Daniel Germán Martínez Muñoz (Usuario github: dmartinezmu).
Leonardo Felipe Betancur Díaz
Producción audiovisual e ilustrativa de hibridación de orbitales. Los requisitos y la guía para instalar manim se encuentran en: Manim 3b1b
El video FINAL RESULTADO FINAL
Explicación de Manim EXPLICACIÓN
MATLAB -> Gráficas
Adobe Audition -> Edición de audio.
Adobe Premiere Pro -> Edición de video.
Adobe Illustrator -> Configuración electronica (Representación por cajas)
Adobe Photoshop -> Edición de imagen.
Sony Vegas -> Edición de video.
Para los 3D Plots:Theorem of Beethoven
Para las gráficas 2D: Talking Physics
Documentación: Manim
Gráficas MATLAB : Evan (2020). plot Hydrogen Atom Molecular Orbital link, MATLAB Central File Exchange. Retrieved June 23, 2020.
Para el óvalo de cassini al usuario del level 314: level 314 youtube channel
Pymol -> Animaciones.
Manim -> Animaciones. Codigo en python:
#!/usr/bin/env python
from big_ol_pile_of_manim_imports import *
import mathAdemás del conocimiento del lenguaje python, es necesario conocer latex.
Gif hecho con Pymol (Módulo de python):
-
Representación del Metano (Tetraédrica).
Gráficas diseñadas cpm MATLAB
-
class IntroErwin(Scene):
def construct(self):
title = TextMobject("Erwin", "Schrodinger")
text = TexMobject(r"\Psi (r,\theta ,\phi )= ", "R(r)", "P(\\theta)", "F(\phi)")
text_2 = TextMobject("Funcion de probabilidad")
text_3 =TexMobject(r"\Psi^{2}")
image = ImageMobject("note")
title.next_to(image, UP, buff=0.3)
title[1].set_color(GREEN)
transform_title = TextMobject("Ecuacion de Schrodinger")
transform_title.to_corner(UP + LEFT)
transform_text = TexMobject(r"\Psi _{nlm}(r,\theta,\varphi)=\sqrt{(\frac{2}{na_{0}})^{3}\tfrac{(n-l-1)!}{2n(n+l)!}}e^{\frac{-\rho}{2}}\rho^{l}L_{n-l-1}^{2l+1}(\rho )Y_{lm}(\theta ,\rho)")
text_2.next_to(transform_text,DOWN, buff=0.3)
text_3.next_to(transform_text,DOWN,buff=1.5)
self.play(
Write(title),
FadeInFrom(image, UP),
)
self.wait(3)
self.play(
LaggedStart(FadeOutAndShiftDown, image)
)
self.wait()
self.play(
Transform(title, transform_title),
Write(text)
)
self.wait(2)
self.play(
Transform(text, transform_text),
Write(text_2),
ShowCreation(text_3)
)
self.wait(5)
self.play(
LaggedStart(FadeOutAndShiftDown, transform_title),
LaggedStart(FadeOutAndShiftDown, transform_text),
LaggedStart(FadeOutAndShiftDown, text_2),
LaggedStart(FadeOutAndShiftDown,title),
LaggedStart(FadeOutAndShiftDown,text),
LaggedStart(FadeOutAndShiftDown, text_3),
)
self.wait(2)El resultado es este:
-
class IntroEcuation(Scene):
def construct(self):
text = TexMobject(r"\Psi (r,\theta ,\phi )= ", "R(r)", "P(\\theta)", "F(\phi)")
framebox1 = SurroundingRectangle(text[1], buff=.1)
framebox2 = SurroundingRectangle(text[2], buff=.1)
framebox3 = SurroundingRectangle(text[3], buff=.1)
t1 = TexMobject("n")
t2 = TexMobject("l")
t3 = TexMobject("ml")
t1.next_to(framebox1, UP, buff=0.1)
t2.next_to(framebox2, UP, buff=0.1)
t3.next_to(framebox3, UP, buff=0.1)
text.set_color(BLUE)
self.play(
Write(text),
)
self.wait(2)
self.play(
ShowCreation(framebox1),
FadeIn(t1)
)
self.wait(3)
self.play(
ReplacementTransform(framebox1.copy(), framebox2),
ReplacementTransform(t1.copy(), t2),
)
self.wait(3)
self.play(
ReplacementTransform(framebox2.copy(), framebox3),
ReplacementTransform(t2.copy(), t3),
)
self.wait(6)
self.play(
LaggedStart(FadeOutAndShiftDown, text),
LaggedStart(FadeOutAndShiftDown, framebox1),
LaggedStart(FadeOutAndShiftDown, framebox2),
LaggedStart(FadeOutAndShiftDown, framebox3),
LaggedStart(FadeOutAndShiftDown, t1),
LaggedStart(FadeOutAndShiftDown, t2),
LaggedStart(FadeOutAndShiftDown, t3),
)
self.wait(2)El resultado es este:
-
class PlotOrbitalS(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
text3d = TextMobject("Orbital S en el hidrogeno")
self.add_fixed_in_frame_mobjects(text3d) # <----- Add this
text3d.to_corner(UL)
sphere = ParametricSurface(
lambda u, v: np.array([
1.5 * np.cos(u) * np.cos(v),
1.5 * np.cos(u) * np.sin(v),
1.5 * np.sin(u)
]), v_min=0, v_max=TAU, u_min=-PI / 2, u_max=PI / 2, checkerboard_colors=[BLUE_E, BLUE_E],
resolution=(15, 32)).scale(1)
self.set_camera_orientation(phi=75 * DEGREES)
self.begin_ambient_camera_rotation(rate=0.2)
self.add(axes)
self.play(LaggedStart(ShowCreation, sphere), ShowCreation(axes), ShowCreation(text3d))
self.wait(10)
self.play (LaggedStart(FadeOutAndShiftDown, sphere),
LaggedStart(FadeOutAndShiftDown, axes),
LaggedStart(FadeOutAndShiftDown, text3d)
)El resultado es este:
-
class PlotOrbitalP(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
text3d = TexMobject(r"P_{x}")
text3d_2 = TexMobject(r"P_{z}")
dot = Dot()
self.add(dot)
self.add_fixed_in_frame_mobjects(text3d)
self.add_fixed_in_frame_mobjects(text3d_2)# <----- Add this
text3d.to_corner(UL)
text3d_2.to_corner(UL)
sphere = ParametricSurface(
lambda u, v: np.array([
1.5 * np.cos(u) * np.cos(v),
1.5 * np.cos(u) * np.sin(v),
1.5 * np.sin(u)
]), v_min=0, v_max=TAU, u_min=-PI / 2, u_max=PI / 2, checkerboard_colors=[RED_E, RED_E],
resolution=(15, 32)).scale(1)
sphere.next_to(dot, RIGHT,buff=-0.1)
sphere_2 = ParametricSurface(
lambda u, v: np.array([
1.5 * np.cos(u) * np.cos(v),
1.5 * np.cos(u) * np.sin(v),
1.5 * np.sin(u)
]), v_min=0, v_max=TAU, u_min=-PI / 2, u_max=PI / 2, checkerboard_colors=[RED_E, RED_E],
resolution=(15, 32)).scale(1)
sphere_2.next_to(dot,LEFT,buff=-0.1)
self.set_camera_orientation(phi=75 * DEGREES)
self.begin_ambient_camera_rotation(rate=0.2)
self.add(axes)
self.play(LaggedStart(ShowCreation, sphere),
LaggedStart(ShowCreation, sphere_2),
ShowCreation(axes),
ShowCreation(text3d)
)
self.wait(5)
self.play(
ReplacementTransform(text3d, text3d_2),
)
self.play(LaggedStart(FadeOutAndShiftDown, sphere),
LaggedStart(FadeOutAndShiftDown, sphere_2),)
vector = np.array([0,0,1])
vector_2 = np.array([0, 0, -1])
sphere.move_to(dot,vector)
sphere_2.move_to(dot,vector_2)
self.play(LaggedStart(ShowCreation, sphere),
LaggedStart(ShowCreation, sphere_2),
)
self.wait(5)
self.play (LaggedStart(FadeOutAndShiftDown, sphere),
LaggedStart(FadeOutAndShiftDown, sphere_2),
LaggedStart(FadeOutAndShiftDown, dot),
LaggedStart(FadeOutAndShiftDown, axes),
LaggedStart(FadeOutAndShiftDown, text3d)
)
El resultado es este:
-
class PlotWave(GraphScene):
CONFIG = {
"x_min": -10,
"x_max": 10,
"y_min": -1,
"y_max": 1,
"y_axis_label": " ",
"x_axis_label": " ",
"graph_origin": ORIGIN,
"function_color": RED,
"axes_color": BLACK,
"include_ticks": False
}
def construct(self):
self.setup_axes(animate=True)
func_graph = self.get_graph(self.func_to_graph, self.function_color)
func_graph2 = self.get_graph(self.func_to_graph2,self.function_color)
n_1 = TexMobject(r"n = 1")
n_1.next_to(func_graph, RIGHT + UP)
n_2 = TexMobject(r"n = 3")
n_2.next_to(func_graph2, RIGHT + UP)
wave_func = TexMobject(r"\Psi _{nlm}(r,\theta,\varphi)")
text_1 = TexMobject(r"\Psi _{nlm}(2,0,0)")
text_2 = TexMobject(r"\Psi _{nlm}(2,1,0)")
text_3 = TexMobject(r"\Psi _{nlm}(2,1,1)")
image_1 = ImageMobject("HW_1")
image_2 = ImageMobject("HW_2")
image_3 = ImageMobject("HW_3")
image_1.to_edge(UP,buff=4)
image_2.next_to(image_1, LEFT, buff=1.5)
image_3.next_to(image_1, RIGHT, buff=1.5)
self.play(ShowCreation(func_graph2), lag_ratio=0.1)
self.play(ShowCreation(n_1))
self.wait(5)
self.play(
LaggedStart(FadeOutAndShiftDown, func_graph2),
LaggedStart(FadeOutAndShiftDown, n_1),
)
self.play(ShowCreation(func_graph), ShowCreation(func_graph2), lag_ratio=0.1)
self.play(ShowCreation(n_2))
self.wait(5)
self.play(
LaggedStart(FadeOutAndShiftDown, func_graph),
LaggedStart(FadeOutAndShiftDown, func_graph2),
LaggedStart(FadeOutAndShiftDown, n_2),
)
self.wait(2)
wave_func.to_edge(UP, buff=1.5)
text_1.to_edge(UP, buff=1.5)
text_2.to_edge(UP, buff=1.5)
text_3.to_edge(UP, buff=1.5)
self.play(
Write(wave_func),
)
self.wait(2)
self.play(
ReplacementTransform(wave_func, text_1),
FadeInFrom(image_1, UP),)
self.wait(2)
self.play(
ReplacementTransform(text_1, text_2),
ReplacementTransform(image_1.copy(),image_2)
)
self.wait(2)
self.play(
ReplacementTransform(text_2, text_3),
ReplacementTransform(image_2.copy(),image_3)
)
self.wait(5)
def func_to_graph(self, x):
return -(np.sin(x/2))
def func_to_graph2(self, x):
return np.sin(x/2)El resultado es este :
-
class Lemniscata (ThreeDScene):
def construct(self):
axes = ThreeDAxes()
text3d = TexMobject(r"P_{x}")
text3d.to_corner(UL)
lemniscata = ParametricFunction(
lambda u: np.array([
2*(np.cos(u))/(1+np.sin(u)**2),
0,
2*(np.sin(u)*np.cos(u))/(1+np.sin(u)**2),
]),color=RED,t_min=-TAU,t_max=TAU)
self.add(axes)
lemniscata.set_shade_in_3d(True)
self.add_fixed_in_frame_mobjects(text3d)
self.set_camera_orientation(phi=80 * DEGREES,theta=-60*DEGREES)
self.begin_ambient_camera_rotation(rate=0.3)
self.play(
ShowCreation(axes),
ShowCreation(lemniscata),
ShowCreation(text3d)
)
self.wait(10)
El resultado es este:
-
class MainIntro(Scene):
def construct(self):
title = TextMobject("ORBITALES")
text_1 = TexMobject(r"S")
text_2 = TexMobject(r"P")
line = Line(ORIGIN, RIGHT * FRAME_WIDTH, buff=1)
line.move_to(ORIGIN)
title.next_to(line,UP)
text_1.next_to(line,RIGHT)
text_2.next_to(line,LEFT)
title.set_color(YELLOW)
text_1.set_color(GREEN)
text_2.set_color(BLUE)
self.play(
ShowCreation(line),
FadeInFromDown(title)
)
self.wait(5)
self.play(
FadeOut(line),
FadeOut(title)
)
self.wait()
text_1.to_corner(UP + LEFT,buff=2)
text_2.to_corner(UP + RIGHT,buff=2)
self.play(
DrawBorderThenFill(text_1),
DrawBorderThenFill(text_2),
)
self.wait(10)El resultado es este:
-
class Hibridation(Scene):
def construct(self):
title = TextMobject("HIBRIDACION")
text_1 = TexMobject(r"SP")
text_2 = TexMobject(r"SP^{2}")
text_3 = TexMobject(r"SP^{3}")
line = Line(ORIGIN, RIGHT * FRAME_WIDTH, buff=1)
line.move_to(ORIGIN)
title.next_to(line,UP)
text_1.to_edge(UP,buff=2)
text_2.next_to(text_1,RIGHT,buff=5)
text_3.next_to(text_1,LEFT,buff =5)
title.set_color(RED)
text_1.set_color(GREEN)
text_2.set_color(BLUE)
text_3.set_color(YELLOW)
self.play(
ShowCreation(line),
FadeInFromDown(title)
)
self.wait(3)
self.play(
FadeOut(line),
FadeOut(title)
)
self.wait()
self.play(
Write(text_1),
ReplacementTransform(text_1.copy(), text_2),
ReplacementTransform(text_2.copy(), text_3),
)
self.wait(10)El resultado es este:
-
En este Issue me ayudaron con lo del orbital P, y el resultado es impresionante. Este es el código del usuario que me ayudó y el issue es: Cassini_oval3d
class S04_3D_Cassini_Oval(ThreeDScene):
def parametric_CO(self, u,v):
# equation for 2d Cassini Oval
M = (foci_A ** 2) * np.cos(2 * u)\
+ (np.sqrt( (foci_B ** 4)-(foci_A ** 4) + ((foci_A ** 4) * (np.cos(2 * u) ** 2)) ))
x = np.cos(u) * np.sqrt(M)
y = np.sin(u) * np.sqrt(M)
# 3d rotation around X axes
z = y * np.sin(v) # be sure to calculate Z first size we modify Y
y = y * np.cos(v)
return np.array([x, y, z])
def construct(self):
# controls how many squares the approximation grid is broken into
parametric_resolution = 24
r_scale = 0.35
boundaries = { "u_min": 0, "u_max": TAU,"v_min": 0, "v_max": PI}
cassini_oval = ParametricSurface(
self.parametric_CO, **boundaries
, checkerboard_colors=[BLUE_E, BLUE_E], fill_opacity=0.65,
resolution=(parametric_resolution, math.floor(parametric_resolution * r_scale))).scale(1.5)
axes = ThreeDAxes()
# self.set_camera_orientation(gamma = 80 * DEGREES, phi = 15 * DEGREES)
# self.add(cassini_oval, axes)
self.play(ShowCreation(axes))
self.play(ShowCreation(cassini_oval))
self.set_camera_orientation(phi=80 * DEGREES,theta=-60*DEGREES)
self.begin_ambient_camera_rotation(rate=0.6)
# use custom camera rotation for multiple angles instead of manim standard
# self.begin_ambient_camera_rotation_multi(rate_theta=0.8, rate_gamma=0.04, rate_phi=0.4)
self.wait(5)
class Hibridacion(Scene):
def construct(self):
tex = TextMobject("Hibridación ","del ","Carbono")
tex[0].set_color(WHITE)
tex[1].set_color(WHITE)
tex[2].set_color(RED)
sp3 = TexMobject("{sp}^3 \\quad ","{sp}^2\\quad","{sp}")
square = Square()
square2 = Square()
square3 = Square()
square.move_to(sp3[0].get_center())
square2.move_to(sp3[1].get_center())
square3.move_to(sp3[2].get_center())
square.scale(0.5)
square2.scale(0.5)
square3.scale(0.5)
hydrogen_atom = Mobject()
title = TextMobject("Concepción clásica")
orbit = Circle(radius=1.3).scale(0.85)
proton = Dot(radius=0.4, color="GREY").scale(0.85)
elec = Dot(radius=0.2, color="BLUE").scale(0.85)
p_charge = TexMobject("H", stroke_width=0.5)
e_charge = TexMobject("-",stroke_width=0.5)
hydrogen_atom2 = Mobject()
orbit2 = Circle(radius=1.3).scale(0.85)
proton2 = Dot(radius=0.4, color="GREY").scale(0.85)
elec2 = Dot(radius=0.2, color="BLUE").scale(0.85)
p_charge2 = TexMobject("H", stroke_width=0.5)
e_charge2 = TexMobject("-",stroke_width=0.5)
orbit2.move_to(orbit.get_center() + RIGHT*1)
elec2.move_to(orbit2.points[0])
proton2.move_to(orbit2.get_center())
e_charge2.move_to(elec2.get_center())
p_charge2.move_to(proton2.get_center())
title.move_to(title.get_center()+UP*2)
elec.move_to(orbit.points[0])
e_charge.move_to(elec.get_center())
p_charge.move_to(proton.get_center())
self.play(ShowCreation(title))
self.play(ShowCreation(orbit))
self.play(GrowFromCenter(proton),
GrowFromCenter(p_charge)
)
self.play(GrowFromCenter(elec),
GrowFromCenter(e_charge)
)
self.play(MoveAlongPath(elec, orbit),
MaintainPositionRelativeTo(e_charge, elec),
run_time=5
)
self.wait(1)
hydrogen_atom.add(orbit,elec, proton, e_charge, p_charge)
atom = hydrogen_atom.copy()
atom2 = hydrogen_atom.copy()
atom3 = hydrogen_atom.copy()
atom2.move_to(hydrogen_atom.get_center() + LEFT*1)
atom3.move_to(hydrogen_atom.get_center() + RIGHT*1)
atom3[1].move_to(atom3[0].points[14])
atom3[3].move_to(atom3[0].points[14])
self.play(
Transform(atom,atom2),
Transform(hydrogen_atom,atom3),run_time =5
)
self.wait(2)
self.remove(atom , hydrogen_atom , title)
self.play(FadeInFromDown(tex))
self.wait(3)
self.remove(tex)
self.play(
Transform(tex, sp3),
FadeInFromDown(square)
)
self.wait(2)
self.play(Transform(square,square2))
self.wait(2)
self.play(Transform(square,square3))
self.wait(2)El resultado es este:
class Config_electro(Scene):
def construct(self):
tex = TextMobject("Configuración ","electrónica del ","Carbono")
tex2 = TextMobject("Estado basal")
tex2.set_color(BLUE)
tex3 = TextMobject("Estado excitado")
tex3.set_color(RED)
metv = ImageMobject("qf.gif")
sp = TexMobject("{sp}^3 \\quad ","{sp}^2\\quad","sp")
tex[0].set_color(WHITE)
tex[1].set_color(WHITE)
tex[2].set_color(RED)
Confi = TexMobject("C={1s}^2 \\quad ","{2s}^2\\quad","{2p}^2")
Metano = TexMobject("H ", "H" , "H" , "H" , "C")
square = Square()
square2 = Square()
square3 = Square()
enlace1 = Line(np.array([0.5,0,0]),np.array([1,0,0]))
enlace2 = Line(np.array([-0.5,0,0]),np.array([-1,0,0]))
enlace3 = Line(np.array([0,0.5,0]),np.array([0,1,0]))
enlace4 = Line(np.array([0,-0.5,0]),np.array([0,-1,0]))
basal = ImageMobject("basalf.png")
excitado = ImageMobject("excitadof.png")
sp3_ = ImageMobject("sp3_blanco.png")
Metano[0].move_to(basal.get_center() + 1.5*UP)
Metano[1].move_to(basal.get_center() + 1.5*DOWN)
Metano[3].move_to(basal.get_center() + 1.5*RIGHT)
Metano[2].move_to(basal.get_center() + 1.5*LEFT)
Metano[4].move_to(basal.get_center())
sq = Square()
sq.scale(0.5)
self.play(FadeInFromDown(tex))
self.wait(3)
self.remove(tex)
self.play(
Transform(tex, Confi)
)
Met = VGroup(enlace1,enlace2 , enlace3 , enlace4 , Metano[0] , Metano[1] , Metano[2] , Metano[3] , Metano[4] )
self.wait(3)
self.play(
Transform(tex, Met)
)
self.wait(3)
T2 = Met
T2.to_corner(UP + RIGHT)
T2.scale(0.5)
aux = sp[0].copy()
tex2.move_to(basal.get_center() + 2*UP)
tex3.move_to(tex2.get_center())
sp[0].move_to(tex2.get_center())
sp[0].set_color(YELLOW)
aux.to_corner(UP + LEFT)
sq.move_to(aux.get_center())
sq.set_color(YELLOW)
sp[1].move_to(aux.get_center() - 1*LEFT)
sp[2].move_to(aux.get_center() - 2*LEFT + 0.1*DOWN)
aux_ = VGroup(aux, sp[1], sp[2])
self.play(
FadeOutAndShift(tex)
)
metv.move_to(T2.get_center() + DOWN*3)
metv.scale(1.3)
self.play(
Write(tex2),
ShowCreation(T2) ,FadeIn(metv),
FadeInFromLarge(basal)
)
self.wait(3)
self.play(
Transform(tex2,tex3),
FadeOutAndShift(basal),
FadeInFromPoint(excitado,[2,2,0])
)
self.wait(3)
self.play(
Write(aux_) ,
Write(sq),
Transform(tex2,sp[0]),
FadeOutAndShift(excitado),
FadeInFromPoint(sp3_,[-2,-2,0])
)
self.wait(3)El resultado es este:
class sp2_(Scene):
def construct(self):
sp = TexMobject("{sp}^3 \\quad ","{sp}^2\\quad","sp")
sp[0].to_corner(UP + LEFT)
sp[1].move_to(sp[0].get_center() - 1*LEFT)
sp[2].move_to(sp[0].get_center() - 2*LEFT + 0.1*DOWN)
sq = Square()
sq.scale(0.5)
sq.set_color(YELLOW)
sq.move_to(sp[1].get_center())
sq.set_color(YELLOW)
aux = VGroup(sp[0], sp[1], sp[2] , sq)
sp2_ = ImageMobject("sp2_blanco.png")
sp2_.scale(1.5)
titulo = TexMobject("{sp}^2")
Compuesto = TextMobject("Eteno")
Compuesto.scale(0.6)
titulo.move_to(sp2_.get_center() + 2*UP)
titulo.set_color(YELLOW)
Eteno = TexMobject("H" , "H" , "H" , "H" , "C" , "C")
enlace1 , enlace2 = Line(np.array([0.5 ,0.1 ,0]) ,np.array([1 ,0.1,0])) , Line(np.array([0.5,-0.1,0]) ,np.array([1,-0.1,0]))
Eteno[4].move_to(enlace1.get_center() + 0.5*RIGHT + 0.1*DOWN)
Eteno[5].move_to(enlace1.get_center() + 0.5*LEFT + 0.1*DOWN)
enlace3 = Line(np.array([0.5 ,0.5 ,0]) ,np.array([1 , 1 ,0]))
enlace4 = Line(np.array([0.5 ,-0.5,0]) ,np.array([1 ,-1 ,0]))
enlace3.move_to(Eteno[4].get_center() + 0.5*RIGHT+ 0.5*UP)
enlace4.move_to(Eteno[4].get_center() + 0.5*RIGHT+ 0.5*DOWN)
enlace5 = Line(np.array([-0.5,-0.5,0]) ,np.array([-1,-1 ,0]))
enlace6 = Line(np.array([-0.5,0.5 ,0]) ,np.array([-1, 1 ,0]))
enlace5.move_to(Eteno[5].get_center() + 0.5*LEFT + 0.5*DOWN)
enlace6.move_to(Eteno[5].get_center() + 0.5*LEFT + 0.5*UP)
Eteno[0].move_to(enlace3.get_center() + 0.5*UP + 0.5*RIGHT)
Eteno[1].move_to(enlace4.get_center() + 0.5*DOWN + 0.5*RIGHT)
Eteno[2].move_to(enlace5.get_center() + 0.5*DOWN + 0.5*LEFT )
Eteno[3].move_to(enlace6.get_center() + 0.5*UP + 0.5*LEFT )
Eteno_Completo = VGroup(enlace1 , enlace2 , enlace3 , enlace4 , enlace5 , enlace6 , Eteno[0] , Eteno[1] , Eteno[2] , Eteno[3] , Eteno[4] , Eteno[5])
Eteno_Completo.scale(0.7)
Eteno_Completo.to_corner(UR)
Compuesto.move_to(Eteno_Completo.get_center() + DOWN)
self.play(
Write(aux),
Write(titulo),
FadeInFromLarge(sp2_),
FadeInFromLarge(Compuesto),
Write(Eteno_Completo), run_time= 4
)
self.wait(2)El resultado es:
class sp_(Scene):
def construct(self):
sp = TexMobject("{sp}^3 \\quad ","{sp}^2\\quad","sp")
sp[0].to_corner(UP + LEFT)
sp[1].move_to(sp[0].get_center() - 1*LEFT)
sp[2].move_to(sp[0].get_center() - 2*LEFT + 0.1*DOWN)
sq = Square()
sq.scale(0.5)
sq.set_color(YELLOW)
sq.move_to(sp[2].get_center())
sq.set_color(YELLOW)
aux = VGroup(sp[0], sp[1], sp[2] , sq)
sp1_ = ImageMobject("sp_blanco.png" )
sp1_.scale(1.5)
titulo = TexMobject("sp")
titulo.move_to(sp1_.get_center() + UP*2)
titulo.set_color(YELLOW)
Compuesto = TextMobject("Etino")
Compuesto.scale(0.6)
Etino = TexMobject("H" , "H" , "C" , "C")
enlace1 , enlace2 , enlace3 = Line(np.array([0.5,0,0]) ,np.array([1,0,0])) , Line(np.array([0.5,0.1,0]) ,np.array([1,0.1,0])) , Line(np.array([0.5,-0.1,0]) ,np.array([1,-0.1,0]))
Etino[2].move_to(enlace1.get_center() + 0.5*RIGHT)
Etino[3].move_to(enlace1.get_center() + 0.5*LEFT )
enlace4 , enlace5 = Line(np.array([0.5,0,0]) ,np.array([1,0,0])) , Line(np.array([0.5,0,0]) ,np.array([1,0,0]))
enlace4.move_to(Etino[2].get_center() + 0.5*RIGHT)
enlace5.move_to(Etino[3].get_center() + 0.5*LEFT )
Etino[0].move_to(enlace4.get_center() + 0.5*RIGHT)
Etino[1].move_to(enlace5.get_center() + 0.5*LEFT )
Etino_Completo = VGroup(Etino[0], Etino[1], Etino[2], Etino[3], enlace1, enlace2, enlace3, enlace4, enlace5 )
Etino_Completo.to_corner(UR)
Etino_Completo.scale(0.7)
Compuesto.move_to(Etino_Completo.get_center() + DOWN)
self.play(
Write(aux),
Write(titulo),
FadeInFromLarge(Compuesto),
FadeInFromLarge(sp1_),
Write(Etino_Completo), run_time= 4
)
self.wait(2)El resultado es este:
class FunctionTracker(Scene):
def construct(self):
x_value = ValueTracker(2020)
# DecimalNumber definition
x_tex = DecimalNumber(x_value.get_value()).add_updater(lambda v: v.set_value(x_value.get_value()))
# TeX labels definition
x_label = TexMobject(" ")
# Grouping of labels and numbers
group = VGroup(x_tex,x_label)
# Set the labels position
x_label.next_to(x_tex,LEFT, buff=0.7,aligned_edge=x_label.get_bottom())
# Grouping numbers and labels
x_group = VGroup(x_label,x_tex).scale(2)
x_group.move_to(UP*2)
# Align labels and numbers
# Get NumberLine,Arrow and label from x
x_number_line_group = self.get_number_line_group(
"x",2020,0.1,step_label=100,v_tracker=x_value,tick_frequency=2
)
x_number_line_group.to_edge(LEFT,buff=1)
# Get NumberLine,Arrow and label from f(x)
self.add(
x_number_line_group,
group
)
self.wait()
self.play(
x_value.set_value,1911,
rate_func=linear,
run_time=10
)
self.wait(3)
def get_numer_labels_to_numberline(self,number_line,x_max=None,x_min=0,buff=0.2,step_label=1,**tex_kwargs):
# This method return the labels of the NumberLine
labels = VGroup()
x_max = number_line.x_max
for x in range(1911,x_max+1,step_label):
x_label = TexMobject(f"{x}",**tex_kwargs)
# See manimlib/mobject/number_line.py CONFIG dictionary
x_label.next_to(number_line.number_to_point(x),DOWN,buff=buff)
labels.add(x_label)
x = 2020
x_label = TexMobject(f"{x}",**tex_kwargs)
x_label.next_to(number_line.number_to_point(x),DOWN,buff=buff)
labels.add(x_label)
return labels
def get_number_line_group(self,label,x_max,unit_size,v_tracker,step_label=1,**number_line_config):
# Set the Label (x,or x**2)
number_label = TexMobject(label)
# Set the arrow
arrow = Arrow(UP,DOWN,buff=0).set_height(0.5)
# Set the number_line
number_line = NumberLine(
x_min=1911,
x_max=x_max,
unit_size=unit_size,
numbers_with_elongated_ticks=[],
**number_line_config
)
# Get the labels from number_line
labels = self.get_numer_labels_to_numberline(number_line,step_label=step_label,height=0.2)
# Set the arrow position
arrow.next_to(number_line.number_to_point(1911),UP,buff=0)
# Grouping arrow and number_label
label = VGroup(arrow,number_label)
# Set the position of number_label
number_label.next_to(arrow,UP,buff=0.1)
# Grouping all elements
numer_group = VGroup(label,number_line,labels)
# Set the updater to the arrow and number_label
label.add_updater(lambda mob: mob.next_to(number_line.number_to_point(v_tracker.get_value()),UP,buff=0))
return numer_groupEl resultado es este:
foci_A = 1
foci_B = 1
class SpDosCarbono1(ThreeDScene):
def parametric_CO(self, u, v):
# 2d Cassini Oval
M = (foci_A ** 2) * np.cos(2 * u) \
+ (np.sqrt((foci_B ** 4) - (foci_A ** 4) + ((foci_A ** 4) * (np.cos(2 * u) ** 2))))
x = np.cos(u) * np.sqrt(M)
y = np.sin(u) * np.sqrt(M)
# 3D Rotación en X
z = y * np.sin(v)
y = y * np.cos(v)
return np.array([x, y, z])
def parametric_CO_z(self, u, v):
# 2d Cassini Oval
M = (foci_A ** 2) * np.cos(2 * u) \
+ (np.sqrt((foci_B ** 4) - (foci_A ** 4) + ((foci_A ** 4) * (np.cos(2 * u) ** 2))))
z = np.cos(u) * np.sqrt(M)
x = np.sin(u) * np.sqrt(M)
# 3D Rotación en Z
y = x * np.sin(v)
x = x * np.cos(v)
return np.array([x, y, z])
def parametric_CO_z2(self, u, v):
#2d Cassini Oval
M = (foci_A ** 2) * np.cos(2 * u) \
+ (np.sqrt((foci_B ** 4) - (foci_A ** 4) + ((foci_A ** 4) * (np.cos(2 * u) ** 2))))
z = np.cos(u) * np.sqrt(M)
x = np.sin(u) * np.sqrt(M)
# 3D Rotación en Z
y = x * np.sin(v)
x = x * np.cos(v)
return np.array([x, y/2, z])
def construct(self):
# Ctdad de subdivisiones en la superficie
parametric_resolution = 50
r_scale = 0.35
boundaries = {"u_min": 0, "u_max": TAU, "v_min": 0, "v_max": PI}
cassini_oval_x = ParametricSurface(
self.parametric_CO, **boundaries
, checkerboard_colors=[BLUE],
resolution=(parametric_resolution,
math.floor(parametric_resolution * r_scale))).scale(1.5)
cassini_oval_z = ParametricSurface(
self.parametric_CO_z, **boundaries
, checkerboard_colors=[BLUE],
resolution=(parametric_resolution,
math.floor(parametric_resolution * r_scale))).scale(1.5)
cassini_oval_z_2 = ParametricSurface(
self.parametric_CO_z2, **boundaries
, checkerboard_colors=[RED],
resolution=(parametric_resolution, math.floor(parametric_resolution * r_scale))).scale(1.5)
axes = ThreeDAxes()
self.set_camera_orientation(phi=80 * DEGREES)
self.begin_ambient_camera_rotation(rate=0.2)
cassini_oval_z.rotate(PI / 2, axis=RIGHT)
self.play(
ShowCreation(axes),
ShowCreation(cassini_oval_x),
ShowCreation(cassini_oval_z),
ShowCreation(cassini_oval_z_2)
)
self.wait(22)El resultado es este:
class SpCarbono1(ThreeDScene):
def parametric_CO(self, u, v):
# 2d Cassini Oval
M = (foci_A ** 2) * np.cos(2 * u) \
+ (np.sqrt((foci_B ** 4) - (foci_A ** 4) + ((foci_A ** 4) * (np.cos(2 * u) ** 2))))
x = np.cos(u) * np.sqrt(M)
y = np.sin(u) * np.sqrt(M)
# 3D Rotación en X
z = y * np.sin(v)
y = y * np.cos(v)
return np.array([x, y, z])
def parametric_CO_z(self, u, v):
# 2d Cassini Oval
M = (foci_A ** 2) * np.cos(2 * u) \
+ (np.sqrt((foci_B ** 4) - (foci_A ** 4) + ((foci_A ** 4) * (np.cos(2 * u) ** 2))))
z = np.cos(u) * np.sqrt(M)
x = np.sin(u) * np.sqrt(M)
# 3D Rotación en Z
y = x * np.sin(v)
x = x * np.cos(v)
return np.array([x, y/2, z])
def parametric_CO_z2(self, u, v):
#2d Cassini Oval
M = (foci_A ** 2) * np.cos(2 * u) \
+ (np.sqrt((foci_B ** 4) - (foci_A ** 4) + ((foci_A ** 4) * (np.cos(2 * u) ** 2))))
z = np.cos(u) * np.sqrt(M)
x = np.sin(u) * np.sqrt(M)
# 3D Rotación en Z
y = x * np.sin(v)
x = x * np.cos(v)
return np.array([x, y/2, z])
def construct(self):
# Ctdad de subdivisiones en la superficie
parametric_resolution = 50
r_scale = 0.35
boundaries = {"u_min": 0, "u_max": TAU, "v_min": 0, "v_max": PI}
cassini_oval_x = ParametricSurface(
self.parametric_CO, **boundaries
, checkerboard_colors=[BLUE],
resolution=(parametric_resolution,
math.floor(parametric_resolution * r_scale))).scale(1.5)
cassini_oval_z = ParametricSurface(
self.parametric_CO_z, **boundaries
, checkerboard_colors=[RED],
resolution=(parametric_resolution,
math.floor(parametric_resolution * r_scale))).scale(1.5)
cassini_oval_z_2 = ParametricSurface(
self.parametric_CO_z2, **boundaries
, checkerboard_colors=[RED],
resolution=(parametric_resolution, math.floor(parametric_resolution * r_scale))).scale(1.5)
axes = ThreeDAxes()
self.set_camera_orientation(phi=80 * DEGREES)
self.begin_ambient_camera_rotation(rate=0.2)
cassini_oval_z.rotate(PI / 2, axis=RIGHT)
self.play(
ShowCreation(axes),
ShowCreation(cassini_oval_x),
ShowCreation(cassini_oval_z),
ShowCreation(cassini_oval_z_2)
)
self.wait(22)El resultado es este:
CÓDIGO FINAL ESTÁ EN EL REPO, Y FUE ESCRITO PARA LA VERSIÓN MÁS RECIENTE DE MANIM
React
Typescript
Django
Laravel
Facebook
Microsoft
Google
Alibaba
D3
Tencent