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# -*- coding: utf-8 -*-
import sys, os, math
sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
from manim import *
from tiktok import *
W = 2.9 # ancho constante de las figuras
FLOOR = -0.6 # piso de la animacion de rodado
def reuleaux(w, bulge=1, **kw):
"""Triangulo de Reuleaux: 3 arcos de radio w centrados en el vertice opuesto."""
R = w / math.sqrt(3)
V = [R * np.array([math.cos(a), math.sin(a), 0])
for a in (PI / 2, PI / 2 + TAU / 3, PI / 2 + 2 * TAU / 3)]
arcs = [ArcBetweenPoints(V[i], V[(i + 1) % 3], angle=bulge * PI / 3) for i in range(3)]
m = VMobject(**kw)
m.set_points(arcs[0].points)
for a in arcs[1:]:
m.append_points(a.points)
return m
class Reuleaux(TikTok):
NAME = "reuleaux"
def construct(self):
self.prepare()
chip = self.chip("Geometría de la calle", AMBAR)
with self.beat(0) as b:
tapa = VGroup(
Circle(radius=1.6, stroke_color="#7A879F", stroke_width=12,
fill_color="#1B2438", fill_opacity=1),
Circle(radius=1.25, stroke_color="#4A5878", stroke_width=5),
VGroup(*[Line(ORIGIN, RIGHT * 1.1, stroke_width=5, color="#4A5878")
.rotate(a, about_point=ORIGIN) for a in np.arange(0, TAU, TAU / 8)]),
).move_to(UP * 3.4)
q = self.fit(Text("¿por qué son redondas?", font=FONT, font_size=52,
weight=BOLD, color=WHITE), 8.0).move_to(UP * 0.7)
b.play(FadeIn(chip, shift=DOWN * 0.3), run_time=0.45)
b.play(FadeIn(tapa, scale=0.7), run_time=0.8)
b.play(Write(q), run_time=0.9)
with self.beat(1) as b:
ans = self.fit(Text("no se pueden caer adentro", font=FONT, font_size=46,
weight=BOLD, color=VERDE), 8.2).move_to(DOWN * 0.7)
b.play(FadeIn(ans, shift=UP * 0.15), run_time=0.7)
# ---- la cuadrada se cae ----
with self.beat(2) as b:
b.play(FadeOut(VGroup(tapa, q, ans)), run_time=0.4)
hole = Square(side_length=2.6, stroke_color="#4A5878", stroke_width=6,
fill_color="#05070D", fill_opacity=1).move_to(UP * 3.2)
cover = Square(side_length=2.5, stroke_color=ROSA, stroke_width=8,
fill_color="#2A1220", fill_opacity=1).move_to(UP * 3.2)
b.play(FadeIn(hole), FadeIn(cover), run_time=0.5)
b.play(Rotate(cover, PI / 4), run_time=0.7)
b.play(cover.animate.shift(DOWN * 2.3).scale(0.82).set_opacity(0.35),
run_time=0.9)
cae = Text("se cae", font=FONT, font_size=44, weight=BOLD, color=ROSA)
cae.move_to(UP * 0.35)
b.play(FadeIn(cae), run_time=0.4)
with self.beat(3) as b:
b.play(FadeOut(VGroup(cover, cae)), run_time=0.3)
lado = Line(hole.get_corner(DL), hole.get_corner(DR),
stroke_width=8, color=CELESTE).shift(DOWN * 0.35)
diag = Line(hole.get_corner(DL), hole.get_corner(UR), stroke_width=8, color=ROSA)
l1 = Text("lado", font=FONT, font_size=34, weight=BOLD,
color=CELESTE).next_to(lado, DOWN, buff=0.12)
l2 = Text("diagonal = 1,41 × lado", font=FONT, font_size=36, weight=BOLD,
color=ROSA).move_to(UP * 0.9)
self.fit(l2, 8.0)
b.play(Create(lado), FadeIn(l1), run_time=0.6)
b.play(Create(diag), run_time=0.6)
b.play(FadeIn(l2, shift=UP * 0.15), run_time=0.6)
# ---- el circulo mide igual en toda direccion ----
with self.beat(4) as b:
b.play(FadeOut(VGroup(hole, lado, diag, l1, l2)), run_time=0.4)
circ = Circle(radius=W / 2, stroke_color=CELESTE, stroke_width=9,
fill_color="#0E2233", fill_opacity=1).move_to(UP * 3.0)
tr = ValueTracker(0)
cal = always_redraw(lambda: DoubleArrow(
circ.get_center() + rotate_vector(RIGHT * W / 2, tr.get_value()),
circ.get_center() - rotate_vector(RIGHT * W / 2, tr.get_value()),
buff=0, color=AMBAR, stroke_width=7, tip_length=0.22))
b.play(FadeIn(circ, scale=0.8), run_time=0.5)
b.play(FadeIn(cal), run_time=0.3)
b.play(tr.animate.set_value(PI), run_time=max(1.0, b.floor - 1.1),
rate_func=linear)
same = Text("mide igual en toda dirección", font=FONT, font_size=38,
weight=BOLD, color=AMBAR).move_to(UP * 0.55)
self.fit(same, 8.2)
b.play(FadeIn(same), run_time=0.4)
with self.beat(5) as b:
no = self.fit(Text("y no es la única", font=FONT, font_size=50,
weight=BOLD, color=WHITE), 8.0).move_to(DOWN * 0.7)
b.play(FadeIn(no, shift=UP * 0.15), run_time=0.7)
# ---- aparece el Reuleaux ----
tri = reuleaux(W, stroke_color=VERDE, stroke_width=9,
fill_color="#0C2A22", fill_opacity=1).move_to(UP * 3.0)
with self.beat(6) as b:
b.play(FadeOut(VGroup(cal, same, no)), run_time=0.3)
b.play(Transform(circ, tri), run_time=1.2)
with self.beat(7) as b:
nom = self.fit(Text("TRIÁNGULO DE REULEAUX", font=FONT, font_size=46,
weight=BOLD, color=VERDE), 8.2).move_to(UP * 0.75)
b.play(Write(nom), run_time=1.0)
# ---- rueda entre dos paredes ----
with self.beat(8) as b:
b.play(FadeOut(VGroup(circ, nom)), run_time=0.4)
base = reuleaux(W, stroke_color=VERDE, stroke_width=9,
fill_color="#0C2A22", fill_opacity=1)
spin = ValueTracker(0)
def rodando():
s = base.copy().rotate(spin.get_value())
s.shift(UP * (FLOOR - s.get_bottom()[1]))
return s
rolling = always_redraw(rodando)
suelo = Line([-4.2, FLOOR, 0], [4.2, FLOOR, 0], stroke_width=7, color="#4A5878")
techo = Line([-4.2, FLOOR + W, 0], [4.2, FLOOR + W, 0],
stroke_width=7, color=AMBAR)
b.play(Create(suelo), Create(techo), run_time=0.5)
b.play(FadeIn(rolling), run_time=0.3)
b.play(spin.animate.set_value(TAU), run_time=max(1.4, b.floor - 0.8),
rate_func=linear)
with self.beat(9) as b:
carga = RoundedRectangle(corner_radius=0.12, width=3.4, height=0.55,
stroke_width=0, fill_color=AMBAR, fill_opacity=1)
carga.move_to([0, FLOOR + W + 0.32, 0])
nivel = self.fit(Text("la carga no sube ni baja", font=FONT, font_size=42,
weight=BOLD, color=AMBAR), 8.0).move_to(UP * 4.3)
b.play(FadeIn(carga, shift=DOWN * 0.15), FadeIn(nivel), run_time=0.6)
b.play(spin.animate.set_value(TAU * 2), run_time=max(1.2, b.floor - 0.7),
rate_func=linear)
with self.beat(10) as b:
b.play(FadeOut(VGroup(rolling, suelo, techo, carga, nivel)), run_time=0.5)
cta = VGroup(
self.fit(Text("ahora ya sabés", font=FONT, font_size=50,
weight=BOLD, color=WHITE), 8.0),
self.fit(Text("por qué son redondas", font=FONT, font_size=54,
weight=BOLD, color=AMBAR), 8.2),
).arrange(DOWN, buff=0.32).move_to(UP * 1.6)
b.play(FadeIn(cta[0], shift=UP * 0.15), run_time=0.5)
b.play(Write(cta[1]), run_time=0.9)
b.play(Circumscribe(cta[1], color=AMBAR, buff=0.28, stroke_width=7), run_time=0.9)
self.finish()
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