Skip to content

Added Source code and gifs of animations #94

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
wants to merge 3 commits into
base: master
Choose a base branch
from
Open

Added Source code and gifs of animations #94

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
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
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
339 changes: 339 additions & 0 deletions fossee-animations/AnalyticFunctions.py
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,339 @@
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)
Loading