(text_scaleUp))
self.wait()
self.play(Create(moving_line.line_ref),run_time=2)
self.wait()
self.play(Create(sin_g.title[0].set_color(r_color)),
sin_g.title[0].animate.scale(text_scaleUp*1.2))
self.wait()
self.add(moving_line.line_moving)
self.add(sin_g)
self.play(value_tracker.animate.set_value(period), run_time = 10, rate_func = linear)
self.play(FadeOut(moving_line))
self.play(FadeOut(sin_g.leaf_lines))
self.play(FadeOut(sin_g.circle))
self.play(FadeOut(sin_g.plane))
self.wait()
self.play(sin_g.title[0].animate.scale(text_scaleDown),
sin_g.title[5].animate.scale(text_scaleDown))
self.play(sin_g.title.animate.set_color(r_color))
self.play((sin_g.title).animate.next_to(sin_g.graph,UP))
self.wait(2)
In above code, you can change the value of b to get different animations.
The the class “class sin_graph(Scene)” above use two more custom VMobjects defined below:
class MovingLine(VMobject):
def __init__(self,value_tracker,radius,th_color, **kwargs):
super().__init__(**kwargs)
self.radius=radius
self.theta_tracker = value_tracker
self.line_moving = Line(np.array([-self.radius,0,0]), np.array([self.radius,0,0]))
self.line_ref =Line(np.array([-self.radius,0,0]), np.array([self.radius,0,0])).set_color(th_color)
self.rotation_center = Dot(self.line_ref.get_center()) # Use Dot as rotation center
# Update rotation center position whenever line_ref moves
self.rotation_center.add_updater(lambda x: x.move_to(self.line_ref.get_center()))
self.line_moving.add_updater(
lambda x: x.become(self.line_ref.copy()).rotate(
self.theta_tracker.get_value(), about_point=self.rotation_center.get_center()
).set_color(th_color)
)
self.add(self.line_ref, self.rotation_center, self.line_moving)
and another one:
class a_sin_b_theta(VMobject):
def __init__(self, value_tracker,r_color,a,b, **kwargs):
super().__init__(**kwargs)
self.radius=a*1.125
background_line_style = {
"stroke_color": BLUE_E,
"stroke_width": 0.5,
"stroke_opacity": 1,
}
self.plane = PolarPlane(radius_max=self.radius, size=self.radius*2,
azimuth_units="degrees",
azimuth_step=12,
background_line_style=background_line_style
).add_coordinates()
ax=self.plane.get_axes()
ax.set_stroke(color=WHITE, width=0.5)
self.graph = always_redraw(
lambda: ParametricFunction(
lambda t: self.plane.polar_to_point(a* np.sin(b* t), t),
t_range=[0, value_tracker.get_value()],
color=r_color,
)
)
self.dot = always_redraw(
lambda: Dot(
fill_color=r_color, fill_opacity=0.8
).scale(0.8).move_to(self.graph.get_end())
)
self.title=VGroup()
self.title.add(MathTex("r", color=WHITE))#0
self.title.add(MathTex(" = ", color=WHITE))#1
self.title.add(MathTex(str(a), color=WHITE)) #2
self.title.add(MathTex("\\sin(", color=WHITE)) #3
self.title.add(MathTex(str(b), color=WHITE))#4
self.title.add(MathTex("\\theta", color=WHITE))#5
self.title.add(MathTex(")", color=WHITE))#6
self.title.arrange(RIGHT, buff=0.1)
self.title.next_to(self.plane, UP, buff=0.05)
self.graph.add_updater(
lambda x: x.become(
ParametricFunction(
lambda t: self.plane.polar_to_point(
a * np.sin(b * t), t
),
t_range=[0, value_tracker.get_value()],
color=r_color,
)
)
)
self.dot.add_updater(
lambda x: x.become(
Dot(fill_color=r_color, fill_opacity=0.8)
.scale(0.7)
.move_to(self.graph.get_end())
)
)
self.leaf_lines=VGroup()
i=0
its=[]
while len(its)<b:
it=(2*i+1)/(2*b)
its.append(it)
th=it*PI
if b%2!=0:
self.leaf_lines.add(Line(np.array([0,0,0]), self.plane.polar_to_point(a * np.sin(b* th), th)))
else:
self.leaf_lines.add(Line(self.plane.polar_to_point(-a * np.sin(b* th), th),
self.plane.polar_to_point(a * np.sin(b* th), th)))
i+=1
self.circle=Circle(radius=a)
self.add(self.graph, self.dot)
Happy manimations!
Hope you enjoy experimenting above codes.
Thanks.
learnsharewithdp 