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circle_on_complex_plane.py
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circle_on_complex_plane.py
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from manimlib.imports import *
def tex(str, color=WHITE):
return TexMobject(str, color=color).scale(0.7)
def xy(x, y):
return np.array([x, y, 0])
class CircleOnComplexPlane(MovingCameraScene):
def construct(self):
self.draw_axis()
self.draw_circle()
self.move_circle()
self.wait()
def draw_axis(self):
min_x, max_x = -6, -2
min_y, max_y = 0, 3.7
ori = xy(-4, 2)
def get_line(s,e):
return Line(s,e , color=BLUE, stroke_width=5)
x_axis = get_line(xy(min_x,ori[1]), xy(max_x,ori[1]))
y_axis = get_line(xy(ori[0], min_y), xy(ori[0], max_y))
t_x1=tex("1").scale(0.85).move_to(xy(-3,2)).shift(RIGHT*0.1+DOWN*0.15)
t_xm1=tex("-1").scale(0.85).move_to(xy(-5, 2)).shift(LEFT * 0.25 + DOWN * 0.15)
t_y1=tex("i").move_to(xy(-4, 3)).shift(LEFT * 0.2+UP*0.2 )
t_ym1=tex("-i").move_to(xy(-4, 1)).shift(LEFT * 0.25+DOWN*0.15 )
self.add(x_axis, y_axis)
self.add(t_x1, t_xm1,t_y1,t_ym1)
self.ori = ori
def draw_circle(self):
ori = self.ori
circle = Circle(radius=1).move_to(ori)
self.add(circle)
self.circle = circle
def move_circle(self):
circle = self.circle
dot = Dot(radius=0.06).move_to(xy(-3,2))
cf = self.camera_frame
self.play(
cf.move_to,self.ori,
cf.scale, 0.5,
run_time=2,
)
self.play(ShowCreation(dot))
vt = ValueTracker(0)
def update_dot(mob):
p = vt.get_value() % 1
mob.move_to(circle.point_from_proportion(p))
dot.add_updater(update_dot)
self.play(vt.set_value, 1.00, rate_func=linear)
dot.remove_updater(update_dot)
## line위 dot
dot2=Dot(radius=0.04, color=YELLOW).move_to(xy(-3,2))
line = Line(dot2.center(),dot2.center())
self.play(
ShowCreation(dot2),
ShowCreation(line),
)
def update_dot2(mob):
y = self.ori[1]
x = dot.get_center()[0]
mob.move_to(xy(x,y))
def update_line(mob):
new_line = Line(dot.get_center(), dot2.get_center())
mob.become(new_line)
dot2.add_updater(update_dot2)
line.add_updater(update_line)
dot.add_updater(update_dot)
vt.set_value(0)
self.play(vt.set_value,2, rate_func=linear, run_time=8)
class CircleOnComplexPlane_COS(Scene):
def construct(self):
self.draw_axis()
self.draw_circle()
self.move_circle()
self.wait(2)
def draw_axis(self):
min_x, max_x = -6, -2
min_y, max_y = -3.7, 3.7
ori = xy(-4, 2)
def get_line(s,e):
return Line(s,e , color=BLUE, stroke_width=5)
x_axis = get_line(xy(min_x,ori[1]), xy(max_x,ori[1]))
y_axis = get_line(xy(ori[0], min_y), xy(ori[0], max_y))
t_x1=tex("1").scale(0.85).move_to(xy(-3,2)).shift(RIGHT*0.1+DOWN*0.15)
t_xm1=tex("-1").scale(0.85).move_to(xy(-5, 2)).shift(LEFT * 0.25 + DOWN * 0.15)
t_y1=tex("i").move_to(xy(-4, 3)).shift(LEFT * 0.2+UP*0.2 )
t_ym1=tex("-i").move_to(xy(-4, 1)).shift(LEFT * 0.25+DOWN*0.15 )
self.add(x_axis, y_axis)
self.add(t_x1, t_xm1,t_y1,t_ym1)
self.ori = ori
def draw_circle(self):
ori = self.ori
circle = Circle(radius=1).move_to(ori)
self.add(circle)
self.circle = circle
def move_circle(self):
circle = self.circle
dot = Dot(radius=0.06).move_to(xy(-3,2))
self.play(ShowCreation(dot))
vt = ValueTracker(0)
def update_dot(mob):
p = vt.get_value() % 1
mob.move_to(circle.point_from_proportion(p))
dot.add_updater(update_dot)
self.play(vt.set_value, 1.00, rate_func=linear)
dot.remove_updater(update_dot)
dot2=Dot(radius=0.04, color=YELLOW).move_to(xy(-3,2))
line = Line(dot2.get_center(),dot2.get_center())
wave = VGroup(Line(dot2.get_center(),dot2.get_center(), color=YELLOW))
self.play(
ShowCreation(dot2),
ShowCreation(line),
ShowCreation(wave),
)
#cosine 라인괘적
def update_dot2(mob):
y = self.ori[1] - (vt.get_value() % 1.0) * 5
x = dot.get_center()[0]
mob.move_to(xy(x,y))
def update_line(mob):
new_line = Line(dot.get_center(), dot2.get_center())
mob.become(new_line)
def update_wave(mob):
line_group = mob.copy()
last_line = line_group[-1]
s = last_line.get_end()
e = dot2.get_center()
#두바퀴째 원을 그릴때, wave끝에서 dot2쪽으로의 선이 그려지지 않게하기위함임
if s[1] < e[1]: return
new_line = Line(s, e, color=YELLOW_D)
line_group.add(new_line)
mob.become(line_group)
dot2.add_updater(update_dot2)
line.add_updater(update_line)
dot.add_updater(update_dot)
wave.add_updater(update_wave)
vt.set_value(0)
self.play(vt.set_value,2, rate_func=linear, run_time=8)
class CircleOnComplexPlane_Imaginary(MovingCameraScene):
def construct(self):
self.draw_axis()
self.draw_circle()
self.move_circle()
self.wait()
def draw_axis(self):
min_x, max_x = -6, -2
min_y, max_y = 0, 3.7
ori = xy(-4, 2)
def get_line(s,e):
return Line(s,e , color=BLUE, stroke_width=5)
x_axis = get_line(xy(min_x,ori[1]), xy(max_x,ori[1]))
y_axis = get_line(xy(ori[0], min_y), xy(ori[0], max_y))
t_x1=tex("1").scale(0.85).move_to(xy(-3,2)).shift(RIGHT*0.1+DOWN*0.15)
t_xm1=tex("-1").scale(0.85).move_to(xy(-5, 2)).shift(LEFT * 0.25 + DOWN * 0.15)
t_y1=tex("i").move_to(xy(-4, 3)).shift(LEFT * 0.2+UP*0.2 )
t_ym1=tex("-i").move_to(xy(-4, 1)).shift(LEFT * 0.25+DOWN*0.15 )
self.add(x_axis, y_axis)
self.add(t_x1, t_xm1,t_y1,t_ym1)
self.ori = ori
def draw_circle(self):
ori = self.ori
circle = Circle(radius=1).move_to(ori)
self.add(circle)
self.circle = circle
def move_circle(self):
circle = self.circle
dot = Dot(radius=0.06).move_to(xy(-3,2))
cf = self.camera_frame
self.play(
cf.move_to,self.ori,
cf.scale, 0.5,
run_time=2,
)
self.play(ShowCreation(dot))
vt = ValueTracker(0)
def update_dot(mob):
p = vt.get_value() % 1
mob.move_to(circle.point_from_proportion(p))
dot.add_updater(update_dot)
self.play(vt.set_value, 1.00, rate_func=linear)
dot.remove_updater(update_dot)
## line위 dot
dot2=Dot(radius=0.04, color=YELLOW).move_to(xy(-3,2))
line = Line(dot2.center(),dot2.center())
self.play(
ShowCreation(dot2),
ShowCreation(line),
)
def update_dot2(mob):
y = dot.get_center()[1]
x = self.ori[0] #고정
mob.move_to(xy(x,y))
def update_line(mob):
new_line = Line(dot.get_center(), dot2.get_center())
mob.become(new_line)
dot2.add_updater(update_dot2)
line.add_updater(update_line)
dot.add_updater(update_dot)
vt.set_value(0)
self.play(vt.set_value,1, rate_func=linear, run_time=4)
self.wait()
self.play(vt.set_value, 2, rate_func=linear, run_time=4)
class CircleOnComplexPlane_SIN(Scene):
def construct(self):
self.draw_axis()
self.draw_circle()
self.move_circle()
self.wait(1)
def draw_axis(self):
min_x, max_x = -6, 2
min_y, max_y = 0, 3.7
ori = xy(-4, 2)
def get_line(s,e):
return Line(s,e , color=BLUE, stroke_width=5)
x_axis = get_line(xy(min_x,ori[1]), xy(max_x,ori[1]))
y_axis = get_line(xy(ori[0], min_y), xy(ori[0], max_y))
t_x1=tex("1").scale(0.85).move_to(xy(-3,2)).shift(RIGHT*0.1+DOWN*0.15)
t_xm1=tex("-1").scale(0.85).move_to(xy(-5, 2)).shift(LEFT * 0.25 + DOWN * 0.15)
t_y1=tex("i").move_to(xy(-4, 3)).shift(LEFT * 0.2+UP*0.2 )
t_ym1=tex("-i").move_to(xy(-4, 1)).shift(LEFT * 0.25+DOWN*0.15 )
self.add(x_axis, y_axis)
self.add(t_x1, t_xm1,t_y1,t_ym1)
self.ori = ori
def draw_circle(self):
ori = self.ori
circle = Circle(radius=1).move_to(ori)
self.add(circle)
self.circle = circle
def move_circle(self):
circle = self.circle
dot = Dot(radius=0.06).move_to(xy(-3,2)) #원위를 움직인느.
self.play(ShowCreation(dot))
vt = ValueTracker(0)
def update_dot(mob):
p = vt.get_value() % 1
mob.move_to(circle.point_from_proportion(p))
dot.add_updater(update_dot)
self.play(vt.set_value, 1.00, rate_func=linear)
dot.remove_updater(update_dot)
dot2=Dot(radius=0.04, color=YELLOW).move_to(self.ori) #사인파를 그리는.
line = Line(dot2.get_center(),dot2.get_center())
wave = VGroup(Line(dot2.get_center(),dot2.get_center(), color=YELLOW))
self.play(
ShowCreation(dot2),
ShowCreation(line),
ShowCreation(wave),
)
#sine 라인괘적을 따라 움직인다.
def update_dot2(mob):
y = dot.get_center()[1] #sin 괘적. 원위의 dot의 y좌표
x = self.ori[0] + (vt.get_value() % 1.0) * 5 #시간의 흐름
mob.move_to(xy(x,y))
def update_line(mob):
new_line = Line(dot.get_center(), dot2.get_center())
mob.become(new_line)
def update_wave(mob):
line_group = mob.copy()
last_line = line_group[-1]
s = last_line.get_end()
e = dot2.get_center()
#두바퀴째 원을 그릴때, wave끝에서 dot2쪽으로의 선이 그려지지 않게하기위함임
if s[0] > e[0]: return
new_line = Line(s, e, color=YELLOW_D)
line_group.add(new_line)
mob.become(line_group)
dot2.add_updater(update_dot2)
line.add_updater(update_line)
dot.add_updater(update_dot)
wave.add_updater(update_wave)
vt.set_value(0)
self.play(vt.set_value, 0.4, rate_func=linear, run_time=3) #1. 처음부분은 천천히 보여주고
self.wait() #2. 잠시 쉬었다가
self.play(vt.set_value,2, rate_func=linear, run_time=8) #3. 나머지 전체를 보여줌
class CircleOnComplexPlane_SINCOS(Scene):
def construct(self):
self.draw_axis()
self.draw_circle()
self.move_circle()
self.wait(1)
def draw_axis(self):
min_x, max_x = -6, 2
min_y, max_y = -3.7, 3.7
ori = xy(-4, 2)
def get_line(s,e):
return Line(s,e , color=BLUE, stroke_width=5)
x_axis = get_line(xy(min_x,ori[1]), xy(max_x,ori[1]))
y_axis = get_line(xy(ori[0], min_y), xy(ori[0], max_y))
t_x1=tex("1").scale(0.85).move_to(xy(-3,2)).shift(RIGHT*0.1+DOWN*0.15)
t_xm1=tex("-1").scale(0.85).move_to(xy(-5, 2)).shift(LEFT * 0.25 + DOWN * 0.15)
t_y1=tex("i").move_to(xy(-4, 3)).shift(LEFT * 0.2+UP*0.2 )
t_ym1=tex("-i").move_to(xy(-4, 1)).shift(LEFT * 0.25+DOWN*0.15 )
self.add(x_axis, y_axis)
self.add(t_x1, t_xm1,t_y1,t_ym1)
self.ori = ori
def draw_circle(self):
ori = self.ori
circle = Circle(radius=1).move_to(ori)
# self.add(circle)
self.circle = circle
def move_circle(self):
circle = self.circle
dot = Dot(radius=0.06).move_to(xy(-3,2)) #원위를 움직인느.
self.play(ShowCreation(dot))
vt = ValueTracker(0)
def update_dot(mob):
p = vt.get_value() % 1
mob.move_to(circle.point_from_proportion(p))
dot_sine=Dot(radius=0.06, color=YELLOW).move_to(self.ori) #사인파를 그리는.
line_sine = Line(dot_sine.get_center(),dot_sine.get_center(), color=YELLOW)
wave_sine = VGroup(Line(dot_sine.get_center(),dot_sine.get_center(), color=YELLOW))
dot_cos = Dot(radius=0.06, color=WHITE).move_to(self.ori) # 사인파를 그리는.
line_cos = Line(dot_cos.get_center(), dot_cos.get_center(), color=WHITE)
wave_cos = VGroup(Line(dot_cos.get_center(), dot_cos.get_center(), color=WHITE))
circle_group = VGroup(Line(dot.get_center(), dot.get_center(), color=RED))
self.play(
ShowCreation(dot_sine),
ShowCreation(line_sine),
ShowCreation(wave_sine),
ShowCreation(dot_cos),
ShowCreation(line_cos),
ShowCreation(wave_cos),
ShowCreation(circle_group)
)
# sine 라인괘적을 따라 움직인다.
def update_dot_sine(mob):
y = dot.get_center()[1] # sin 괘적. 원위의 dot의 y좌표
x = self.ori[0] + (vt.get_value() % 1.0) * 5 # 시간의 흐름
mob.move_to(xy(x, y))
def update_line_sine(mob):
new_line = Line(dot_sine.get_center(), dot.get_center(),color=YELLOW)
mob.become(new_line)
def update_wave_sine(mob):
line_group = mob.copy()
last_line = line_group[-1]
s = last_line.get_end()
e = dot_sine.get_center()
#두바퀴째 원을 그릴때, wave끝에서 dot2쪽으로의 선이 그려지지 않게하기위함임
if s[0] > e[0]: return
new_line = Line(s, e, color=YELLOW_D)
line_group.add(new_line)
mob.become(line_group)
# cos 라인괘적을 따라 움직인다.
def update_dot_cos(mob):
y = self.ori[1] - (vt.get_value() % 1.0) * 5 # 시간의 흐름
x = dot.get_center()[0] # cos 괘적. 원위의 dot의 x좌표
mob.move_to(xy(x, y))
def update_line_cos(mob):
new_line = Line(dot_cos.get_center(), dot.get_center(),color=WHITE)
mob.become(new_line)
def update_wave_cos(mob):
line_group = mob.copy()
last_line = line_group[-1]
s = last_line.get_end()
e = dot_cos.get_center()
# 두바퀴째 원을 그릴때, wave끝에서 dot2쪽으로의 선이 그려지지 않게하기위함임
if s[1] < e[1]: return
new_line = Line(s, e, color=WHITE)
line_group.add(new_line)
mob.become(line_group)
def update_circle_group(mob):
line_group = mob.copy()
last_line = line_group[-1]
s = last_line.get_end()
e = dot.get_center()
new_line = Line(s, e, color=RED)
line_group.add(new_line)
mob.become(line_group)
dot_sine.add_updater(update_dot_sine)
line_sine.add_updater(update_line_sine)
wave_sine.add_updater(update_wave_sine)
dot_cos.add_updater(update_dot_cos)
line_cos.add_updater(update_line_cos)
wave_cos.add_updater(update_wave_cos)
dot.add_updater(update_dot)
circle_group.add_updater(update_circle_group)
vt.set_value(0)
self.play(vt.set_value, 0.4, rate_func=linear, run_time=4) #1. 처음부분은 천천히 보여주고
self.wait() #2. 잠시 쉬었다가
self.play(vt.set_value,1, rate_func=linear, run_time=4) #3. 나머지 전체를 보여줌
self.wait()
vt.set_value(0)
self.play(vt.set_value, 1, rate_func=linear, run_time=3) # 3. 나머지 전체를 보여줌
class CircelOnComplexPlane_SINCOS2(MovingCameraScene):
def construct(self):
self.draw_axis()
self.draw_cosine()
self.draw_sine()
self.draw_circle()
self.wait()
def draw_axis(self):
min_x, max_x = -6, 2
min_y, max_y = -3.7, 3.7
ori = xy(-4, 2)
def get_line(s,e):
return Line(s,e , color=BLUE, stroke_width=5)
x_axis = get_line(xy(min_x,ori[1]), xy(max_x,ori[1]))
y_axis = get_line(xy(ori[0], min_y), xy(ori[0], max_y))
t_x1=tex("1").scale(0.85).move_to(xy(-3,2)).shift(RIGHT*0.1+DOWN*0.15)
t_xm1=tex("-1").scale(0.85).move_to(xy(-5, 2)).shift(LEFT * 0.25 + DOWN * 0.15)
t_y1=tex("i").move_to(xy(-4, 3)).shift(LEFT * 0.2+UP*0.2 )
t_ym1=tex("-i").move_to(xy(-4, 1)).shift(LEFT * 0.25+DOWN*0.15 )
self.add(x_axis, y_axis)
self.add(t_x1, t_xm1,t_y1,t_ym1)
self.ori = ori
def draw_cosine(self):
max_len = 5
#origin_point:원점, starting_point:그래프 시작점, curve_len:그래프의 길이
def get_cosine_graph(op, sp, curve_len):
t = np.arange(0,2*np.pi,0.1) # 0~2pi까지 0.1간격
dt = curve_len / len(t)
y_t = np.cos(t)
g = VGroup(Line(sp,sp))
for i in range(0, len(t)):
end_p = g[-1].get_end()
px = op[0] + y_t[i]
py = end_p[1] - dt
new_line = Line(end_p, xy(px,py))
g.add(new_line)
return g
ori = self.ori
cos_t = tex(r"\cos \theta").move_to(xy(-5.5,-0.5))
graph_start_pos = xy(ori[0]+1, ori[1])
cos_graph = get_cosine_graph(ori, graph_start_pos, max_len )
self.add(cos_graph, cos_t)
vt = ValueTracker(0)
#1. dot가 코사인 그래프를 따라서 한번 왔다 갔다
def update_dot(mob):
alpha = vt.get_value() % 1.0
subs = cos_graph.submobjects
len_subs = len(subs)
if len_subs == 0 : return
pos = int(alpha * len_subs)
mob.move_to(subs[pos])
dot = Dot(color=WHITE).move_to(graph_start_pos)
self.add(dot)
dot.add_updater(update_dot)
self.play(vt.set_value, 1, rate_func=there_and_back, run_time=4)
# dot.remove_updater(update_dot)
#2. 코사인그래프를 shrink
def update_cos_graph(mob):
# vt: 0 0.5 1
# size: 0 2.5 5(=max_len)
tgt_size = vt.get_value() * max_len
new_graph = get_cosine_graph(ori, graph_start_pos, tgt_size)
mob.become(new_graph)
cos_graph.add_updater(update_cos_graph)
vt.set_value(1)
self.remove(cos_t)
self.play(vt.set_value, 0, rate_func=linear, run_time=4)
cos_graph.remove_updater(update_cos_graph)
#3. 전부 shrink된다음에 왔다 갔다
vt.set_value(0)
self.play(vt.set_value, 2, rate_func=linear, run_time=3)
dot.remove_updater(update_dot)
self.wait()
self.cos_dot = dot
def draw_sine(self):
max_len = 5
#origin_point:원점, starting_point:그래프 시작점, curve_len:그래프의 길이
def get_sine_graph(op, sp, curve_len):
t = np.arange(0,2*np.pi,0.1) # 0~2pi까지 0.1간격
dt = curve_len / len(t)
y_t = np.sin(t)
g = VGroup(Line(sp,sp, color=YELLOW))
for i in range(0, len(t)):
end_p = g[-1].get_end()
px = end_p[0] + dt
py = op[1] + y_t[i]
new_line = Line(end_p, xy(px,py), color=YELLOW)
g.add(new_line)
return g
ori = self.ori
sin_t = tex(r"\sin \theta",color=YELLOW).move_to(xy(-2.25, 3.2))
graph_start_pos = ori
sin_graph = get_sine_graph(ori, graph_start_pos, max_len )
self.add(sin_graph, sin_t)
vt = ValueTracker(0)
#1. dot가 사인 그래프를 따라서 한번 왔다 갔다
def update_dot(mob):
alpha = vt.get_value() % 1.0
subs = sin_graph.submobjects
len_subs = len(subs)
if len_subs == 0 : return
pos = int(alpha * len_subs)
mob.move_to(subs[pos])
dot = Dot(color=YELLOW).move_to(graph_start_pos)
self.add(dot)
dot.add_updater(update_dot)
self.play(vt.set_value, 1, rate_func=there_and_back, run_time=4)
#2. 사인그래프를 shrink
def update_sin_graph(mob):
# vt: 0 0.5 1
# size: 0 2.5 5(=max_len)
tgt_size = vt.get_value() * max_len
new_graph = get_sine_graph(ori, graph_start_pos, tgt_size)
mob.become(new_graph)
sin_graph.add_updater(update_sin_graph)
vt.set_value(1)
self.remove(sin_t)
self.play(vt.set_value, 0, rate_func=linear, run_time=4)
sin_graph.remove_updater(update_sin_graph)
#3. 전부 shrink된다음에 왔다 갔다
vt.set_value(0)
self.play(vt.set_value, 2, rate_func=linear, run_time=3)
dot.remove_updater(update_dot)
self.wait()
self.sin_dot = dot
def draw_circle(self):
ori = self.ori
cos_dot = self.cos_dot
sin_dot = self.sin_dot
cf = self.camera_frame
#1. frame 확대
self.play(
cf.move_to, ori,
cf.scale,0.5,
run_time=2,
)
#2.1 text
cos_t = tex(r"\cos \theta").scale(0.8).move_to(cos_dot).shift(UP*0.3)
sin_t = tex(r"\sin \theta").scale(0.8).move_to(sin_dot).shift(UP*0.3)
self.add(cos_t, sin_t)
#2.2 (dot+tex)만 move
left, right = xy(-5,2), xy(3,2)
top, bottom = xy(-4,3), xy(-4,1)
circle = Circle(radius=1, color=RED).move_to(ori)
circle_dot = Dot(radius=0,color=RED).move_to(right)
vt = ValueTracker(0)
def update_circle_dot(mob):
alpha = vt.get_value() % 1.0
mob.move_to(circle.point_from_proportion(alpha))
def update_cos_dot(mob):
p = xy(circle_dot.get_center()[0], 2)
mob.move_to(p)
def update_sin_dot(mob):
p = xy(-4, circle_dot.get_center()[1])
mob.move_to(p)
def update_cos_t(mob):
mob.move_to(cos_dot).shift(UP*0.3)
def update_sin_t(mob):
mob.move_to(sin_dot).shift(UP*0.3)
circle_dot.add_updater(update_circle_dot)
cos_dot.add_updater(update_cos_dot)
sin_dot.add_updater(update_sin_dot)
cos_t.add_updater(update_cos_t)
sin_t.add_updater(update_sin_t)
self.add(circle_dot)
self.play(vt.set_value, 2, rate_func=linear, run_time=4)
#3. 원그림
circle_group = VGroup(Line(circle_dot.get_center(), circle_dot.get_center(), color=RED))
cos_line = Line(cos_dot.get_center(), circle_dot.get_center(), color=WHITE)
sin_line = Line(sin_dot.get_center(), circle_dot.get_center(), color=YELLOW)
self.add(circle_group, cos_line, sin_line)
def update_circle_group(mob):
g = mob.copy()
last_pos = mob[-1].get_end()
new_line = Line(last_pos, circle_dot.get_center(), color=RED)
g.add(new_line)
mob.become(g)
def update_cos_line(mob):
new_line = Line(cos_dot.get_center(), circle_dot.get_center(), color=WHITE)
mob.become(new_line)
def update_sin_line(mob):
new_line = Line(sin_dot.get_center(), circle_dot.get_center(), color=YELLOW)
mob.become(new_line)
circle_group.add_updater(update_circle_group)
cos_line.add_updater(update_cos_line)
sin_line.add_updater(update_sin_line)
vt.set_value(0)
self.play(vt.set_value, 0.37, rate_func=linear, run_time=4)
self.wait()
self.play(vt.set_value, 1, rate_func=linear, run_time=5)
self.wait()
vt.set_value(0)
self.play(vt.set_value, 1, rate_func=linear, run_time=4)