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from manimlib.imports import *
import numpy as np
import math
class deltaTransformation(GraphScene):
CONFIG = {
"x_min": -3,
"x_max": 3,
"y_min": -5,
"y_max": 5,
"graph_origin": ORIGIN,
"function_color": RED,
"axes_color": BLUE,
"x_axis_label": "$t$",
"y_axis_label": "$f(t)$",
"x_labeled_nums": range(-3, 4, 1),
# "y_axis_height": 4,
# "x_axis_width": 6,
}
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)
self.setup_axes(animate=True,scalee=0.8)
function=TextMobject("$f(t) = 2{ \delta }_{ 0 }(t)+3{ \delta }_{ 1 }(t)+4{ \delta }_{ 2 }(t)$").scale(0.4).shift(5*RIGHT+3*UP).set_color(RED)
self.play(FadeIn(function))
twoDGraph=[
Line(start=(0,0,0),end=(0,2*y_each_unit,0),color=GREEN),
Line(start=(1*x_each_unit,0,0),end=(x_each_unit,3*y_each_unit,0),color=GREEN),
Line(start=(2*x_each_unit,0,0),end=(2*x_each_unit,4*y_each_unit,0),color=GREEN)
]
groupGraph=VGroup(twoDGraph[1],twoDGraph[2],self.axes,twoDGraph[0])
self.play(Write(twoDGraph[0]),ShowCreation(twoDGraph[1]),ShowCreation(twoDGraph[2]))
self.wait(1.2)
self.play(ApplyMethod(groupGraph.scale,0.7))
self.play(ApplyMethod(groupGraph.shift,5*LEFT),ApplyMethod(function.move_to,5*LEFT+3*UP))
self.graph_origin=2*RIGHT+2.5*DOWN
self.x_axis_width=6
self.x_axis_label="$|z|$"
self.y_axis_label="$|F(t)|$"
self.x_min=-3
self.x_max=6
self.y_min=-1
self.y_max=7
self.x_labeled_nums=range(-3,7,1)
self.setup_axes(animate=True,scalee=0.6)
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)
rightSideGraphs=[
self.get_graph(lambda x:2,x_min=0,x_max=6,color=GREEN),
self.get_graph(lambda x:2+3/x,x_min=0.6,x_max=6,color=GREEN),
self.get_graph(lambda x:2+(3/x)+(4/x**2),x_min=1.24,x_max=6,color=GREEN)
]
graphCoeff=[
TextMobject("$2$").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*2+UP*y_each_unit*2+DOWN*y_each_unit*0.5).set_color(RED),
TextMobject("$2+\\frac { 3 }{ |z| }$").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*3+UP*y_each_unit*2).set_color(RED),
TextMobject("$2+\\frac { 3 }{ |z| } +\\frac { 4 }{ { |z| }^{ 2 } } $").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*3.5+UP*y_each_unit*2).set_color(RED)
]
self.play(ReplacementTransform(twoDGraph[0],rightSideGraphs[0]),FadeIn(graphCoeff[0]))
self.wait(0.5)
self.play(FadeOut(rightSideGraphs[0]),ReplacementTransform(twoDGraph[1],rightSideGraphs[1]),ReplacementTransform(graphCoeff[0],graphCoeff[1]))
self.wait(0.5)
self.play(FadeOut(rightSideGraphs[1]),ReplacementTransform(twoDGraph[2],rightSideGraphs[2]),ReplacementTransform(graphCoeff[1],graphCoeff[2]))
self.wait(2)
class graphCont(GraphScene,MovingCameraScene):
CONFIG = {
"x_min": -3,
"x_max": 6,
"y_min": -1,
"y_max": 7,
"graph_origin": 2*RIGHT+2.5*DOWN,
"function_color": RED,
"axes_color": BLUE,
"x_axis_label": "$|z|$",
"y_axis_label": "$|F(t)|$",
"exclude_zero_label": True,
"x_labeled_nums": range(-3, 7, 1),
"x_axis_width": 6,
}
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)
coeff=TextMobject("$2+\\frac { 3 }{ |z| } +\\frac { 4 }{ { |z| }^{ 2 } } $").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*3.5+UP*y_each_unit*2).set_color(RED)
self.setup_axes(scalee=0.6)
graph=self.get_graph(lambda x:2+(3/x)+(4/x**2),x_min=1.24,x_max=6,color=GREEN)
xAxis=self.get_graph(lambda x:0,x_min=1.24,x_max=6).shift(3*LEFT)
self.add(graph)
self.add(coeff)
self.play(ApplyMethod((self.axes).shift,3*LEFT),ApplyMethod(coeff.shift,3*LEFT),ApplyMethod(graph.shift,3*LEFT))
topText=TextMobject("Here we get","output","for","any value of $|z|$").scale(0.4).shift(3*UP+3*RIGHT).set_color_by_tex_to_color_map({"output":YELLOW,"any value of $|z|$":BLUE})
topText1=TextMobject("Except for $|z|=0$").scale(0.7).shift(2.5*UP+3*RIGHT).set_color(RED)
dot1=Dot(color=WHITE,radius=0.06)
dot2=Dot(color=WHITE,radius=0.06)
self.play(Write(topText))
self.play(MoveAlongPath(dot1,graph),MoveAlongPath(dot2,xAxis),run_time=2)
self.play(Write(topText1))
self.play(FadeOut(dot1),FadeOut(dot2))
self.wait(0.5)
path=self.get_graph(lambda x:2+(3/x)+(4/x**2),x_min=1.24,x_max=0.8)
path1=self.get_graph(lambda x:0,x_min=1.24,x_max=0.8)
graphUpdated=self.get_graph(lambda x:2+(3/x)+(4/x**2),x_min=0.8,x_max=6,color=GREEN)
self.camera_frame.save_state()
self.play(FadeOut(graph),Write(graphUpdated))
self.play(self.camera_frame.set_width, 30,
MoveAlongPath(dot1,path),MoveAlongPath(dot2,path1),run_time=2)
self.wait(1)
self.play(FadeOut(dot1),FadeOut(dot2),FadeOut(graphUpdated),FadeIn(graph),self.camera_frame.set_width,15)
self.wait(1)
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