Watch this animation first.
The manim code to generate the above animation is given below:
class ValueSliderLine(VMobject):
def __init__(self,variable='x',range=[-5,5,1],tracker=ValueTracker(0), **kwargs):
super().__init__(**kwargs)
self.number_line = NumberLine(
x_range=range,
length=5,
color=BLUE,
include_numbers=True,
).scale(0.75)
self.pointer = Dot(point=self.number_line.n2p(tracker.get_value()),radius=0.08)
self.label = MathTex(variable).add_updater(lambda m: m.next_to(self.pointer, UP)).scale(0.8)
self.tracker = tracker
self.pointer.add_updater(
lambda m: m.move_to(self.number_line.n2p(self.tracker.get_value()))
)
self.Value_slider = VGroup(self.label, self.number_line,self.pointer)
class PolarPlane_WithSettings(VMobject):
def __init__(self, radius=2, **kwargs):
super().__init__(**kwargs)
self.radius = radius * 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)
class a_plus_b_cos_c_theta(Scene):
"""Animate r= a cos(b*theta) in polar coordinates"""
def construct(self):
r_color = YELLOW
a = 1
b = 2
c = 3
a_value_tracker = ValueTracker(a)
b_value_tracker = ValueTracker(b)
c_value_tracker = ValueTracker(1)
def period(c):
return abs(c*TAU)
polar_plane = PolarPlane_WithSettings(radius=a+b).plane
ftext = MathTex("r=a+b\\cos(\\theta/c)").next_to(polar_plane, UP,buff=0.05)
func = lambda t: polar_plane.polar_to_point(a+b * np.cos(t/c), t)
graph = ParametricFunction(func, t_range=[0, period(c)], color=r_color)
def graph_update_fun(x):
if (c_value_tracker.get_value()).is_integer() and (c_value_tracker.get_value() != 0):
x.become(ParametricFunction(lambda t:
polar_plane.polar_to_point(a_value_tracker.get_value()+
b_value_tracker.get_value() * np.cos(t/int(c_value_tracker.get_value())), t),
t_range=[0, period(int(c_value_tracker.get_value()))], color=r_color))
graph.add_updater(graph_update_fun)
graph_group=VGroup(polar_plane,ftext,graph)
graph_group.shift(LEFT*2)
a_slider = ValueSliderLine(variable='a', range=[-a, a, 1], tracker=a_value_tracker)
b_slider = ValueSliderLine(variable='b', range=[-b, b, 1], tracker=b_value_tracker)
c_slider = ValueSliderLine(variable='c', range=[1, c, 1], tracker=c_value_tracker)
slider_group=VGroup(a_slider.Value_slider,b_slider.Value_slider,
c_slider.Value_slider).arrange(DOWN,buff=1.0).next_to(graph_group,RIGHT,buff=1.0)
scene_group=VGroup(graph_group,slider_group)
scene_group.scale(0.75)
self.play(Create(polar_plane))
self.play(Create(ftext))
self.wait()
self.play(Create(slider_group))
self.play(Create(graph))
self.play(slider_group[0].animate.scale(1.2))
self.play(a_value_tracker.animate.set_value(-a), run_time=2, rate_functions=linear)
self.play(a_value_tracker.animate.set_value(a), run_time=1, rate_functions=linear)
self.play(slider_group[0].animate.scale(1.0 / 1.2))
self.play(slider_group[1].animate.scale(1.2))
self.play(b_value_tracker.animate.set_value(-b), run_time=2, rate_functions=linear)
self.play(b_value_tracker.animate.set_value(b), run_time=1, rate_functions=linear)
self.play(slider_group[1].animate.scale(1.0 / 1.2))
self.wait()
c_val=c_value_tracker.get_value()
c_inc=1
while c_val
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