mirror of
https://github.com/3b1b/manim.git
synced 2025-09-19 04:41:56 +00:00
First draft of SecondProof
This commit is contained in:
Grant Sanderson
parent
cb0134ddb9
commit
d9a45a82e0
1 changed files with 229 additions and 39 deletions
|
|
@ -2474,8 +2474,9 @@ class NobodyLikesHomework(TeacherStudentsScene):
|
|||
class SecondProof(SpecialThreeDScene):
|
||||
CONFIG = {
|
||||
"sphere_config": {
|
||||
"resolution": (50, 50),
|
||||
}
|
||||
"resolution": (30, 30),
|
||||
},
|
||||
"n_random_subsets": 12,
|
||||
}
|
||||
|
||||
def construct(self):
|
||||
|
|
@ -2486,20 +2487,23 @@ class SecondProof(SpecialThreeDScene):
|
|||
self.cut_cross_section()
|
||||
self.show_theta()
|
||||
self.enumerate_rings()
|
||||
self.ask_about_ring_area()
|
||||
self.ask_about_ring_circumference()
|
||||
self.ask_about_shadow_area()
|
||||
self.ask_about_2_to_1_correspondance()
|
||||
self.show_all_shadow_rings()
|
||||
self.ask_about_global_correspondance()
|
||||
|
||||
def setup_shapes(self):
|
||||
sphere = self.get_sphere()
|
||||
u_values, v_values = sphere.get_u_values_and_v_values()
|
||||
rings = VGroup(*[VGroup() for u in u_values])
|
||||
for piece in sphere:
|
||||
rings[piece.u_index].add(piece)
|
||||
sphere.set_stroke(WHITE, width=0.25)
|
||||
self.add(sphere)
|
||||
self.sphere = sphere
|
||||
|
||||
u_values, v_values = sphere.get_u_values_and_v_values()
|
||||
rings = VGroup(*[VGroup() for u in u_values])
|
||||
for piece in sphere:
|
||||
rings[piece.u_index].add(piece.copy())
|
||||
self.set_ring_colors(rings)
|
||||
self.rings = rings
|
||||
|
||||
self.axes = self.get_axes()
|
||||
|
|
@ -2511,17 +2515,18 @@ class SecondProof(SpecialThreeDScene):
|
|||
def divide_into_rings(self):
|
||||
rings = self.rings
|
||||
|
||||
self.play(ApplyFunction(self.set_ring_colors, rings))
|
||||
self.play(FadeIn(rings), FadeOut(self.sphere))
|
||||
self.play(
|
||||
rings.space_out_submobjects, 1.5,
|
||||
rate_func=there_and_back_with_pause,
|
||||
run_time=3
|
||||
)
|
||||
self.wait(2)
|
||||
rings.save_state()
|
||||
|
||||
def show_shadows(self):
|
||||
rings = self.rings
|
||||
north_rings = self.get_northern_hemisphere(rings)
|
||||
north_rings = rings[:len(rings) // 2]
|
||||
ghost_rings = rings.copy()
|
||||
ghost_rings.set_fill(opacity=0.0)
|
||||
ghost_rings.set_stroke(opacity=0.2)
|
||||
|
|
@ -2572,9 +2577,11 @@ class SecondProof(SpecialThreeDScene):
|
|||
def correspond_to_every_other_ring(self):
|
||||
rings = self.rings
|
||||
shadows = self.shadows
|
||||
shadows.submobjects.reverse()
|
||||
|
||||
every_other_ring = rings[1::2]
|
||||
every_other_ring.set_fill(opacity=0.5)
|
||||
# every_other_ring.set_fill(opacity=0.5)
|
||||
every_other_ring.set_stroke(width=0)
|
||||
self.move_camera(
|
||||
phi=70 * DEGREES,
|
||||
theta=-135 * DEGREES,
|
||||
|
|
@ -2584,8 +2591,12 @@ class SecondProof(SpecialThreeDScene):
|
|||
],
|
||||
run_time=2,
|
||||
)
|
||||
shadows_copy = shadows.copy()
|
||||
shadows.fade(1)
|
||||
self.play(
|
||||
TransformFromCopy(shadows, every_other_ring),
|
||||
ReplacementTransform(
|
||||
shadows_copy, every_other_ring
|
||||
),
|
||||
run_time=2,
|
||||
)
|
||||
self.wait(5)
|
||||
|
|
@ -2600,11 +2611,13 @@ class SecondProof(SpecialThreeDScene):
|
|||
|
||||
back_half = self.get_hemisphere(rings, UP)
|
||||
front_half = self.get_hemisphere(rings, DOWN)
|
||||
front_half_ghost = front_half.copy()
|
||||
|
||||
# shaded_back_half = back_half.copy()
|
||||
# for piece in shaded_back_half:
|
||||
# piece.points = np.array(list(reversed(piece.points)))
|
||||
# shaded_back_half.scale(0.99)
|
||||
# for piece in shaded_back_half.family_members_with_points():
|
||||
# piece.points = piece.points[::-1]
|
||||
# shaded_back_half.scale(0.999)
|
||||
# shaded_back_half.set_fill(opacity=0.5)
|
||||
|
||||
radius = self.sphere_config["radius"]
|
||||
circle = Circle(radius=radius)
|
||||
|
|
@ -2620,14 +2633,21 @@ class SecondProof(SpecialThreeDScene):
|
|||
FadeOut(ghost_rings),
|
||||
)
|
||||
self.remove(every_other_ring_copy)
|
||||
# self.add(shaded_back_half)
|
||||
self.play(
|
||||
FadeIn(circle),
|
||||
FadeOutAndShift(front_half, IN)
|
||||
# FadeOutAndShift(front_half, IN)
|
||||
FadeOut(front_half),
|
||||
front_half_ghost.set_fill, None, 0.2,
|
||||
front_half_ghost.set_stroke, WHITE, 1, 0.0,
|
||||
)
|
||||
self.wait()
|
||||
|
||||
self.back_half = back_half
|
||||
self.circle = circle
|
||||
self.set_variables_as_attrs(
|
||||
back_half, front_half,
|
||||
front_half_ghost,
|
||||
slice_circle=circle
|
||||
)
|
||||
|
||||
def show_theta(self):
|
||||
theta_tracker = ValueTracker(0)
|
||||
|
|
@ -2657,10 +2677,12 @@ class SecondProof(SpecialThreeDScene):
|
|||
self.move_camera(theta=-60 * DEGREES)
|
||||
|
||||
self.add(theta_group, lit_ring)
|
||||
angle = PI * 8 / 50
|
||||
for angle in [angle, 0, PI, angle]:
|
||||
n_rings = len(self.rings) - 1
|
||||
lit_ring_index = int((30 / 180) * n_rings)
|
||||
angle = PI * lit_ring_index / n_rings
|
||||
for alpha in [angle, 0, PI, angle]:
|
||||
self.play(
|
||||
theta_tracker.set_value, angle,
|
||||
theta_tracker.set_value, alpha,
|
||||
theta_mob_opacity_tracker.set_value, 1,
|
||||
Animation(self.camera.phi_tracker),
|
||||
run_time=2,
|
||||
|
|
@ -2718,37 +2740,199 @@ class SecondProof(SpecialThreeDScene):
|
|||
theta=-70 * DEGREES,
|
||||
)
|
||||
|
||||
self.theta_tracker = theta_tracker
|
||||
self.lit_ring = lit_ring
|
||||
self.theta_group = theta_group
|
||||
self.set_variables_as_attrs(
|
||||
theta_tracker, lit_ring, theta_group,
|
||||
brace, brace_label, d_theta,
|
||||
alt_R_line, theta_mob_opacity_tracker,
|
||||
)
|
||||
|
||||
def enumerate_rings(self):
|
||||
pass # Skip, for now...
|
||||
|
||||
def ask_about_ring_area(self):
|
||||
pass
|
||||
def ask_about_ring_circumference(self):
|
||||
theta = self.theta_tracker.get_value()
|
||||
radius = self.sphere_config["radius"]
|
||||
circle = Circle(
|
||||
radius=radius * np.sin(theta)
|
||||
)
|
||||
circle.shift(radius * np.cos(theta) * OUT)
|
||||
circle.set_stroke(Color("red"), 5)
|
||||
|
||||
to_fade = VGroup(
|
||||
self.R_label, self.radial_line,
|
||||
self.brace, self.brace_label
|
||||
)
|
||||
|
||||
self.move_camera(
|
||||
phi=0 * DEGREES,
|
||||
theta=-90 * DEGREES,
|
||||
added_anims=[FadeOut(to_fade)]
|
||||
)
|
||||
self.play(ShowCreation(circle))
|
||||
self.wait()
|
||||
self.move_camera(
|
||||
phi=70 * DEGREES,
|
||||
theta=-70 * DEGREES,
|
||||
added_anims=[
|
||||
FadeIn(to_fade),
|
||||
FadeOut(circle),
|
||||
]
|
||||
)
|
||||
self.wait()
|
||||
|
||||
def ask_about_shadow_area(self):
|
||||
pass
|
||||
lit_ring = self.lit_ring
|
||||
lit_ring_copy = lit_ring.copy()
|
||||
lit_ring_copy.clear_updaters()
|
||||
|
||||
all_shadows = self.shadows
|
||||
all_shadows.set_fill(BLUE_E, 0.5)
|
||||
for piece in all_shadows.family_members_with_points():
|
||||
piece.set_stroke(width=0)
|
||||
|
||||
radius = self.sphere_config["radius"]
|
||||
shadow = self.get_shadow(lit_ring)
|
||||
theta = self.theta_tracker.get_value()
|
||||
d_theta = self.d_theta
|
||||
|
||||
def get_dashed_line(angle):
|
||||
p0 = np.cos(angle) * OUT + np.sin(angle) * RIGHT
|
||||
p0 *= radius
|
||||
p1 = np.array([*p0[:2], 0])
|
||||
result = DashedLine(p0, p1)
|
||||
result.set_stroke(WHITE, 1)
|
||||
result.add_to_back(
|
||||
result.copy().set_stroke(BLACK, 2)
|
||||
)
|
||||
result.set_shade_in_3d(True)
|
||||
return result
|
||||
|
||||
dashed_lines = VGroup(*[
|
||||
get_dashed_line(t)
|
||||
for t in [theta, theta + d_theta]
|
||||
])
|
||||
|
||||
self.play(
|
||||
ReplacementTransform(lit_ring_copy, shadow),
|
||||
FadeOut(self.R_label),
|
||||
FadeOut(self.radial_line),
|
||||
Animation(self.camera.phi_tracker),
|
||||
*map(ShowCreation, dashed_lines),
|
||||
run_time=2,
|
||||
)
|
||||
self.wait(2)
|
||||
|
||||
self.set_variables_as_attrs(
|
||||
dashed_lines,
|
||||
lit_shadow=shadow,
|
||||
)
|
||||
|
||||
def ask_about_2_to_1_correspondance(self):
|
||||
pass
|
||||
theta_tracker = ValueTracker(0)
|
||||
get_theta = theta_tracker.get_value
|
||||
new_lit_ring = updating_mobject_from_func(
|
||||
lambda: self.get_ring_from_theta(
|
||||
self.rings, get_theta()
|
||||
).copy().set_color(PINK)
|
||||
)
|
||||
|
||||
self.add(new_lit_ring)
|
||||
for angle in [PI, 0, PI]:
|
||||
self.play(
|
||||
theta_tracker.set_value, angle,
|
||||
Animation(self.camera.phi_tracker),
|
||||
run_time=3
|
||||
)
|
||||
self.remove(new_lit_ring)
|
||||
self.remove(theta_tracker)
|
||||
|
||||
def show_all_shadow_rings(self):
|
||||
lit_ring_copy = self.lit_ring.copy()
|
||||
lit_ring_copy.clear_updaters()
|
||||
self.remove(self.lit_ring)
|
||||
theta_group_copy = self.theta_group.copy()
|
||||
theta_group_copy.clear_updaters()
|
||||
self.remove(self.theta_group, *self.theta_group)
|
||||
to_fade = VGroup(
|
||||
theta_group_copy, self.alt_R_line,
|
||||
self.brace, self.brace_label,
|
||||
lit_ring_copy, self.lit_shadow,
|
||||
self.slice_circle,
|
||||
self.dashed_lines,
|
||||
)
|
||||
|
||||
R_label = self.R_label
|
||||
radial_line = self.radial_line
|
||||
R_label.rotate(
|
||||
-90 * DEGREES,
|
||||
axis=RIGHT, about_point=radial_line.get_center()
|
||||
)
|
||||
shadows = self.shadows
|
||||
shadows.set_fill(opacity=1)
|
||||
self.set_ring_colors(shadows, [GREEN_E, GREEN_D])
|
||||
|
||||
self.play(
|
||||
FadeOut(to_fade),
|
||||
LaggedStart(FadeIn, shadows),
|
||||
self.theta_mob_opacity_tracker.set_value, 0,
|
||||
ApplyMethod(
|
||||
self.camera.phi_tracker.set_value, 60 * DEGREES,
|
||||
run_time=2,
|
||||
),
|
||||
ApplyMethod(
|
||||
self.camera.theta_tracker.set_value, -130 * DEGREES,
|
||||
run_time=2,
|
||||
),
|
||||
)
|
||||
self.play(
|
||||
ShowCreation(radial_line),
|
||||
FadeIn(R_label),
|
||||
Animation(self.camera.phi_tracker),
|
||||
)
|
||||
self.begin_ambient_camera_rotation()
|
||||
self.wait()
|
||||
|
||||
rings = self.rings
|
||||
rings_copy = rings.saved_state.copy()
|
||||
self.play(
|
||||
FadeOut(R_label),
|
||||
FadeOut(radial_line),
|
||||
FadeIn(rings_copy)
|
||||
)
|
||||
self.remove(rings_copy)
|
||||
rings.restore()
|
||||
self.add(rings)
|
||||
|
||||
def ask_about_global_correspondance(self):
|
||||
pass
|
||||
rings = self.rings
|
||||
subset_size = len(rings) // 2
|
||||
|
||||
def get_highlighted_subset():
|
||||
subset = random.sample(list(rings), subset_size)
|
||||
result = VGroup(*subset).copy()
|
||||
result.set_color(PINK)
|
||||
return result
|
||||
|
||||
for x in range(self.n_random_subsets):
|
||||
subset = get_highlighted_subset()
|
||||
self.add(subset)
|
||||
self.wait(0.5)
|
||||
self.remove(subset)
|
||||
|
||||
#
|
||||
def set_ring_colors(self, rings, colors=[BLUE_E, BLUE_D]):
|
||||
for i, ring in enumerate(rings):
|
||||
color = colors[i % len(colors)]
|
||||
ring.set_fill(color)
|
||||
# for piece in ring[::2]:
|
||||
# piece.set_color(BLUE_E)
|
||||
# piece.points = np.array([
|
||||
# *piece.points[3:-1],
|
||||
# *piece.points[:3],
|
||||
# piece.points[3]
|
||||
# ])
|
||||
ring.set_stroke(color, width=0.25)
|
||||
for piece in ring:
|
||||
piece.insert_n_anchor_points(4)
|
||||
piece.on_sphere = True
|
||||
piece.points = np.array([
|
||||
*piece.points[3:-1],
|
||||
*piece.points[:3],
|
||||
piece.points[3]
|
||||
])
|
||||
return rings
|
||||
|
||||
def get_shadow(self, mobject):
|
||||
|
|
@ -2789,10 +2973,8 @@ class SecondProof(SpecialThreeDScene):
|
|||
theta_mob = TexMobject("\\theta")
|
||||
theta_mob.rotate(90 * DEGREES, RIGHT)
|
||||
vect = np.cos(theta / 2) * OUT + np.sin(theta / 2) * RIGHT
|
||||
theta_mob.next_to(
|
||||
arc.radius * normalize(vect),
|
||||
vect,
|
||||
buff=SMALL_BUFF
|
||||
theta_mob.move_to(
|
||||
(arc.radius + 0.25) * normalize(vect),
|
||||
)
|
||||
theta_mob.set_background_stroke(width=1)
|
||||
|
||||
|
|
@ -2811,6 +2993,14 @@ class SecondProof(SpecialThreeDScene):
|
|||
return rings[index]
|
||||
|
||||
|
||||
class SecondProofHigherRes(SecondProof):
|
||||
CONFIG = {
|
||||
"sphere_config": {
|
||||
"resolution": (60, 60),
|
||||
},
|
||||
}
|
||||
|
||||
|
||||
class RangeFrom0To180(Scene):
|
||||
def construct(self):
|
||||
angle = Integer(0, unit="^\\circ")
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue