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Inplicit_Function_Project.py
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Inplicit_Function_Project.py
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from manim import *
__date__ = "2021.10.15 - 2021.10.17"
__version__ = "Manim Community Edition v0.11.0"
__product-link__ = "https://t.bilibili.com/582441580167000977?tab=2"
'''
python -m manim render manimlib\Projects\Implicit_graph.manimCE.py -s -pqh
C:\TDDownload\manim_master_2021.9.5\manin_master_9.5\media\images\Implicit_graph.manimCE\ImplicitFunctionExample_ManimCE_v0.11.0.png
'''
class ImplicitFunctionExample(MovingCameraScene):
def construct(self):
self.camera.frame.scale(1.5)
x, y = RIGHT, UP
'''
Length = 21 (14*1.5);
Height = 12 (8*1.5);
EDGE TO THE CENTER{
LEFT: 7; RIGHR: 14;
UP: 4; DOWN: 8;
}
'''
self.camera.frame.move_to(3.5*RIGHT+2*DOWN)
func_tex = MathTex(
r'x^{2}+y^{2}-cx^{2}y^{2}=1',
substrings_to_isolate=['x', 'y', 'c']
)
title_1 = Tex("b) Algebratic Proof").move_to(9.2*RIGHT+3.63*UP)
bound_title = Underline(title_1, buff=0.08)
self.add(bound_title, title_1)
formulas_in_mathtex = [
(r'x^{2}+y^{2}-x^{2}y^{2}', '=', '1'),
(r'for\ x', '=', r'\pm1\ \implies\ x^{2}=1'),
(r'1+y^{2}-1\cdot y^{2}','=','1'),
(r'\quad y^{2}-y^{2}', '=', '1-1'),
(r'\quad 0', '=', '0'),
(r'\therefore \forall_y ', r'\in', r'\mathbb{R} \ \Longleftarrow \ x=\pm1'),
(r'\because',r'\,x^{2}+y^{2}-x^{2}y^{2}'),
(r'is\ ',r'a\ symmetric\ polynomial'),
(r'\therefore \forall_x ', r'\in', r'\mathbb{R} \ \Longleftarrow \ y=\pm1')
#(r'\therefore\ ', r'for\ y', '=', r'\pm1\ ', r'\implies\ ', r' x ', r'\in', r'\mathbb{R}'),
]
for index, obj in enumerate(formulas_in_mathtex):
formulas_in_mathtex[index] = MathTex(
*formulas_in_mathtex[index],
substrings_to_isolate=['x', 'y']
).set_color_by_tex('x', RED).set_color_by_tex('y', YELLOW)\
if index != 7 else MathTex(
*formulas_in_mathtex[index]
)
if index == 0:
formulas_in_mathtex[index].move_to(10.5*RIGHT+2.7*UP)
else:
formulas_in_mathtex[index].next_to(
formulas_in_mathtex[index-1],
DOWN
)
formulas_in_mathtex[5].shift(0.7*LEFT).add_background_rectangle(color=BLUE)
formulas_in_mathtex[8].shift(0.7*LEFT).add_background_rectangle(color=BLUE)
f1s = SurroundingRectangle(formulas_in_mathtex[5])
f2s = SurroundingRectangle(formulas_in_mathtex[8], color=RED)
center1 = f1s.get_corner(UP+LEFT)
center2 = f2s.get_corner(UP+LEFT)
self.add(*formulas_in_mathtex, f1s, f2s)
func_tex.set_color("#76DDC0").set_color_by_tex('x', RED).set_color_by_tex('y', YELLOW).set_color_by_tex('c', GREEN)
plane = NumberPlane()
plane.add_coordinates()
graph = ImplicitFunction(
lambda x, y: (x**2) + (y**2) - (x**2) * (y**2) - 1,
x_range=[-config.frame_width / 2, config.frame_width / 2],
min_depth=1,
max_quads=2000,
color=ORANGE,
stroke_width=1.5*DEFAULT_STROKE_WIDTH
)
Other_c_val = [0, 1, -2, -1/2]
other_color = ["#FF0000", "#DC75CD", "#FFFF00", "#00FF00"]
other_graphs = VGroup(
*[ImplicitFunction(
lambda x, y: (x**2) + (y**2) + c*(x**2) * (y**2) - 1,
x_range=[-config.frame_width / 2, config.frame_width / 2],
min_depth=1,
max_quads=2000,
color=_color,
fill_opacity = 0,
stroke_width=0.5*DEFAULT_STROKE_WIDTH) for c, _color in\
zip(Other_c_val, other_color)
]
)
self.add(other_graphs)
self.add(plane, graph, func_tex.move_to(3.5*UP+4.5*LEFT))
c_is_neg_1 = Tex('(c=-1)', substrings_to_isolate=['c']).set_color(ORANGE).\
set_color_by_tex('c', GREEN)
c_val_indication = VGroup(
*[Tex(f'(c={num})', substrings_to_isolate=['c']).set_color(_color).\
set_color_by_tex('c', GREEN)\
for num, _color in zip(Other_c_val, other_color)]
)
c_is_neg_1.next_to(func_tex, DOWN)
c_val_indication[0].next_to(c_is_neg_1, RIGHT)
c_val_indication[1].move_to(-6*x+2*y)
c_val_indication[2].next_to(c_val_indication[1], RIGHT)
c_val_indication[3].next_to(c_is_neg_1, LEFT)
self.add(c_is_neg_1, c_val_indication)
dots_kwargs = dict(
color=BLUE_D,
fill_opacity=0.8,
radius=0.5*DEFAULT_DOT_RADIUS
)
dots_kwargs2 = dict(
color=BLUE,
fill_opacity=.0 ,
radius=0.5*DEFAULT_DOT_RADIUS,
stroke_width=0.5*DEFAULT_STROKE_WIDTH
)
dots = VGroup(
Dot(point=LEFT+UP, **dots_kwargs), Circle(**dots_kwargs2).move_to(LEFT+UP),
Dot(point=LEFT+DOWN, **dots_kwargs), Circle(**dots_kwargs2).move_to(LEFT+DOWN),
Dot(point=RIGHT+UP, **dots_kwargs), Circle(**dots_kwargs2).move_to(RIGHT+UP),
Dot(point=RIGHT+DOWN, **dots_kwargs), Circle(**dots_kwargs2).move_to(RIGHT+DOWN)
)
self.add(dots)
connections = VGroup(
d1:=Dot(2.5*RIGHT+UP, color=RED),
d2:=Dot(1.5*RIGHT+DOWN, color=RED),
d3:=Dot(3.5*UP+RIGHT, color=YELLOW),
d4:=Dot(3*UP+LEFT, color=YELLOW),
DashedLine(d1, center2, color=RED),
DashedLine(d2, center2, color=RED),
DashedLine(d3, center1, color=YELLOW),
DashedLine(d4, center1, color=YELLOW)
)
self.add(connections)
# TODO Part C
# Proving by implicit differenciation
# Give Myself a little break by adding the logal
banner = ManimBanner().move_to(13*RIGHT-4.35*UP).scale(1/4)
self.add(banner)
title_2 = Tex("C) Implicit Differenciation").move_to(-4.3*UP-4*RIGHT)
bound_title2 = Underline(title_2).next_to(title_2, DOWN)
# NOTE !!! DON't Use * with tuple, don't use frac with splits
formulas_set2 = [
func_tex.copy().next_to(bound_title2, DOWN).shift(0.9*LEFT+0.2*DOWN), #0
r"\Longrightarrow", #1
r'{d\over dx}x^{2}+{d\over dx}y^{2}+{d\over dx}cx^{2}y^{2}={d\over dx}\left(1\right)', #2
r"\Longrightarrow", #3
r"2x+2yy'+2cxy^{2}+2cx^{2}yy'=0", #4
r"y'\left(2y+2cx^{2}y\right)=-2cxy^{2}-2x, ",#5
r"\ \ y' = {-2cxy^{2}-2x\over \left(2y+2cx^{2}y\right)}", #6
r"=-{cxy^{2}+x\over y\left(1+cx^{2}\right)}=", #7
r"{x-xy^{2}\over y\left(1-x^{2}\right)}", #8
r"(when\ c=-1)", #9
]
MathTex().break_up_tex_strings
for i in range(1, 10):
formulas_set2[i] = MathTex(
formulas_set2[i],
substrings_to_isolate=['x', 'y', 'c', 'd']
).set_color_by_tex('x', RED).set_color_by_tex('y', YELLOW).\
set_color_by_tex('d', GREY).set_color_by_tex('c', GREEN)
for i in range(1, 5):
formulas_set2[i].next_to(formulas_set2[i-1], RIGHT)
formulas_set2[5].move_to(-3.6*x-6.75*y)
for i in range(6, 10):
formulas_set2[i].next_to(formulas_set2[i-1])
formulas_set2 = VGroup(*formulas_set2)
self.add(SurroundingRectangle(formulas_set2[8], color=BLUE))
self.add(title_2, bound_title2, formulas_set2)