Explicaciones científicas y desarrollos matemáticos
Próximamente, tutoriales de Manim
from manim import *
LME_color = "#27a0b3"
class ExpZ_1(Scene):
def construct(self):
##------------------------------
## Logo LME en la esquina
##------------------------------
brand = Text(
"LED Me Explain",
fill_opacity = 0.5,
color = WHITE,
font = "Arial Rounded MT Bold",
t2c = {"[:1]":LME_color,"[3:4]":LME_color,"[5:6]":LME_color} ## Los espacios no cuentan como caracteres
).scale(0.4).to_edge(DR)
# Añade el logo
self.add(brand)
##---------------------------------
##---------------------------------
##------------------------------
## Titulo y subtitulo del video
##------------------------------
title = Tex( # Crea el título
r"¿Cómo se ve la transformación ", r'$z$',r'$\,\rightarrow\,$',r'$e^z$',r' ?',
).scale_to_fit_width(config["frame_width"]-4)
title_math = MathTex(r'z',r'\rightarrow',r'e^z', tex_template = TexFontTemplates.libertine).move_to(title[2], aligned_edge = DOWN).scale(1.2).shift(RIGHT*.1)
title_math[0].set_color(TEAL_C)
title_math[2].set_color(PURPLE_C)
# Crea el rectangulo que rodea al grupo
frameTitle = SurroundingRectangle(title, LME_color, buff = 1)
subtitle = Text( # Crea el subtítulo
"Variable Compleja",
color = LIGHT_GREY
).scale(0.6).next_to(frameTitle,DOWN, aligned_edge = RIGHT)
# Aparece el titulo
self.play(
FadeIn(title[0]),
FadeIn(title[4]),
FadeIn(title_math)
)
# Crea el rectangulo
self.play(Create(frameTitle))
# Escribe el subtitulo
self.play(Write(subtitle) , run_time = 0.7)
self.wait(1.5) # Espera un momento
# Desaparece el titulo, subtitulo y el rectangulo
self.play(
FadeOut(title[0], scale=0.7),
FadeOut(title[4], scale=0.7),
FadeOut(title_math, scale = 0.7),
FadeOut(subtitle, scale=0.7),
FadeOut(frameTitle)
)
##---------------------------------
##---------------------------------
##------------------------------
## 1. Título, enunciado y animación del problema
##------------------------------
header = Title(r'Esta es la transformación ',r'$z$',r'$\,\rightarrow\,$',r'$e^z$', scale_factor = 1.5).set_z_index(1)
header_math = MathTex(r'z',r'\rightarrow',r'e^z', tex_template = TexFontTemplates.libertine).move_to(header[2], aligned_edge = DOWN).scale(1.4).shift(UR*0.1).set_z_index(1)
header_math[0].set_color(TEAL_C)
header_math[2].set_color(PURPLE_C)
self.play(
FadeIn(header[0]),
FadeIn(header[-1]),
FadeIn(header_math)
)
self.wait()
square_1 = Square(color = TEAL_C)
rectPlane = NumberPlane(x_range=(-8, 8, 1)).set_opacity(0.3)
lbl_x_axis = MathTex(r'Re', tex_template = TexFontTemplates.libertine).next_to(RIGHT*5,UP).set_opacity(0.3)
lbl_y_axis = MathTex(r'Im', tex_template = TexFontTemplates.libertine).next_to(UP*2,RIGHT).set_opacity(0.3)
lbl_x1 = Tex(r'$-1$', tex_template = TexFontTemplates.libertine).next_to(LEFT,DR*0.2,aligned_edge = LEFT).scale(0.7).set_opacity(0.7).set_z_index(1)
lbl_x2 = Tex(r'$1$', tex_template = TexFontTemplates.libertine).next_to(RIGHT,DR*0.2,aligned_edge = LEFT).shift(RIGHT*0.1).scale(0.7).set_opacity(0.7).set_z_index(1)
lbl_y1 = Tex(r'$-1$', tex_template = TexFontTemplates.libertine).next_to(DOWN,UR*0.2,aligned_edge = LEFT).scale(0.7).set_opacity(0.7).set_z_index(1)
lbl_y2 = Tex(r'$1$', tex_template = TexFontTemplates.libertine).next_to(UP,UR*0.2,aligned_edge = LEFT).shift(RIGHT*0.1).scale(0.7).set_opacity(0.7).set_z_index(1)
self.play(Create(rectPlane, run_time=3, lag_ratio=0.1))
self.play(
FadeIn(lbl_x_axis),
FadeIn(lbl_y_axis)
)
self.play(Create(square_1))
self.play(
FadeIn(lbl_x1),
FadeIn(lbl_x2),
FadeIn(lbl_y1),
FadeIn(lbl_y2)
)
self.wait(2)
self.play(
FadeOut(rectPlane),
FadeOut(lbl_x_axis),
FadeOut(lbl_y_axis),
FadeOut(lbl_x1),
FadeOut(lbl_x2),
FadeOut(lbl_y1),
FadeOut(lbl_y2)
)
header_mini = Tex(r'$z$',r'$\,\rightarrow\,$',r'$e^z$', tex_template = TexFontTemplates.libertine).scale(1.5).to_edge(UL*1.5).set_z_index(1)
header_mini[0].set_color(TEAL_C)
header_mini[2].set_color(PURPLE_C)
self.play(
ApplyMethod(header_math.become,header_mini),
FadeOut(header[0], target_position = header_mini, scale = 0.5),
FadeOut(header[-1], target_position = header_mini, scale = 0.5)
)
polarPlane = PolarPlane(radius_max = 8).set_opacity(0.3).set_fill(opacity=0)
line_a1 = Line(ORIGIN, polarPlane.polar_to_point(4,1),stroke_width=2).set_opacity(0.3).set_z_index(1)
line_a2 = Line(ORIGIN, polarPlane.polar_to_point(4,TAU-1),stroke_width=2).set_opacity(0.3).set_z_index(1)
lbl_a1 = Tex(r'$1$ rad', tex_template = TexFontTemplates.libertine).move_to(line_a1.get_end()+UP*0.2).scale(0.7).set_opacity(0.7).set_z_index(1)
lbl_a2 = Tex(r'$-1$ rad', tex_template = TexFontTemplates.libertine).move_to(line_a2.get_end()+DOWN*0.2).scale(0.7).set_opacity(0.7).set_z_index(1)
lbl_r1 = Tex(r'$e^{-1}$', tex_template = TexFontTemplates.libertine).move_to(polarPlane.polar_to_point(np.exp(-1),0)+DOWN*0.2+RIGHT*0.3).scale(0.7).set_opacity(0.7).set_z_index(1)
lbl_r2 = Tex(r'$e^1$', tex_template = TexFontTemplates.libertine).move_to(polarPlane.polar_to_point(np.exp(1),0)+DOWN*0.2+RIGHT*0.1).scale(0.7).set_opacity(0.7).set_z_index(1)
lbl_y_axis.next_to(UP*3,RIGHT)
self.play(Create(polarPlane), run_time=3, lag_ratio=0.1)
self.play(
FadeIn(lbl_x_axis),
FadeIn(lbl_y_axis)
)
def expZTransform(mobject):
mobject.apply_complex_function(lambda z: np.exp(z)) #lambda z: np.exp(z)-np.exp((z-z.conjugate())/2) Convierte el primer cuadrante en un circulo
mobject.set_color(PURPLE_C)
return mobject
self.play(ApplyFunction(expZTransform,square_1), run_time = 2)
self.play(
Create(line_a1),
Create(line_a2),
FadeIn(lbl_a1),
FadeIn(lbl_a2),
FadeIn(lbl_r1),
FadeIn(lbl_r2)
)
self.wait(2)
self.play(
FadeOut(line_a1),
FadeOut(line_a2),
FadeOut(lbl_x_axis),
FadeOut(lbl_y_axis),
FadeOut(lbl_a1),
FadeOut(lbl_a2),
FadeOut(lbl_r1),
FadeOut(lbl_r2),
FadeOut(polarPlane),
FadeOut(square_1),
FadeOut(header_math)
)
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