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EulerWave.py
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EulerWave.py
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#from big_ol_pile_of_manim_imports import *
from manimlib.imports import *
line_1_rate_prev=0
line_1_rate_pres=2
line_2_rate_prev=0
line_2_rate_pres=2
subline_1_rate_prev=0
subline_1_rate_pres=2
subline_2_rate_prev=0
subline_2_rate_pres=2
#circle
#dot oscillating
#2 lines rotating
#dotted lines
#sine wave
class CheckFormulaByTXT(Scene):
CONFIG={
"camera_config":{"background_color": BLACK},
"svg_type":"text",
"text": TexMobject(""),
"file":"",
"svg_scale":0.9,
"angle":0,
"flip_svg":False,
"fill_opacity": 1,
"remove": [],
"stroke_color": WHITE,
"fill_color": WHITE,
"stroke_width": 3,
"numbers_scale":0.5,
"show_numbers": True,
"animation": False,
"direction_numbers": UP,
"color_numbers": RED,
"space_between_numbers":0,
"show_elements":[],
"color_element":BLUE,
"set_size":"width",
"remove_stroke":[],
"show_stroke":[],
"warning_color":RED,
"stroke_":1
}
def construct(self):
self.imagen=self.text
self.imagen.set_width(FRAME_WIDTH)
if self.imagen.get_height()>FRAME_HEIGHT:
self.imagen.set_height(FRAME_HEIGHT)
self.imagen.scale(self.svg_scale)
if self.flip_svg==True:
self.imagen.flip()
if self.show_numbers==True:
self.print_formula(self.imagen.copy(),
self.numbers_scale,
self.direction_numbers,
self.remove,
self.space_between_numbers,
self.color_numbers)
self.return_elements(self.imagen.copy(),self.show_elements)
for st in self.remove_stroke:
self.imagen[st].set_stroke(None,0)
for st in self.show_stroke:
self.imagen[st].set_stroke(None,self.stroke_)
if self.animation==True:
self.play(DrawBorderThenFill(self.imagen))
else:
c=0
for j in range(len(self.imagen)):
permission_print=True
for w in self.remove:
if j==w:
permission_print=False
if permission_print:
self.add(self.imagen[j])
c = c + 1
self.personalize_image()
self.wait()
def personalize_image(self):
pass
def print_formula(self,text,inverse_scale,direction,exception,buff,color):
text.set_color(self.warning_color)
self.add(text)
c = 0
for j in range(len(text)):
permission_print=True
for w in exception:
if j==w:
permission_print=False
if permission_print:
self.add(text[j].set_color(self.stroke_color))
c = c + 1
c=0
for j in range(len(text)):
permission_print=True
element = TexMobject("%d" %c,color=color)
element.scale(inverse_scale)
element.next_to(text[j],direction,buff=buff)
for w in exception:
if j==w:
permission_print=False
if permission_print:
self.add_foreground_mobjects(element)
c = c + 1
def return_elements(self,formula,adds):
for i in adds:
self.add_foreground_mobjects(formula[i].set_color(self.color_element),
TexMobject("%d"%i,color=self.color_element,background_stroke_width=0).scale(self.numbers_scale).next_to(formula[i],self.direction_numbers,buff=self.space_between_numbers))
class Check_Formula(CheckFormulaByTXT):
CONFIG={
"text": TextMobject(
"if",
r"$\theta$",
"increases with time",
#"time",
#"increases",
#r"$\theta$",
#"increases",
#r"$\newline$",
"then, the Complex Number",
"z",
"Rotates",
"about the origin",
)
}
class Introduction(Scene):
def construct(self):
intro_text_1=TextMobject("Geometric intuition behind")
intro_text_2 = TexMobject(
"\\,\\,\\,{",
"e",
"^{",
"i",
"\\theta",
"}",
"-",
"e",
"^{",
"i",
"(",
"-",
"\\theta",
")",
"}",
"\\over",
"{",
"2",
"i",
"}",
"}",
"=",
"sin",
"(",
"\\theta",
")",
)
intro_text_1.scale(2)
intro_text_2.scale(2)
intro_text_2.move_to(intro_text_1.get_center()+DOWN)
#color_theta = [5,13,25]
#color_e = [1,2,8]
#color_i=[3,4,9,10,19]
#for i in color_theta:
#intro_text[i].set_color(RED)
#for i in color_e:
#intro_text[i].set_color(BLUE)
#for i in color_i:
#intro_text[i].set_color(PURPLE)
#intro_text[17].set_color("#49A88F") #color 2
#intro_text[18].set_color("#49A88F") #color 2
#intro_text[23].set_color(YELLOW) #color sin
self.play(Write(intro_text_1))
self.play(ApplyMethod(intro_text_1.shift,UP))
self.wait(.5)
self.play(Write(intro_text_2[0:40]), run_time = 3, lag_ratio=0.2)
self.wait(2)
class Graph(GraphScene):
CONFIG={
"x_min":0,
"x_max":5,
"y_min":0,
"y_max":3,
"x_axis_width": 10,
"y_axis_width": 7.5,
"x_axis_label": 'Real',
"y_axis_label": 'Img',
"x_tick_frequency": .5,
"y_tick_frequency": .5,
"graph_origin": np.array([-5.5,-3,0]),
"axes_color": YELLOW,
"x_label_color": RED,
"y_label_color": PURPLE,
"label_nums_color": YELLOW,
"x_labeled_nums" :range(0,6,1),
"y_labeled_nums" :range(0,4,1),
"y_label_direction": LEFT,
}
def construct(self):
wordings=TextMobject("Consider the", "Argand plane")
wordings.to_edge(UP)
wordings[1].set_color(PURPLE)
self.play(Write(wordings))
self.setup_axes(animate=True)
complex_point = Dot(color = RED)
complex_point.move_to(self.coords_to_point(2.5,2.5))
complex_r = Line(self.graph_origin, self.coords_to_point(2.5,2.5), color= BLUE)
complex_theta = Arc(complex_r.get_angle(), radius= .9, start_angle= 0,arc_center=self.graph_origin,)
theta = TexMobject("\\theta").next_to(complex_theta, buff = 0.1)
self.play(ShowCreation(complex_point))
self.play(
ApplyMethod(complex_point.move_to, self.coords_to_point(2.5,2.5)),
ShowCreation(complex_r),
ShowCreation(complex_theta),
)
self.wait()
def update_theta(complex_theta, dt):
new_theta = Arc(complex_r.get_angle(), radius= .9, start_angle= 0,arc_center=self.graph_origin,)
complex_theta.become(new_theta)
#indicate theta
def update_point(complex_point, dt):
new_point = complex_point.move_to(complex_r.points[-1])
complex_point.become(new_point)
complex_point.add_updater(update_point)
complex_theta.add_updater(update_theta)
self.play(ApplyMethod(complex_r.set_angle,PI/3))
self.play(ApplyMethod(complex_r.set_angle,PI/6))
self.play(ApplyMethod(complex_r.set_angle,PI/4))
self.play(WiggleOutThenIn(complex_theta))
self.play(ShowCreation(theta))
complex_theta.remove_updater(update_theta)
complex_point.remove_updater(update_point)
#indicate r
r=TexMobject("r").move_to(complex_r.get_center()+.5*UP)
complex_r.add_updater(lambda x:x.put_start_and_end_on(self.graph_origin,complex_point.get_center()))
follow_line_1 = Line(complex_r.points[-1],complex_r.points[-1]+RIGHT+UP )
follow_line_2 = Line(complex_r.points[-1]+RIGHT+UP,complex_r.points[-1]+DOWN+LEFT )
follow_line_3 = Line(complex_r.points[-1]+DOWN+LEFT,complex_r.points[-1] )
self.play(MoveAlongPath(complex_point,follow_line_1, run_time=.5))
self.play(MoveAlongPath(complex_point,follow_line_2, run_time=.5))
self.play(MoveAlongPath(complex_point,follow_line_3, run_time=.5))
self.play(WiggleOutThenIn(complex_r))
self.play(ShowCreation(r))
self.wait()
z=TexMobject("z","=r \\,{e}^{i \\theta}")
z.move_to(complex_point.get_center()+RIGHT)
self.play(ReplacementTransform(r,z[0]), ReplacementTransform(theta,z[1]))
self.wait(2)
class IntroToSpinnning(GraphScene):
CONFIG={
"x_min":-10,
"x_max":10,
"y_min":-10,
"y_max":10,
"x_axis_width": 13,
"y_axis_height": 7.5,
"x_axis_label": 'Real',
"y_axis_label": 'Img',
"x_tick_frequency": 10,
"y_tick_frequency": 10,
"graph_origin":ORIGIN,
"axes_color": YELLOW,
"x_label_color": RED,
"y_label_color": PURPLE,
"label_nums_color": YELLOW,
#"x_labeled_nums" :range(-5,11,2),
#"y_labeled_nums" :range(-5,11,2),
"y_label_direction": LEFT,
"color_a":RED,
"color_b":GREEN,
}
def construct(self):
def update_theta(z_theta,dt):
new_theta= Arc(z_r.get_angle(), start_angle=0,radius=.5)
z_theta.become(new_theta)
self.setup_axes(animate=True)
z = Dot(color= self.color_a).move_to(self.graph_origin)
z_r= Line(self.graph_origin,z.get_center(),color= self.color_b)
z_theta=Arc(z_r.get_angle(), radius=.5)
theta=TexMobject("\\theta =").move_to(z_theta.points[1]+RIGHT*.5+.5*UP)
theta.scale(.75)
Exp_1=TexMobject(
"\\text{Suppose} \\,",
"\\theta \\, \\text{increases}",
"\\text{over time}",
"\\text{the Complex Number} \\, Z",
"\\text{Rotates about the origin}",
"\\text{in Anti-Clockwise direction}"
).move_to(3*UP+2.5*LEFT)
Exp_1.scale(.75)
Exp_1a=TexMobject("\\theta \\, \\text{decreases}","\\text{in Clockwise direction}").scale(.75)
Exp_arcAC= CurvedArrow(LEFT+UP,RIGHT+UP,angle=-TAU/4,color=MAROON_A)
Exp_arcC= CurvedArrow(LEFT+DOWN,RIGHT+DOWN,angle=TAU/4,color=MAROON_A)
Exp_1[1].set_color(BLUE)
Exp_1[5].set_color(BLUE)
#Exp_1[2].set_color_by_tex("Rotates", GREEN)
VGroup(*Exp_1).arrange_submobjects(DOWN,buff=.075,aligned_edge=LEFT)
Exp_1.to_corner(UL)
#Exp_1[1].next_to(Exp_1[0])
#Exp_1[2].next_to(Exp_1[1])
Exp_1a[0].move_to(Exp_1[1].get_center())
Exp_1a[0].set_color(RED)
Exp_1a[1].move_to(Exp_1[5].get_center()+LEFT*.435)
Exp_1a[1].set_color(RED)
#Exp_1[0].move_to(Exp_1[5].get_center()+.5*DOWN)
#Exp_1[8].next_to(Exp_1[7])
#Exp_1[9].next_to(Exp_1[8])
z_label=TextMobject("z")
z_label.add_updater(lambda x:x.next_to(z))
theta_var = DecimalNumber(z_r.get_angle(),show_ellipsis=False, include_sign = False).next_to(theta)
theta_var.scale(.75)
self.play(ShowCreation(z), ShowCreation(z_r),ShowCreation(z_label))
z_r.add_updater(lambda x:x.put_start_and_end_on(self.graph_origin, z.get_center()))
self.play(ApplyMethod(z.move_to,self.coords_to_point(2,4)))
self.play(ShowCreation(z_theta),ShowCreation(theta))
self.add(theta_var)
z_theta.add_updater(update_theta)
theta_var.add_updater(lambda x: x.set_value(z_r.get_angle()*(180/PI)))
z.add_updater(lambda x:x.move_to(z_r.points[-1]))
self.play(ShowCreation(Exp_1[0]))
self.play(ShowCreation(Exp_1[1]),ShowCreation(Exp_1[2]), run_time=2)
self.play(ShowCreation(Exp_1[3]))
self.play(ShowCreation(Exp_1[4:]), run_time=2)
self.play(WiggleOutThenIn(Exp_1[1]))
self.play(WiggleOutThenIn(Exp_1[5]),ShowCreation(Exp_arcAC))
self.play(Uncreate(Exp_arcAC))
self.play(Rotating(z_r,radians= TAU+0.61730789, about_point= self.graph_origin, run_time=1))
self.play(Transform(Exp_1[5], Exp_1a[1]), Transform(Exp_1[1],Exp_1a[0]), run_time=3)
self.play(WiggleOutThenIn(Exp_1[1]))
self.play(WiggleOutThenIn(Exp_1[5]),ShowCreation(Exp_arcC))
self.play(Uncreate(Exp_arcC))
self.play(Rotating(z_r,radians= -TAU-0.41730789, start_angle=z_r.get_angle(),about_point= self.graph_origin),run_time=1)
self.wait(2)
class Spin(GraphScene):
CONFIG={
"x_min":-10,
"x_max":10,
"y_min":-10,
"y_max":10,
"x_axis_width": 13,
"y_axis_height": 7.5,
"x_axis_label": 'Real',
"y_axis_label": 'Img',
"x_tick_frequency": 10,
"y_tick_frequency": 10,
"graph_origin":ORIGIN,
"axes_color": WHITE,
#"x_labeled_nums" :range(-5,11,2),
#"y_labeled_nums" :range(-5,11,2),
"y_label_direction": LEFT,
"color_a":RED,
"color_b":GREEN,
}
def construct(self):
intro_1=TextMobject("Consider Two Complex Numbers").to_corner(UR)
#intro_2= TexMobject("{e}^{i \\, \\theta} \\,","\\text{and} \\, \\,","{e}^{i \\, (-\\theta)}").move_to(intro_1.get_center()+.75*DOWN)
#intro_2. scale(2)
#self.play(ShowCreation(intro_1))
#self.play(ShowCreation(intro_2))
self.setup_axes(animate=False)
z1=Dot(self.graph_origin,color= self.color_a)
z1_shadow=Dot(self.graph_origin,color=GREY)
z1_r=Line(self.graph_origin, self.coords_to_point(1,0), color=self.color_a)
z1_r_shadow=Line(self.graph_origin, self.coords_to_point(1,0), color=GREY)
z1_theta= Arc(z1_r.get_angle(), radius=0.5 ,start_angle = 0)
z1_theta_shadow = Arc(z1_r_shadow.get_angle(),radius=0.5, start_angle = 0, color= GREY)
z2=Dot(self.graph_origin,color= self.color_b)
z2_r=Line(self.graph_origin, self.coords_to_point(-1,0), color =self.color_b)
z1_r.add_updater(lambda x:x.put_start_and_end_on(self.graph_origin, z1.get_center()))
z1_r_shadow.add_updater(lambda x:x.put_start_and_end_on(self.graph_origin, z1_shadow.get_center()))
def update_theta(z1_theta,dt):
new_theta=Arc(z1_r.get_angle(), start_angle = 0)
z1_theta.become(new_theta)
def update_theta_shadow(z1_theta,dt):
new_theta=Arc(z1_r_shadow.get_angle(), start_angle = 0,color = GREY)
z1_theta_shadow.become(new_theta)
z1_theta.add_updater(update_theta)
z1_theta_shadow.add_updater(update_theta_shadow)
z2_r.add_updater(lambda x:x.put_start_and_end_on(self.graph_origin, z2.get_center()))
self.play(ShowCreation(z1),ShowCreation(z1_r))
self.play(ApplyMethod(z1.move_to, self.coords_to_point(3,3)))
self.play(ShowCreation(z1_theta))
z1_label=TexMobject("z = {e}^{i \\theta}",color = self.color_a).next_to(z1, buff= .05)
self.play(ShowCreation(z1_label))
z1_shadow.move_to(z1.get_center())
self.add(z1_r_shadow,z1_shadow,z1_theta_shadow)
self.play(ApplyMethod(z1_shadow.move_to, self.coords_to_point(3,-3)), run_time=2)
z1_shadow_label=TexMobject("z = {e}^{i (-\\theta)}", color = GREY).next_to(z1_shadow, buff = .05)
self.play(ShowCreation(z1_shadow_label))
self.play(Uncreate(z1_shadow),Uncreate(z1_r_shadow),Uncreate(z1_theta_shadow),Uncreate(z1_theta))
self.play(ShowCreation(z2),ShowCreation(z2_r))
self.play( ApplyMethod(z2.move_to, self.coords_to_point(-3,3)))
z2_label= TexMobject("z_2 = - {e}^{i (-\\theta)}", color=self.color_b).move_to(z2.get_center()+LEFT*1.5)
z1_sublabel=TexMobject("z_1 = {e}^{i \\theta}", color=self.color_a).next_to(z1)
self.play(ReplacementTransform(z1_shadow_label,z2_label))
self.play(ReplacementTransform(z1_label, z1_sublabel))
self.play( ApplyMethod(z2.move_to, self.coords_to_point(-1.5,1.5)),ApplyMethod(z1.move_to, self.coords_to_point(1.5,1.5)))
z1_label2= TexMobject("z_1 = \\dfrac{{e}^{i (\\theta)}}{2}", color=self.color_a).next_to(z1, buff = .05)
z1_label2.scale(.75)
z2_label2= TexMobject("z_2 = - \\dfrac{{e}^{i (-\\theta)}}{2}", color=self.color_b).move_to(z2.get_center()+LEFT*1.5)
z2_label2.scale(.75)
self.play(Transform(z1_sublabel, z1_label2), Transform(z2_label,z2_label2))
self.wait(2)
class Stroboscope(Scene):
CONFIG={
"radians_1": 0, #starting angle of line 1
"radians_2": PI, #starting angle of line 2
"amp": 2,
"t_offset": 0,
"rate": 0.05,
"x_min":10, #xmin and max are to define the bounds of the horizontal graph
"x_max": 9.427,
"color_1": RED,
"color_2": GREEN,
"color_3": BLUE,
"flash": True,
"add_dot_copies": True,
}
def construct(self):
total_time = 10
flash_rect = FullScreenRectangle(stroke_width=0,fill_color=WHITE,fill_opacity=0.2,)
flash=FadeOut(
flash_rect,
rate_func=squish_rate_func(smooth, 0, 0.1)
)
time_label = TextMobject("Time = ")
time_label.shift(MED_SMALL_BUFF * LEFT)
time_tracker = ValueTracker(0)
time = DecimalNumber(0)
time.next_to(time_label, RIGHT)
time.add_updater(lambda d, dt: d.set_value(time_tracker.get_value()))
time_group = VGroup(time_label, time)
time_group.center().to_edge(UP)
times=np.arange(0, total_time + 1, .75)
self.play(ShowCreation(time_group))
dot_copies = VGroup()
z_sum_copies = VGroup()
def update_line_1(line_1,dt):
global line_1_rate_prev
global line_1_rate_pres
line_1.put_start_and_end_on(circle.get_center(), circle.get_center()+RIGHT*(self.amp/2))
a=dot.get_center()[1]
b=line_1.get_length()
alpha_la=4*np.arctan((2*b-np.sqrt(4*(b**2)-a**2))/(a+0.00001))
beta_la=PI/2-alpha_la/2
ap=PI-alpha_la/2
bp=PI/2-beta_la
line_1.set_angle(bp)
line_1_rate_pres = dot.get_center()[1]
if line_1_rate_pres>line_1_rate_prev:
line_1.set_color(self.color_1)
if line_1_rate_pres<line_1_rate_prev:
line_1.set_color(self.color_2)
line_1_rate_prev=line_1_rate_pres
def update_line_2(line_2,dt):
global line_2_rate_prev
global line_2_rate_pres
line_2.put_start_and_end_on(circle.get_center(), circle.get_center()+LEFT*(self.amp/2))
a=dot.get_center()[1]
b=line_2.get_length()
alpha_la=4*np.arctan((2*b-np.sqrt(4*(b**2)-a**2))/(a+0.00001))
beta_lc=PI/2-alpha_la/2
ap=PI-alpha_la/2
bp=PI/2-beta_lc
line_2.set_angle(bp+2*beta_lc)
line_2_rate_pres = dot.get_center()[1]
if line_2_rate_pres>line_2_rate_prev:
line_2.set_color(self.color_2)
if line_2_rate_pres<line_2_rate_prev:
line_2.set_color(self.color_1)
line_2_rate_prev=line_2_rate_pres
def update_subline_1(subline_1, dt):
global subline_1_rate_prev
global subline_1_rate_pres
subline_1_rate_pres = dot.get_center()[1]
if subline_1_rate_pres>subline_1_rate_prev:
subline_1.put_start_and_end_on(line_1.points[-1], dot.get_center())
if subline_1_rate_pres<subline_1_rate_prev:
subline_1.put_start_and_end_on(line_2.points[-1], dot.get_center())
subline_1_rate_prev=subline_1_rate_pres
def update_subline_2(subline_2, dt):
global subline_2_rate_prev
global subline_2_rate_pres
subline_2_rate_pres = dot.get_center()[1]
if subline_2_rate_pres>subline_2_rate_prev:
subline_2.put_start_and_end_on(line_2.points[-1], dot.get_center())
if subline_2_rate_pres<subline_2_rate_prev:
subline_2.put_start_and_end_on(line_1.points[-1], dot.get_center())
subline_2_rate_prev=subline_2_rate_pres
circle = Circle(radius = self.amp, color = self.color_3).move_to(LEFT*5)
sin_fn = FunctionGraph(lambda x:self.amp*np.sin(x), x_min =0 , x_max = self.x_max,color=GREY).shift(5*LEFT)
sin=DashedVMobject(sin_fn,num_dashes = 60)
sin.set_stroke(YELLOW, 2)
dot = Dot().move_to(sin_fn.points[0])
line_1 = Line(circle.get_center(), circle.get_center()+RIGHT*(self.amp/2), color = self.color_1)
line_2 = Line(circle.get_center(), circle.get_center()+LEFT*(self.amp/2), color = self.color_2 )
z1=Dot(line_1.points[-1],color= self.color_1)
z2=Dot(line_2.points[-1],color= self.color_2)
z1_label=TexMobject("z_1 = \\dfrac {{e}^{i (\\theta)}}{2}","z1",color = self.color_1).move_to(z1.get_center()+UP*.5)
z1_label.scale(.5)
z2_label= TexMobject("z_2 = -\\dfrac {{e}^{i (-\\theta)}}{2}","z2", color=self.color_2).move_to(z2.get_center()+UP*.5)
z2_label.scale(.5)
z_sum=Line(circle.get_center(), dot.get_center()+UP,color=YELLOW)
self.play(
ShowCreation(circle),
ShowCreation(line_1),
ShowCreation(line_2),
ShowCreation(z1),
ShowCreation(z2),
)
self.play(
ShowCreation(z1_label[0]),
ShowCreation(z2_label[0]),
run_time=2,
)
self.wait(2)
self.play(
Uncreate(z1),
Uncreate(z2),
#Uncreate(z1_label[0]),
#Uncreate(z2_label[0])
)
#self.play(
# Transform(z1_label[0],z1_label[1]),
# Transform(z2_label[0],z2_label[1]),
#)
z1_label[1].move_to(line_1.get_center()+.3*RIGHT+.2*UP)
z2_label[1].move_to(line_2.get_center()+.3*LEFT+.2*UP)
self.play(
ApplyMethod(line_1.set_angle,PI/6),
ApplyMethod(line_2.set_angle, 5*PI/6),
Transform(z1_label[0],z1_label[1]),
Transform(z2_label[0],z2_label[1]),
#run_time=5
)
z1_label[1].move_to(line_1.get_center()+.3*RIGHT)
z2_label[1].move_to(line_1.get_center()+.3*RIGHT)
dot.move_to(circle.get_center()+UP)
z_sum_label=TexMobject("z_1 + z_2", color= YELLOW).move_to(dot.get_center()+.3*UP)
z_sum_label.scale(.75)
subline_1 = DashedLine(line_1.points[-1], dot.get_center(), color = self.color_1)
subline_2 = DashedLine(line_2.points[-1], dot.get_center(), color = self.color_2 )
self.play(
ShowCreation(subline_1),
ShowCreation(subline_2)
)
self.play(
ShowCreation(dot),
ShowCreation(z_sum),
ShowCreation(z_sum_label),
)
self.play(
ApplyMethod(dot.move_to,(5*LEFT)),
ApplyMethod(line_1.set_angle,0),
ApplyMethod(line_2.set_angle, PI),
Uncreate(z_sum),
Uncreate(z_sum_label),
Uncreate(z1_label[0]),
Uncreate(z2_label[0]),
Uncreate(subline_2),
Uncreate(subline_1),
run_time=3
)
subline_1 = DashedLine(circle.get_center(), circle.get_center()+RIGHT*(self.amp/2), color = self.color_1)
subline_2 = DashedLine(circle.get_center(), circle.get_center()+LEFT*(self.amp/2), color = self.color_2 )
self.add(subline_1,subline_2)
z_sum.put_start_and_end_on(circle.get_center(),circle.get_center()+.0000001*UP)
self.add(z_sum)
def update_circle(circle, dt):
new_circle = Circle(radius = self.amp, color = self.color_3).move_to(RIGHT*dot.get_center()[0])
circle.become(new_circle)
self.play(ApplyMethod(dot.move_to, sin_fn.points[0]+.001*UP))
z_sum.add_updater(lambda x:x.put_start_and_end_on(line_1.points[0], dot.get_center()))
self.play(ApplyMethod(dot.move_to, sin_fn.points[0]+.001*DOWN))
circle.add_updater(update_circle)
line_1.add_updater(update_line_1)
line_2.add_updater(update_line_2)
subline_1.add_updater(update_subline_1)
subline_2.add_updater(update_subline_2)
self.add(dot)
for t1, t2 in zip(times, times[1:]):
dot_copy = dot.copy()
#z_sum_copy = z_sum.copy()
dot_copy.clear_updaters()
#z_sum_copy.clear_updaters()
dot_copies.add(dot_copy)
#z_sum_copies.add(z_sum_copy)
self.add(dot_copy, dot,) #z_sum, z_sum_copy)
sin_fn.save_state()
kw = {
"rate_func": lambda alpha:interpolate(
t1 / total_time,
t2 / total_time,
alpha
)
}
anims = [
MoveAlongPath(dot, sin_fn, **kw),
ApplyMethod(
time_tracker.increment_value, 1,
rate_func=linear
),
]
anims.append(flash)
self.play(*anims, run_time=1)
sin_fn.restore()
self.play(FadeOut(time_group))
self.play(ShowCreation(sin),run_time=5)
self.wait()
class Oscillator(Scene):
# !!!!WORKS ONLY IN LOW QUALITY rate=.05, radians=PI/64!!!! and rate =.01, radians= PI/320 FOR HIGH QUALITY
CONFIG={
"radians_1": 0, #starting angle of line 1
"radians_2": PI, #starting angle of line 2
"amp": 2,
"t_offset": 0,
"rate": 0.01,
"x_min":-4, #xmin and max are to define the bounds of the horizontal graph
"x_max": 9,
"color_1": RED,
"color_2": GREEN,
"color_3": BLUE,
}
def construct(self):
phase = self.rate #You add the rate even before staring the movemetn of sine wave, so the sine wave will already be .05 displaced while creation, therefore to compensate that add the rate
def update_sin(sin, dt):
New_sin = FunctionGraph(lambda x:self.amp*np.sin(x- (self.t_offset+self.rate) + phase), #look at FunctoinGraph in functions.py in mobjects
x_min = 0 , x_max = self.x_max).shift(RIGHT*self.x_min) #shift.left is to the center the circle over the left bonud of graph
self.t_offset += self.rate
sin.become(New_sin)
def update_line_1(line_1, dt):
line_1.set_angle(self.radians_1)
self.radians_1-=PI/320 #adds PI/64 radians every frame, Found this factor by chance; saw that there were 8 oscillations, when the factor was PI/4, hence PI/64
def update_line_2(line_2, dt):
line_2.set_angle(self.radians_2)
self.radians_2+=PI/320
circle = Circle(radius = self.amp, color = self.color_3).move_to(LEFT*4)
sin = FunctionGraph(lambda x:self.amp*np.sin(x - (self.t_offset+self.rate)+ phase), x_min = 0 , x_max = self.x_max).shift(RIGHT*self.x_min)
dot = Dot().move_to(sin.points[0]) #points are arrays holding certain points on a shape. 0 denotes the first point and -1 denotes the last point as in a normal array
line_1 = Line(circle.get_center(), circle.get_center()+RIGHT*(self.amp/2), color = self.color_1)
line_2 = Line(circle.get_center(), circle.get_center()+LEFT*(self.amp/2), color = self.color_2 )
subline_1 = DashedLine(circle.get_center(), circle.get_center()+RIGHT*(self.amp/2), color = self.color_1)
subline_2 = DashedLine(circle.get_center(), circle.get_center()+LEFT*(self.amp/2), color = self.color_2 )
self.play(
ShowCreation(circle),
ShowCreation(dot),
ShowCreation(sin),
ShowCreation(line_1),
ShowCreation(line_2),
ShowCreation(subline_1),
ShowCreation(subline_2),
)
self.wait()
sin.add_updater(update_sin)
dot.add_updater(lambda m: m.move_to(sin.points[0]))
subline_1.add_updater(lambda m: m.put_start_and_end_on(line_1.points[-1], dot.get_center())) #[-1] end of the line (array)
subline_2.add_updater(lambda m: m.put_start_and_end_on(line_2.points[-1], dot.get_center()))
line_1.add_updater(update_line_1)
line_2.add_updater(update_line_2)
self.wait(15)
line_1.remove_updater(update_line_1)
line_2.remove_updater(update_line_2)
sin.remove_updater(update_sin)
self.wait()
class HenceProved(Scene):
def construct(self):
end=TexMobject("Hence Proved",":)").scale(2)
self.play(ShowCreation(end[0]), run_time=2)
self.play(ShowCreation(end[1]), run_time=2)