1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
|
# -*- 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 # constant width of the shapes
FLOOR = -0.6 # floor of the rolling animation
def reuleaux(w, bulge=1, **kw):
"""Reuleaux triangle: 3 arcs of radius w centred on the opposite vertex."""
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", AMBER)
with self.beat(0) as b:
lid = 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(lid, 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=C_GREEN), 8.2).move_to(DOWN * 0.7)
b.play(FadeIn(ans, shift=UP * 0.15), run_time=0.7)
# ---- the square one falls in ---
with self.beat(2) as b:
b.play(FadeOut(VGroup(lid, 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=C_PINK, 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)
falls = Text("se cae", font=FONT, font_size=44, weight=BOLD, color=C_PINK)
falls.move_to(UP * 0.35)
b.play(FadeIn(falls), run_time=0.4)
with self.beat(3) as b:
b.play(FadeOut(VGroup(cover, falls)), run_time=0.3)
side = Line(hole.get_corner(DL), hole.get_corner(DR),
stroke_width=8, color=C_SKY).shift(DOWN * 0.35)
diag = Line(hole.get_corner(DL), hole.get_corner(UR), stroke_width=8, color=C_PINK)
l1 = Text("lado", font=FONT, font_size=34, weight=BOLD,
color=C_SKY).next_to(side, DOWN, buff=0.12)
l2 = Text("diagonal = 1,41 × lado", font=FONT, font_size=36, weight=BOLD,
color=C_PINK).move_to(UP * 0.9)
self.fit(l2, 8.0)
b.play(Create(side), 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)
# ---- the circle measures the same in every direction ---
with self.beat(4) as b:
b.play(FadeOut(VGroup(hole, side, diag, l1, l2)), run_time=0.4)
circ = Circle(radius=W / 2, stroke_color=C_SKY, stroke_width=9,
fill_color="#0E2233", fill_opacity=1).move_to(UP * 3.0)
tr = ValueTracker(0)
caliper = 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=AMBER, stroke_width=7, tip_length=0.22))
b.play(FadeIn(circ, scale=0.8), run_time=0.5)
b.play(FadeIn(caliper), 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=AMBER).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)
# ---- the Reuleaux appears ---
tri = reuleaux(W, stroke_color=C_GREEN, stroke_width=9,
fill_color="#0C2A22", fill_opacity=1).move_to(UP * 3.0)
with self.beat(6) as b:
b.play(FadeOut(VGroup(caliper, same, no)), run_time=0.3)
b.play(Transform(circ, tri), run_time=1.2)
with self.beat(7) as b:
nm_key = self.fit(Text("TRIÁNGULO DE REULEAUX", font=FONT, font_size=46,
weight=BOLD, color=C_GREEN), 8.2).move_to(UP * 0.75)
b.play(Write(nm_key), run_time=1.0)
# ---- it rolls between two walls ---
with self.beat(8) as b:
b.play(FadeOut(VGroup(circ, nm_key)), run_time=0.4)
base = reuleaux(W, stroke_color=C_GREEN, stroke_width=9,
fill_color="#0C2A22", fill_opacity=1)
spin = ValueTracker(0)
def rolling_t():
s = base.copy().rotate(spin.get_value())
s.shift(UP * (FLOOR - s.get_bottom()[1]))
return s
rolling = always_redraw(rolling_t)
ground = Line([-4.2, FLOOR, 0], [4.2, FLOOR, 0], stroke_width=7, color="#4A5878")
ceiling = Line([-4.2, FLOOR + W, 0], [4.2, FLOOR + W, 0],
stroke_width=7, color=AMBER)
b.play(Create(ground), Create(ceiling), 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:
load_amt = RoundedRectangle(corner_radius=0.12, width=3.4, height=0.55,
stroke_width=0, fill_color=AMBER, fill_opacity=1)
load_amt.move_to([0, FLOOR + W + 0.32, 0])
level = self.fit(Text("la carga no sube ni baja", font=FONT, font_size=42,
weight=BOLD, color=AMBER), 8.0).move_to(UP * 4.3)
b.play(FadeIn(load_amt, shift=DOWN * 0.15), FadeIn(level), 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, ground, ceiling, load_amt, level)), run_time=0.5)
count_txt = 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=AMBER), 8.2),
).arrange(DOWN, buff=0.32).move_to(UP * 1.6)
b.play(FadeIn(count_txt[0], shift=UP * 0.15), run_time=0.5)
b.play(Write(count_txt[1]), run_time=0.9)
b.play(Circumscribe(count_txt[1], color=AMBER, buff=0.28, stroke_width=7), run_time=0.9)
self.finish()
|
