mirror of
https://github.com/3b1b/manim.git
synced 2025-08-01 17:29:06 +08:00
Setup for borsuk_addition animations
This commit is contained in:
Grant Sanderson
246
active_projects/borsuk_addition.py
Normal file
246
active_projects/borsuk_addition.py
Normal file
@ -0,0 +1,246 @@
|
||||
from big_ol_pile_of_manim_imports import *
|
||||
from old_projects.lost_lecture import GeometryProofLand
|
||||
from old_projects.quaternions import SpecialThreeDScene
|
||||
|
||||
|
||||
class TopologyWordBreak(Scene):
|
||||
def construct(self):
|
||||
word = TextMobject("Topology")
|
||||
word.scale(2)
|
||||
colors = [BLUE, YELLOW, RED]
|
||||
classes = VGroup(*[VGroup() for x in range(3)])
|
||||
for letter in word:
|
||||
genus = len(letter.submobjects)
|
||||
letter.target_color = colors[genus]
|
||||
letter.generate_target()
|
||||
letter.target.set_color(colors[genus])
|
||||
classes[genus].add(letter.target)
|
||||
signs = VGroup()
|
||||
for group in classes:
|
||||
new_group = VGroup()
|
||||
for elem in group[:-1]:
|
||||
new_group.add(elem)
|
||||
sign = TexMobject("\\simeq")
|
||||
new_group.add(sign)
|
||||
signs.add(sign)
|
||||
new_group.add(group[-1])
|
||||
group.submobjects = list(new_group.submobjects)
|
||||
group.arrange_submobjects(RIGHT)
|
||||
|
||||
word[2].target.shift(0.1 * DOWN)
|
||||
word[7].target.shift(0.1 * DOWN)
|
||||
|
||||
classes.arrange_submobjects(DOWN, buff=LARGE_BUFF, aligned_edge=LEFT)
|
||||
classes.shift(2 * RIGHT)
|
||||
|
||||
genus_labels = VGroup(*[
|
||||
TextMobject("Genus %d:" % d).scale(1.5).next_to(
|
||||
classes[d], LEFT, MED_LARGE_BUFF
|
||||
)
|
||||
for d in range(3)
|
||||
])
|
||||
genus_labels.shift(SMALL_BUFF * UP)
|
||||
|
||||
self.play(Write(word))
|
||||
self.play(LaggedStart(
|
||||
ApplyMethod, word,
|
||||
lambda m: (m.set_color, m.target_color),
|
||||
run_time=1
|
||||
))
|
||||
self.play(
|
||||
LaggedStart(MoveToTarget, word),
|
||||
LaggedStart(FadeIn, signs),
|
||||
LaggedStart(FadeInFromDown, genus_labels),
|
||||
)
|
||||
self.wait(3)
|
||||
|
||||
|
||||
class TopologyProofLand(GeometryProofLand):
|
||||
CONFIG = {
|
||||
"text": "Topology proof land"
|
||||
}
|
||||
|
||||
|
||||
class GreenLine(Scene):
|
||||
def construct(self):
|
||||
self.add(Line(LEFT, RIGHT, color=GREEN))
|
||||
|
||||
|
||||
class Thief(Scene):
|
||||
def construct(self):
|
||||
self.play(Write(TextMobject("Thief")))
|
||||
self.wait()
|
||||
|
||||
|
||||
class FunctionGInSymbols(Scene):
|
||||
def construct(self):
|
||||
p_tex = "\\vec{\\textbf{p}}"
|
||||
f_of_p = TexMobject("f", "(", p_tex, ")",)
|
||||
f_of_p.shift(2.5 * LEFT + 2.5 * UP)
|
||||
f_of_neg_p = TexMobject("f", "(", "-", p_tex, ")")
|
||||
g_of_p = TexMobject("g", "(", p_tex, ")")
|
||||
g_of_p[0].set_color(YELLOW)
|
||||
for mob in f_of_p, f_of_neg_p, g_of_p:
|
||||
mob.set_color_by_tex(p_tex, BLUE)
|
||||
dec_rhs = DecimalMatrix([[2.71], [8.28]])
|
||||
dec_rhs.next_to(f_of_p, RIGHT)
|
||||
minus = TexMobject("-")
|
||||
equals = TexMobject("=")
|
||||
equals.next_to(f_of_p, RIGHT)
|
||||
zero_zero = IntegerMatrix([[0], [0]])
|
||||
|
||||
for matrix in dec_rhs, zero_zero:
|
||||
matrix.space_out_submobjects(0.8)
|
||||
matrix.brackets.scale(0.8)
|
||||
matrix.next_to(equals, RIGHT)
|
||||
|
||||
f_of_neg_p.next_to(equals, RIGHT)
|
||||
|
||||
f = f_of_p.get_part_by_tex("f")
|
||||
p = f_of_p.get_part_by_tex(p_tex)
|
||||
f_brace = Brace(f, UP, buff=SMALL_BUFF)
|
||||
f_brace.add(f_brace.get_text("Continuous function"))
|
||||
p_brace = Brace(p, DOWN, buff=SMALL_BUFF)
|
||||
p_brace.add(p_brace.get_text("Sphere point").match_color(p))
|
||||
|
||||
f_of_p.save_state()
|
||||
f_of_p.space_out_submobjects(2)
|
||||
f_of_p.scale(2)
|
||||
f_of_p.fade(1)
|
||||
|
||||
self.play(f_of_p.restore)
|
||||
self.play(GrowFromCenter(f_brace))
|
||||
self.wait()
|
||||
self.play(GrowFromCenter(p_brace))
|
||||
self.wait()
|
||||
self.play(
|
||||
FadeInFromDown(equals),
|
||||
Write(dec_rhs),
|
||||
FadeOut(f_brace),
|
||||
FadeOut(p_brace),
|
||||
)
|
||||
self.wait(2)
|
||||
self.play(WiggleOutThenIn(f))
|
||||
self.wait()
|
||||
self.play(
|
||||
FadeOutAndShift(dec_rhs, DOWN),
|
||||
FadeInFromDown(f_of_neg_p)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
# Rearrange
|
||||
f_of_neg_p.generate_target()
|
||||
f_of_p.generate_target()
|
||||
group = VGroup(f_of_p.target, minus, f_of_neg_p.target)
|
||||
group.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
|
||||
group.next_to(equals, LEFT)
|
||||
|
||||
self.play(
|
||||
MoveToTarget(f_of_p, path_arc=PI),
|
||||
MoveToTarget(f_of_neg_p, path_arc=-PI),
|
||||
FadeInFromLarge(minus),
|
||||
FadeInFrom(zero_zero, LEFT)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
# Define g
|
||||
def_eq = TexMobject(":=")
|
||||
def_eq.next_to(f_of_p, LEFT)
|
||||
g_of_p.next_to(def_eq, LEFT)
|
||||
rect = SurroundingRectangle(VGroup(g_of_p, f_of_neg_p))
|
||||
rect.set_stroke(width=1)
|
||||
|
||||
self.play(
|
||||
FadeInFromLarge(g_of_p),
|
||||
FadeInFrom(def_eq, LEFT)
|
||||
)
|
||||
self.play(ShowCreation(rect))
|
||||
self.wait()
|
||||
self.play(FadeOut(rect))
|
||||
|
||||
# Show g is odd
|
||||
g_of_neg_p = TexMobject("g", "(", "-", p_tex, ")")
|
||||
eq2 = TexMobject("=")
|
||||
rhs = TexMobject(
|
||||
"f", "(", "-", p_tex, ")", "-",
|
||||
"f", "(", p_tex, ")", "=",
|
||||
"-", "g", "(", p_tex, ")",
|
||||
)
|
||||
for mob in g_of_neg_p, rhs:
|
||||
mob.set_color_by_tex(p_tex, BLUE)
|
||||
mob.set_color_by_tex("g", YELLOW)
|
||||
g_of_neg_p.next_to(g_of_p, DOWN, aligned_edge=LEFT, buff=LARGE_BUFF)
|
||||
eq2.next_to(g_of_neg_p, RIGHT, SMALL_BUFF)
|
||||
rhs.next_to(eq2, RIGHT, SMALL_BUFF)
|
||||
neg_g_of_p = rhs[-5:]
|
||||
neg_g_of_p.save_state()
|
||||
neg_g_of_p.next_to(eq2, RIGHT, SMALL_BUFF)
|
||||
|
||||
self.play(
|
||||
FadeIn(g_of_neg_p),
|
||||
FadeIn(eq2),
|
||||
FadeIn(neg_g_of_p),
|
||||
)
|
||||
self.wait()
|
||||
self.play(CircleThenFadeAround(g_of_neg_p[2:4]))
|
||||
self.wait()
|
||||
self.play(CircleThenFadeAround(neg_g_of_p))
|
||||
self.wait()
|
||||
self.play(neg_g_of_p.restore)
|
||||
rects = VGroup(*map(SurroundingRectangle, [f_of_p, f_of_neg_p]))
|
||||
self.play(LaggedStart(
|
||||
ShowCreationThenDestruction, rects,
|
||||
lag_ratio=0.8
|
||||
))
|
||||
self.play(
|
||||
TransformFromCopy(f_of_p, rhs[6:10]),
|
||||
TransformFromCopy(f_of_neg_p, rhs[:5]),
|
||||
FadeIn(rhs[5]),
|
||||
FadeIn(rhs[-6]),
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
class FunctionGInputSpace(SpecialThreeDScene):
|
||||
def setup(self):
|
||||
# axes = ThreeDAxes()
|
||||
# sphere = Sphere(resolution=(24, 48))
|
||||
sphere = self.get_sphere()
|
||||
sphere.scale(2)
|
||||
|
||||
sphere.set_fill(BLUE_E, opacity=0.5)
|
||||
|
||||
self.set_camera_orientation(
|
||||
phi=70 * DEGREES,
|
||||
theta=-120 * DEGREES,
|
||||
)
|
||||
self.begin_ambient_camera_rotation(rate=0.02)
|
||||
# self.add(axes)
|
||||
self.add(sphere)
|
||||
|
||||
self.sphere = sphere
|
||||
|
||||
def construct(self):
|
||||
self.show_input_dot()
|
||||
self.show_antipodal_point()
|
||||
self.show_equator()
|
||||
self.deform_towards_north_pole()
|
||||
|
||||
def show_input_dot(self):
|
||||
self.play(Write(sphere))
|
||||
|
||||
def show_antipodal_point(self):
|
||||
pass
|
||||
|
||||
def show_equator(self):
|
||||
pass
|
||||
|
||||
def deform_towards_north_pole(self):
|
||||
pass
|
||||
|
||||
#
|
||||
def func(self, point):
|
||||
pass
|
||||
|
||||
def draw_path(self, path):
|
||||
pass
|
||||
@ -1459,6 +1459,7 @@ class GeometryProofLand(Scene):
|
||||
PINK, RED, YELLOW, GREEN, GREEN_A, BLUE,
|
||||
MAROON_E, MAROON_B, YELLOW, BLUE,
|
||||
],
|
||||
"text": "Geometry proof land",
|
||||
}
|
||||
|
||||
def construct(self):
|
||||
@ -1469,6 +1470,7 @@ class GeometryProofLand(Scene):
|
||||
colors = list(self.colors)
|
||||
random.shuffle(colors)
|
||||
word_outlines.set_color_by_gradient(*colors)
|
||||
word_outlines.set_stroke(width=5)
|
||||
|
||||
circles = VGroup()
|
||||
for letter in word:
|
||||
@ -1485,14 +1487,16 @@ class GeometryProofLand(Scene):
|
||||
LaggedStart(MoveToTarget, circles),
|
||||
run_time=2
|
||||
)
|
||||
self.add(word_outlines, circles)
|
||||
self.play(LaggedStart(
|
||||
ShowCreationThenDestruction, word_outlines,
|
||||
run_time=4
|
||||
))
|
||||
FadeIn, word_outlines,
|
||||
run_time=3,
|
||||
rate_func=there_and_back,
|
||||
), Animation(circles))
|
||||
self.wait()
|
||||
|
||||
def get_geometry_proof_land_word(self):
|
||||
word = TextMobject("Geometry proof land")
|
||||
word = TextMobject(self.text)
|
||||
word.rotate(-90 * DEGREES)
|
||||
word.scale(0.25)
|
||||
word.shift(3 * RIGHT)
|
||||
@ -1502,6 +1506,7 @@ class GeometryProofLand(Scene):
|
||||
word.center()
|
||||
word.to_edge(UP)
|
||||
word.set_color_by_gradient(*self.colors)
|
||||
word.set_background_stroke(width=0)
|
||||
return word
|
||||
|
||||
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
from big_ol_pile_of_manim_imports import *
|
||||
from active_projects.quaternions import *
|
||||
from old_projects.quaternions import *
|
||||
|
||||
W_COLOR = YELLOW
|
||||
I_COLOR = GREEN
|
||||
Reference in New Issue
Block a user