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Added Source code and gifs of animations #94

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Added Source code and gifs of animations #94

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a6babf5
Merge pull request #8 from FOSSEE/master
GSri30 Jul 28, 2020
561c350
added gifs and code of animations
GSri30 Jul 29, 2020
42478ad
Added readme
GSri30 Jul 29, 2020
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339 changes: 339 additions & 0 deletions fossee-animations/AnalyticFunctions.py
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Original file line number Diff line number Diff line change
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from manimlib.imports import *
import numpy as np

class intro(Scene):
def construct(self):
t1=TextMobject("A","property")
t1.set_color_by_tex_to_color_map({"property":GREEN})
t2=TextMobject("of")
t3=TextMobject("Analytic","functions")
t3.set_color_by_tex_to_color_map({"Analytic":RED})
t1.shift(UP)
t1.scale(1.5)
t3.shift(DOWN)
t3.scale(1.7)

self.play(Write(t1))
self.play(Write(t2))
self.play(Write(t3))
self.wait(2)

class definition(Scene):
def construct(self):
t1=TextMobject("Theorem:")
t1.set_color(GREEN)
t1.to_edge(UP+LEFT)
t2=TextMobject("If f is")
t2.next_to(t1,DOWN,buff=0.5)
t3=TextMobject("analytic")
t3.set_color(RED)
t3_dup=TextMobject("analytic")
t3.next_to(t2,RIGHT,buff=0.3)
t3_dup.next_to(t2,RIGHT,buff=0.3)
t4=TextMobject("on a domain D, and if $f'(x) $=0 $\\forall$ z $\\in$ D, then")
t4.next_to(t3,RIGHT,buff=0.3)
t5=TextMobject("f is constant in D")
t5.next_to(t2,DOWN,buff=0.3)
t5.shift(1.3*RIGHT)
r=Rectangle(height=2,width=26,fill_color=BLUE,fill_opacity=0.7,color=BLUE)
r.shift(5*LEFT+DOWN*0.8)
self.play(FadeIn(t1))
self.play(Write(t2))
self.play(Write(t3))
self.play(Write(t4))
self.play(Write(t5))
self.wait(2)
self.play(ReplacementTransform(t3_dup,r))
self.wait(1)
t6a=TextMobject("f is said to be analytic in D if and only if u(x,y) and v(x,y) have continuous first partial derivatives on D and $u{ _{ x } }=v{ _{ y } }$ and $u{ _{ y } }= -v{ _{ x } }$ where f(z)=u(x,y)+iv(x,y)")
#t6b=TextMobject()
t6a.scale(0.7)
t6a.set_color(WHITE)
t6a.shift(DOWN*0.7)
self.add(t6a)
self.wait(4)

class connection1(Scene):
def construct(self):
t1=TextMobject("Let's","analyse","this")
factorial=TextMobject("!")
factorial.scale(2.5)
factorial.next_to(t1,RIGHT,buff=0.6)
factorial.set_color(GREEN)
t1.set_color_by_tex_to_color_map({"analyse":BLUE})
self.play(Write(t1))
self.play(Write(factorial))
self.wait(2)

class pictorial(Scene):
def construct(self):
t1=TextMobject("Consider some domain, D")
img = ImageMobject('amoeba.png')
img.scale(4)
img.shift(LEFT*3)
self.play(Write(t1))
self.wait(1)
self.play(FadeOut(t1))
self.play(ShowCreation(img))
t2=TextMobject("Now consider some disc, $B_{ r }(a)$ inside D")
t2.scale(0.7)
t3=TextMobject("which represents a set of complex numbers,")
t3.scale(0.7)
number=TextMobject("$|z-z_{ 0 }|\\le r$")
number.scale(1.5)
t2.shift(3.5*RIGHT+2*UP)
t3.shift(3.5*RIGHT+2*UP)
number.shift(4*RIGHT+2*UP)
self.play(Write(t2))
self.wait(1.5)
self.play(ReplacementTransform(t2,t3))
self.wait(1.5)
self.play(ReplacementTransform(t3,number))
self.wait(2)
center=Dot(color=BLACK,radius=0.03)
center.shift(2.5*LEFT)
line=DashedLine(start=LEFT*2.5,end=LEFT*2.1,color=BLACK)
line.scale(0.7)
r=TextMobject("r")
r.scale(0.4)
r.shift(LEFT*2.3+UP*0.1)
c1=Circle(radius=0.4,fill_color=PURPLE_E,fill_opacity=0.7,color=PURPLE_E)
c2=Circle(radius=1.7,fill_color=PURPLE_E,fill_opacity=0.7,color=PURPLE_E)
c2.shift(3*RIGHT)
c1.shift(2.5*LEFT)
self.play(ReplacementTransform(number,c1))
self.play(Write(center),ShowCreation(line))
self.play(Write(r))
self.wait(2)

self.play(FadeOut(line),FadeOut(center),FadeOut(r))
an=TextMobject("a")
an.scale(0.5)
an.shift(2.8*RIGHT)
self.play(ReplacementTransform(c1,c2))
center.move_to(3*RIGHT)
self.add(center)
self.play(Write(an))
self.wait(1.2)

t4=TextMobject("Let c $\\in B_{ r }(a)$")
t4.shift(2.5*DOWN+3.3*RIGHT)
t4.scale(0.7)
self.play(Write(t4))
self.wait(0.2)
c=Dot(radius=0.03,color=BLACK)
c.shift(3.9*RIGHT+UP)
cn=TextMobject("c")
cn.scale(0.5)
cn.shift(RIGHT*3.9+UP*1.2)
self.play(Write(c))
self.play(Write(cn))
self.wait(1)

t5=TextMobject("Now pick a point b $\\in B_{ r }(a)$ as shown")
t5.shift(2.5*DOWN+3.3*RIGHT)
t5.scale(0.7)
b=Dot(radius=0.03,color=BLACK)
b.shift(3.9*RIGHT)
bn=TextMobject("b")
bn.scale(0.5)
bn.shift(RIGHT*3.9+DOWN*0.2)

self.play(ReplacementTransform(t4,t5))
self.play(Write(b))
self.play(Write(bn))
self.wait(1)

dl1=DashedLine(start=RIGHT*3,end=RIGHT*3.9,color=BLACK)
dl2=DashedLine(start=RIGHT*3.9,end=RIGHT*3.9+UP,color=BLACK)
self.play(Write(dl1),Write(dl2))
self.wait(0.5)

t6=TextMobject("Since given $\grave { f\left( z \\right) } $=0,")
t7=TextMobject("$u_{ x }=u_{ y }=v_{ x }=v_{ y }$=0")
t8=TextMobject("$u_{ y }=v_{ y }=0$ implies u(b)=u(c) and v(b)=v(c)")
t9=TextMobject("and $u_{ x }=v_{ x }=0$ implies u(a)=u(b) and v(a)=v(b)")
t9a=TextMobject("(i.e. a,b,c are coincident)")
t6.scale(0.7)
t7.scale(0.7)
t8.scale(0.7)
t9.scale(0.7)
t9a.scale(0.7)
t6.shift(2.5*DOWN+3.3*RIGHT)
t7.shift(2.5*DOWN+3.3*RIGHT)
t8.shift(2.5*DOWN+3.3*RIGHT)
t9.shift(2.5*DOWN+3.3*RIGHT)
t9a.shift(2.3*UP+3.3*RIGHT)
self.play(ReplacementTransform(t5,t6))
self.wait(1.5)
self.play(ReplacementTransform(t6,t7))
self.wait(1.5)
self.play(ReplacementTransform(t7,t8))
self.wait(1.5)
self.play(FadeOut(dl2))
self.play(ApplyMethod(c.shift,DOWN),ApplyMethod(cn.shift,DOWN))
self.wait(1)
self.play(ReplacementTransform(t8,t9))
self.play(FadeOut(dl1))
self.play(ApplyMethod(b.shift,LEFT*0.9),ApplyMethod(c.shift,LEFT*0.9),ApplyMethod(bn.shift,LEFT*0.9),ApplyMethod(cn.shift,LEFT*0.9))
self.wait(1)
self.play(Write(t9a))
self.wait(1.4)

self.play(FadeOut(t9a))
t10=TextMobject("Since c was an arbitrary point in $B_{ r }(a)$")
t11=TextMobject("Thus u and v are constant in $B_{ r }(a)$")
t12=TextMobject("$\\therefore $ f is constant in $B_{ r }(a)$")
t10.scale(0.7)
t11.scale(0.7)
t12.scale(0.7)
t10.shift(2.5*DOWN+3.3*RIGHT)
t11.shift(2.5*DOWN+3.3*RIGHT)
t12.shift(2.5*DOWN+3.3*RIGHT)
self.play(ReplacementTransform(t9,t10))
self.wait(1.5)
self.play(ReplacementTransform(t10,t11))
self.wait(1.5)
self.play(ReplacementTransform(t11,t12))
self.wait(2)
self.play(FadeOut(t12),FadeOut(center),FadeOut(an),FadeOut(c),FadeOut(cn),FadeOut(b),FadeOut(bn))
self.wait(0.4)
c1=Circle(radius=0.4,fill_color=PURPLE_E,fill_opacity=0.7,color=PURPLE_E)
c1.shift(2.5*LEFT)
self.play(ReplacementTransform(c2,c1))
self.wait(1)

t13=TextMobject("Now let b $\\notin B_{ r }(a)$ and be an arbitrary point in D")
t13.scale(0.7)
t13.shift(2*UP+3.3*RIGHT)
c3=Circle(radius=0.4,fill_color=GREEN_E,fill_opacity=0.7,color=GREEN_E)
c3.shift(2*LEFT+UP)
a=Dot(color=BLACK,radius=0.03)
an=TextMobject("a")
b=Dot(color=BLACK,radius=0.03)
bn=TextMobject("b")
an.scale(0.4)
bn.scale(0.4)
a.shift(3.5*LEFT+DOWN)
an.shift(3.5*LEFT+DOWN*0.8)
b.shift(2*LEFT+UP)
bn.shift(2*LEFT+1.2*UP)
self.play(Write(t13))
self.play(ApplyMethod(c1.shift,LEFT+DOWN))
self.play(Write(a),Write(an))
self.play(Write(c3))
self.play(Write(b),Write(bn))
self.wait(1.4)

t14=TextMobject("Since D is connected, $\\exists$ some curve connecting a and b")
t14.scale(0.7)
t14.shift(2*UP+2.9*RIGHT)
arc=ArcBetweenPoints(start=3.5*LEFT+DOWN,end=2*LEFT+UP,angle=TAU/6,color=DARK_BROWN)
self.play(ReplacementTransform(t13,t14))
self.wait(0.5)
self.play(ShowCreation(arc))
self.wait(1.5)

t15=TextMobject("$\\therefore$ we can draw discs along the same curve")
t15.scale(0.7)
t15.shift(2*UP+3.1*RIGHT)
circles=[0,0,0,0]
circles_dup=[0,0,0,0]
circles[0]=Circle(radius=0.34,color=BLUE)
circles[1]=Circle(radius=0.24,color=YELLOW)
circles[2]=Circle(radius=0.3,color=GREEN)
circles[3]=Circle(radius=0.35,color=RED)
circles[0].shift(2.9*LEFT+0.7*DOWN)
circles[1].shift(2.65*LEFT+0.3*DOWN)
circles[2].shift(2.3*LEFT)
circles[3].shift(2*LEFT+0.4*UP)

c1_dup=Circle(radius=0.4,color=WHITE)
c1_dup.shift(3.5*LEFT+DOWN)
circles_dup[0]=Circle(radius=0.34,color=WHITE)
circles_dup[1]=Circle(radius=0.24,color=WHITE)
circles_dup[2]=Circle(radius=0.3,color=WHITE)
circles_dup[3]=Circle(radius=0.35,color=WHITE)
circles_dup[0].shift(2.9*LEFT+0.7*DOWN)
circles_dup[1].shift(2.65*LEFT+0.3*DOWN)
circles_dup[2].shift(2.3*LEFT)
circles_dup[3].shift(2*LEFT+0.4*UP)
c3_dup=Circle(radius=0.4,color=WHITE)
c3_dup.shift(2*LEFT+UP)

self.play(ReplacementTransform(t14,t15))
self.play(Write(circles[0]))
self.play(Write(circles[1]))
self.play(Write(circles[2]))
self.play(Write(circles[3]))
self.wait(1)

t16=TextMobject("Since f is constant in the disc")
t17=TextMobject("around the point 'a', similarly f should be constant")
t18=TextMobject("in it's neighbouring disk and so on.")
#t19=TextMobject("Since the two disks overlap, the two constants must be equal.Similarly if we continue,we reach disc b. $\\therefore$ we get f(a)=f(b).Thus f is constant in D")
t19=TextMobject("Since the two discs overlap,")
t20=TextMobject("the two constants must be equal")
t21=TextMobject("Similarly if we continue,we reach disc b")
t22=TextMobject("$\\therefore$ we get f(a)=f(b)")
t23=TextMobject("Thus f is constant in D")
t16.scale(0.7)
t17.scale(0.7)
t18.scale(0.7)
t19.scale(0.7)
t20.scale(0.7)
t21.scale(0.7)
t22.scale(0.7)
t23.scale(0.7)
t16.shift(2*UP+3.15*RIGHT)
t17.next_to(t16,DOWN,buff=0.3)
t18.next_to(t17,DOWN,buff=0.3)
g1=VGroup(t16,t17,t18)
g2=VGroup(t19,t20,t21)
self.play(ReplacementTransform(t15,t16))
self.play(Write(t17))
self.play(Write(t18))
self.wait(1.4)

self.play(FadeOut(g1))
t19.shift(2*UP+3.15*RIGHT)
self.play(Write(t19),FadeIn(c1_dup),FadeIn(circles_dup[0]))
t20.next_to(t19,DOWN,buff=0.3)
self.play(Write(t20))
t21.next_to(t20,DOWN,buff=0.3)
self.play(FadeOut(c1_dup),FadeOut(circles_dup[0]))
self.play(Write(t21))
self.play(FadeIn(c1_dup))
self.play(FadeIn(circles_dup[0]))
self.play(FadeIn(circles_dup[1]))
self.play(FadeIn(circles_dup[2]))
self.play(FadeIn(circles_dup[3]))
self.play(FadeIn(c3_dup))
self.wait(0.7)
self.play(FadeOut(circles_dup[0]),FadeOut(circles_dup[1]),FadeOut(circles_dup[2]),FadeOut(circles_dup[3]))
self.wait(1.4)

self.play(FadeOut(g2),FadeOut(c1_dup),FadeOut(c3_dup))
t22.shift(2*UP+3.15*RIGHT)
self.play(Write(t22))
self.wait(1)
t23.shift(2*UP+3.15*RIGHT)
t23.scale(1.3)
self.play(ReplacementTransform(t22,t23))
self.wait(1)

self.play(FadeOut(circles[0]),FadeOut(circles[1]),FadeOut(circles[2]),FadeOut(circles[3]))
self.play(FadeOut(arc))
self.play(ApplyMethod(c3.shift,1.5*LEFT+2*DOWN),ApplyMethod(bn.shift,1.35*LEFT+1.95*DOWN),ApplyMethod(b.shift,1.5*LEFT+2*DOWN))
self.wait(2)

class conclusion(Scene):
def construct(self):
t1=TextMobject("Hence the","property","is","satisfied")
t2=TextMobject("$\\forall$ z $\\in$ D")
t1.shift(UP)
t2.next_to(t1,DOWN,buff=0.4)
t1.set_color_by_tex_to_color_map({"property":BLUE,"satisfied":YELLOW})
self.play(Write(t1))
self.play(Write(t2))
self.wait(3)
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