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from manimlib.imports import *
import numpy as np
def returnSum(k,x):
summ=0
for i in range(1,k+1,2):
summ+=((np.sin(2*np.pi*i*x))/i)
return summ
def returnFunc(self,k):
graph=self.get_graph(lambda x:(4/np.pi)*returnSum(k,x),color=WHITE,x_max=1,x_min=-1)
return graph
class fourierSeries(GraphScene,MovingCameraScene):
CONFIG = {
"x_min": -3,
"x_max": 3,
"x_axis_width": 13,
"y_min": -3,
"y_max": 3,
"graph_origin": ORIGIN,
"function_color": RED,
"axes_color": BLUE,
"x_axis_label": "$x$",
"y_axis_label": "$y$",
"exclude_zero_label": True,
"x_labeled_nums": range(-2, 3, 1),
}
def setup(self):
GraphScene.setup(self)
MovingCameraScene.setup(self)
def construct(self):
x_each_unit = self.x_axis_width / (self.x_max - self.x_min)
y_each_unit = self.y_axis_height / (self.y_max - self.y_min)
equation=TextMobject("$f(x)=\\frac { 4 }{ \pi } \sum _{ k=1,3,5.. }^{ \infty }{ \\frac { 1 }{ k } \sin { 2\pi kx } }$").shift(5*RIGHT+3*UP).set_color(RED).scale(0.4)
self.add(equation)
self.setup_axes(animate=True)
line1=Line(start=(-x_each_unit,y_each_unit,0),end=(-(1/2)*x_each_unit,y_each_unit,0),color=RED)
line2=Line(start=(-(1/2)*x_each_unit,y_each_unit,0),end=(-(1/2)*x_each_unit,-y_each_unit,0),color=RED)
line3=Line(start=(-(1/2)*x_each_unit,-y_each_unit,0),end=(0,-y_each_unit,0),color=RED)
line4=Line(start=(0,-y_each_unit,0),end=(0,y_each_unit,0),color=RED)
line5=Line(start=(0,y_each_unit,0),end=((1/2)*x_each_unit,y_each_unit,0),color=RED)
line6=Line(start=((1/2)*x_each_unit,y_each_unit,0),end=((1/2)*x_each_unit,-y_each_unit,0),color=RED)
line7=Line(start=((1/2)*x_each_unit,-y_each_unit,0),end=(x_each_unit,-y_each_unit,0),color=RED)
self.play(ShowCreation(line1))
self.play(ShowCreation(line2))
self.play(ShowCreation(line3))
self.play(ShowCreation(line4))
self.play(ShowCreation(line5))
self.play(ShowCreation(line6))
self.play(ShowCreation(line7))
self.wait(0.5)
labels=[
TextMobject("$f_{ k=1 }(x)$"),
TextMobject("$f_{ k=3 }(x)$"),
TextMobject("$f_{ k=5 }(x)$"),
TextMobject("$f_{ k=7 }(x)$"),
TextMobject("$f_{ k=9 }(x)$"),
TextMobject("$f_{ k=11 }(x)$"),
TextMobject("$f_{ k=13 }(x)$"),
TextMobject("$f_{ k=15 }(x)$"),
TextMobject("$f_{ k=17 }(x)$"),
TextMobject("$f_{ k=19 }(x)$"),
TextMobject("$f_{ k=85 }(x)$")
]
p=0
for i in range(1,20,2):
if(i==1):
graphInitial=returnFunc(self,1)
label=labels[p].scale(0.5).shift(y_each_unit*1.5*UP+RIGHT*x_each_unit*0.3)
self.play(ShowCreation(graphInitial),Write(labels[0]))
old=graphInitial
oldLabel=label
else:
graph=returnFunc(self,i)
graphLabel=labels[p].scale(0.5).shift(y_each_unit*1.5*UP+RIGHT*x_each_unit*0.3)
self.play(ReplacementTransform(old,graph),ReplacementTransform(oldLabel,graphLabel))
old=graph
oldLabel=graphLabel
p+=1
graphFinal=returnFunc(self,85)
labelFinal=labels[10].scale(0.5).shift(y_each_unit*1.5*UP+RIGHT*x_each_unit*0.3)
self.play(FadeOut(old),FadeOut(oldLabel))
self.play(ShowCreation(graphFinal),Write(labelFinal))
self.wait(1)
self.camera_frame.save_state()
self.play(self.camera_frame.set_width, 2.25,self.camera_frame.move_to, y_each_unit*UP+RIGHT*x_each_unit*0.3)
self.wait(1)
self.play(self.camera_frame.set_width,14,self.camera_frame.move_to,0)
self.wait(2)
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