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highD.py
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from manimlib.imports import *
##########
#force_skipping
#revert_to_original_skipping_status
##########
class Slider(NumberLine):
CONFIG = {
"color" : WHITE,
"x_min" : -1,
"x_max" : 1,
"unit_size" : 2,
"center_value" : 0,
"number_scale_val" : 0.75,
"label_scale_val" : 1,
"numbers_with_elongated_ticks" : [],
"line_to_number_vect" : LEFT,
"line_to_number_buff" : MED_LARGE_BUFF,
"dial_radius" : 0.1,
"dial_color" : YELLOW,
"include_real_estate_ticks" : True,
}
def __init__(self, **kwargs):
NumberLine.__init__(self, **kwargs)
self.rotate(np.pi/2)
self.init_dial()
if self.include_real_estate_ticks:
self.add_real_estate_ticks()
def init_dial(self):
dial = Dot(
radius = self.dial_radius,
color = self.dial_color,
)
dial.move_to(self.number_to_point(self.center_value))
re_dial = dial.copy()
re_dial.set_fill(opacity = 0)
self.add(dial, re_dial)
self.dial = dial
self.re_dial = re_dial
self.last_sign = -1
def add_label(self, tex):
label = TexMobject(tex)
label.scale(self.label_scale_val)
label.move_to(self.get_top())
label.shift(MED_LARGE_BUFF*UP)
self.add(label)
self.label = label
def add_real_estate_ticks(
self,
re_per_tick = 0.05,
colors = [BLUE, RED],
max_real_estate = 1,
):
self.real_estate_ticks = VGroup(*[
self.get_tick(self.center_value + u*np.sqrt(x + re_per_tick))
for x in np.arange(0, max_real_estate, re_per_tick)
for u in [-1, 1]
])
self.real_estate_ticks.set_stroke(width = 3)
self.real_estate_ticks.set_color_by_gradient(*colors)
self.add(self.real_estate_ticks)
self.add(self.dial)
return self.real_estate_ticks
def set_value(self, x):
re = (x - self.center_value)**2
for dial, val in (self.dial, x), (self.re_dial, re):
dial.move_to(self.number_to_point(val))
return self
def set_center_value(self, x):
self.center_value = x
return self
def change_real_estate(self, d_re):
left_over = 0
curr_re = self.get_real_estate()
if d_re < -curr_re:
left_over = d_re + curr_re
d_re = -curr_re
self.set_real_estate(curr_re + d_re)
return left_over
def set_real_estate(self, target_re):
if target_re < 0:
raise Exception("Cannot set real estate below 0")
self.re_dial.move_to(self.number_to_point(target_re))
self.update_dial_by_re_dial()
return self
def get_dial_supplement_animation(self):
return UpdateFromFunc(self.dial, self.update_dial_by_re_dial)
def update_dial_by_re_dial(self, dial = None):
dial = dial or self.dial
re = self.get_real_estate()
sign = np.sign(self.get_value() - self.center_value)
if sign == 0:
sign = -self.last_sign
self.last_sign *= -1
dial.move_to(self.number_to_point(
self.center_value + sign*np.sqrt(abs(re))
))
return dial
def get_value(self):
return self.point_to_number(self.dial.get_center())
def get_real_estate(self):
return self.point_to_number(self.re_dial.get_center())
def copy(self):
return self.deepcopy()
class SliderScene(Scene):
CONFIG = {
"n_sliders" : 4,
"slider_spacing" : MED_LARGE_BUFF,
"slider_config" : {},
"center_point" : None,
"total_real_estate" : 1,
"ambiently_change_sliders" : False,
"ambient_velocity_magnitude" : 1.0,
"ambient_acceleration_magnitude" : 1.0,
"ambient_jerk_magnitude" : 1.0/2,
}
def setup(self):
if self.center_point is None:
self.center_point = np.zeros(self.n_sliders)
sliders = VGroup(*[
Slider(center_value = cv, **self.slider_config)
for cv in self.center_point
])
sliders.arrange(RIGHT, buff = self.slider_spacing)
sliders[0].add_numbers()
sliders[0].set_value(
self.center_point[0] + np.sqrt(self.total_real_estate)
)
self.sliders = sliders
self.add_labels_to_sliders()
self.add(sliders)
def add_labels_to_sliders(self):
if len(self.sliders) <= 4:
for slider, char in zip(self.sliders, "xyzw"):
slider.add_label(char)
for slider in self.sliders[1:]:
slider.label.align_to(self.sliders[0].label, UP)
else:
for i, slider in enumerate(self.sliders):
slider.add_label("x_{%d}"%(i+1))
return self
def reset_dials(self, values, run_time = 1, **kwargs):
target_vector = self.get_target_vect_from_subset_of_values(values, **kwargs)
radius = np.sqrt(self.total_real_estate)
def update_sliders(sliders):
curr_vect = self.get_vector()
curr_vect -= self.center_point
curr_vect *= radius/get_norm(curr_vect)
curr_vect += self.center_point
self.set_to_vector(curr_vect)
return sliders
self.play(*[
ApplyMethod(slider.set_value, value)
for value, slider in zip(target_vector, self.sliders)
] + [
UpdateFromFunc(self.sliders, update_sliders)
], run_time = run_time)
def get_target_vect_from_subset_of_values(self, values, fixed_indices = None):
if fixed_indices is None:
fixed_indices = []
curr_vector = self.get_vector()
target_vector = np.array(self.center_point, dtype = 'float')
unspecified_vector = np.array(self.center_point, dtype = 'float')
unspecified_indices = []
for i in range(len(curr_vector)):
if i < len(values) and values[i] is not None:
target_vector[i] = values[i]
else:
unspecified_indices.append(i)
unspecified_vector[i] = curr_vector[i]
used_re = get_norm(target_vector - self.center_point)**2
left_over_re = self.total_real_estate - used_re
if left_over_re < -0.001:
raise Exception("Overspecified reset")
uv_norm = get_norm(unspecified_vector - self.center_point)
if uv_norm == 0 and left_over_re > 0:
unspecified_vector[unspecified_indices] = 1
uv_norm = get_norm(unspecified_vector - self.center_point)
if uv_norm > 0:
unspecified_vector -= self.center_point
unspecified_vector *= np.sqrt(left_over_re)/uv_norm
unspecified_vector += self.center_point
return target_vector + unspecified_vector - self.center_point
def set_to_vector(self, vect):
assert len(vect) == len(self.sliders)
for slider, value in zip(self.sliders, vect):
slider.set_value(value)
def get_vector(self):
return np.array([slider.get_value() for slider in self.sliders])
def get_center_point(self):
return np.array([slider.center_value for slider in self.sliders])
def set_center_point(self, new_center_point):
self.center_point = np.array(new_center_point)
for x, slider in zip(new_center_point, self.sliders):
slider.set_center_value(x)
return self
def get_current_total_real_estate(self):
return sum([
slider.get_real_estate()
for slider in self.sliders
])
def get_all_dial_supplement_animations(self):
return [
slider.get_dial_supplement_animation()
for slider in self.sliders
]
def initialize_ambiant_slider_movement(self):
self.ambiently_change_sliders = True
self.ambient_change_end_time = np.inf
self.ambient_change_time = 0
self.ambient_velocity, self.ambient_acceleration, self.ambient_jerk = [
self.get_random_vector(magnitude)
for magnitude in [
self.ambient_velocity_magnitude,
self.ambient_acceleration_magnitude,
self.ambient_jerk_magnitude,
]
]
##Ensure counterclockwise rotations in 2D
if len(self.ambient_velocity) == 2:
cross = np.cross(self.get_vector(), self.ambient_velocity)
if cross < 0:
self.ambient_velocity *= -1
self.add_foreground_mobjects(self.sliders)
def wind_down_ambient_movement(self, time = 1, wait = True):
self.ambient_change_end_time = self.ambient_change_time + time
if wait:
self.wait(time)
if self.skip_animations:
self.ambient_change_time += time
def ambient_slider_movement_update(self):
#Set velocity_magnitude based on start up or wind down
velocity_magnitude = float(self.ambient_velocity_magnitude)
if self.ambient_change_time <= 1:
velocity_magnitude *= smooth(self.ambient_change_time)
time_until_end = self.ambient_change_end_time - self.ambient_change_time
if time_until_end <= 1:
velocity_magnitude *= smooth(time_until_end)
if time_until_end < 0:
self.ambiently_change_sliders = False
return
center_point = self.get_center_point()
target_vector = self.get_vector() - center_point
if get_norm(target_vector) == 0:
return
vectors_and_magnitudes = [
(self.ambient_acceleration, self.ambient_acceleration_magnitude),
(self.ambient_velocity, velocity_magnitude),
(target_vector, np.sqrt(self.total_real_estate)),
]
jerk = self.get_random_vector(self.ambient_jerk_magnitude)
deriv = jerk
for vect, mag in vectors_and_magnitudes:
vect += self.frame_duration*deriv
if vect is self.ambient_velocity:
unit_r_vect = target_vector / get_norm(target_vector)
vect -= np.dot(vect, unit_r_vect)*unit_r_vect
vect *= mag/get_norm(vect)
deriv = vect
self.set_to_vector(target_vector + center_point)
self.ambient_change_time += self.frame_duration
def get_random_vector(self, magnitude):
result = 2*np.random.random(len(self.sliders)) - 1
result *= magnitude / get_norm(result)
return result
def update_frame(self, *args, **kwargs):
if self.ambiently_change_sliders:
self.ambient_slider_movement_update()
Scene.update_frame(self, *args, **kwargs)
def wait(self, time = 1):
if self.ambiently_change_sliders:
self.play(Animation(self.sliders, run_time = time))
else:
Scene.wait(self,time)
##########
class MathIsATease(Scene):
def construct(self):
randy = Randolph()
lashes = VGroup()
for eye in randy.eyes:
for angle in np.linspace(-np.pi/3, np.pi/3, 12):
lash = Line(ORIGIN, RIGHT)
lash.set_stroke(DARK_GREY, 2)
lash.set_width(0.27)
lash.next_to(ORIGIN, RIGHT, buff = 0)
lash.rotate(angle + np.pi/2)
lash.shift(eye.get_center())
lashes.add(lash)
lashes.do_in_place(lashes.stretch, 0.8, 1)
lashes.shift(0.04*DOWN)
fan = SVGMobject(
file_name = "fan",
fill_opacity = 1,
fill_color = YELLOW,
stroke_width = 2,
stroke_color = YELLOW,
height = 0.7,
)
VGroup(*fan[-12:]).set_fill(YELLOW_E)
fan.rotate(-np.pi/4)
fan.move_to(randy)
fan.shift(0.85*UP+0.25*LEFT)
self.add(randy)
self.play(
ShowCreation(lashes, lag_ratio = 0),
randy.change, "tease",
randy.look, OUT,
)
self.add_foreground_mobjects(fan)
eye_bottom_y = randy.eyes.get_bottom()[1]
self.play(
ApplyMethod(
lashes.apply_function,
lambda p : [p[0], eye_bottom_y, p[2]],
rate_func = Blink.CONFIG["rate_func"],
),
Blink(randy),
DrawBorderThenFill(fan),
)
self.play(
ApplyMethod(
lashes.apply_function,
lambda p : [p[0], eye_bottom_y, p[2]],
rate_func = Blink.CONFIG["rate_func"],
),
Blink(randy),
)
self.wait()
class TODODeterminants(TODOStub):
CONFIG = {
"message" : "Determinants clip"
}
class CircleToPairsOfPoints(Scene):
def construct(self):
plane = NumberPlane(written_coordinate_height = 0.3)
plane.scale(2)
plane.add_coordinates(y_vals = [-1, 1])
background_plane = plane.copy()
background_plane.set_color(GREY)
background_plane.fade()
circle = Circle(radius = 2, color = YELLOW)
x, y = [np.sqrt(2)/2]*2
dot = Dot(2*x*RIGHT + 2*y*UP, color = LIGHT_GREY)
equation = TexMobject("x", "^2", "+", "y", "^2", "=", "1")
equation.set_color_by_tex("x", GREEN)
equation.set_color_by_tex("y", RED)
equation.to_corner(UP+LEFT)
equation.add_background_rectangle()
coord_pair = TexMobject("(", "-%.02f"%x, ",", "-%.02f"%y, ")")
fixed_numbers = coord_pair.get_parts_by_tex("-")
fixed_numbers.set_fill(opacity = 0)
coord_pair.add_background_rectangle()
coord_pair.next_to(dot, UP+RIGHT, SMALL_BUFF)
numbers = VGroup(*[
DecimalNumber(val).replace(num, dim_to_match = 1)
for val, num in zip([x, y], fixed_numbers)
])
numbers[0].set_color(GREEN)
numbers[1].set_color(RED)
def get_update_func(i):
return lambda t : dot.get_center()[i]/2.0
self.add(background_plane, plane)
self.play(ShowCreation(circle))
self.play(
FadeIn(coord_pair),
Write(numbers, run_time = 1),
ShowCreation(dot),
)
self.play(
Write(equation),
*[
Transform(
number.copy(),
equation.get_parts_by_tex(tex),
remover = True
)
for tex, number in zip("xy", numbers)
]
)
self.play(FocusOn(dot, run_time = 1))
self.play(
Rotating(
dot, run_time = 7, in_place = False,
rate_func = smooth,
),
MaintainPositionRelativeTo(coord_pair, dot),
*[
ChangingDecimal(
num, get_update_func(i),
tracked_mobject = fixed_num
)
for num, i, fixed_num in zip(
numbers, (0, 1), fixed_numbers
)
]
)
self.wait()
######### Rotation equations ##########
rot_equation = TexMobject(
"\\Rightarrow"
"\\big(\\cos(\\theta)x - \\sin(\\theta)y\\big)^2 + ",
"\\big(\\sin(\\theta)x + \\cos(\\theta)y\\big)^2 = 1",
)
rot_equation.scale(0.9)
rot_equation.next_to(equation, RIGHT)
rot_equation.add_background_rectangle()
words = TextMobject("Rotational \\\\ symmetry")
words.next_to(ORIGIN, UP)
words.to_edge(RIGHT)
words.add_background_rectangle()
arrow = Arrow(
words.get_left(), rot_equation.get_bottom(),
path_arc = -np.pi/6
)
randy = Randolph(color = GREY_BROWN)
randy.to_corner(DOWN+LEFT)
self.play(
Write(rot_equation, run_time = 2),
FadeOut(coord_pair),
FadeOut(numbers),
FadeOut(dot),
FadeIn(randy)
)
self.play(randy.change, "confused", rot_equation)
self.play(Blink(randy))
self.play(
Write(words, run_time = 1),
ShowCreation(arrow),
randy.look_at, words
)
plane.remove(*plane.coordinate_labels)
self.play(
Rotate(
plane, np.pi/3,
run_time = 4,
rate_func = there_and_back
),
Animation(equation),
Animation(rot_equation),
Animation(words),
Animation(arrow),
Animation(circle),
randy.change, "hooray"
)
self.wait()
class GreatSourceOfMaterial(TeacherStudentsScene):
def construct(self):
self.teacher_says(
"It's a great source \\\\ of material.",
target_mode = "hooray"
)
self.change_student_modes(*["happy"]*3)
self.wait(3)
class CirclesSpheresSumsSquares(ExternallyAnimatedScene):
pass
class BackAndForth(Scene):
def construct(self):
analytic = TextMobject("Analytic")
analytic.shift(FRAME_X_RADIUS*LEFT/2)
analytic.to_edge(UP, buff = MED_SMALL_BUFF)
geometric = TextMobject("Geometric")
geometric.shift(FRAME_X_RADIUS*RIGHT/2)
geometric.to_edge(UP, buff = MED_SMALL_BUFF)
h_line = Line(LEFT, RIGHT).scale(FRAME_X_RADIUS)
h_line.to_edge(UP, LARGE_BUFF)
v_line = Line(UP, DOWN).scale(FRAME_Y_RADIUS)
self.add(analytic, geometric, h_line, v_line)
pair = TexMobject("(", "x", ",", "y", ")")
pair.shift(FRAME_X_RADIUS*LEFT/2 + FRAME_Y_RADIUS*UP/3)
triplet = TexMobject("(", "x", ",", "y", ",", "z", ")")
triplet.shift(FRAME_X_RADIUS*LEFT/2 + FRAME_Y_RADIUS*DOWN/2)
for mob in pair, triplet:
arrow = DoubleArrow(LEFT, RIGHT)
arrow.move_to(mob)
arrow.shift(2*RIGHT)
mob.arrow = arrow
circle_eq = TexMobject("x", "^2", "+", "y", "^2", "=", "1")
circle_eq.move_to(pair)
sphere_eq = TexMobject("x", "^2", "+", "y", "^2", "+", "z", "^2", "=", "1")
sphere_eq.move_to(triplet)
plane = NumberPlane(x_unit_size = 2, y_unit_size = 2)
circle = Circle(radius = 2, color = YELLOW)
plane_group = VGroup(plane, circle)
plane_group.scale(0.4)
plane_group.next_to(h_line, DOWN, SMALL_BUFF)
plane_group.shift(FRAME_X_RADIUS*RIGHT/2)
self.play(Write(pair))
# self.play(ShowCreation(pair.arrow))
self.play(ShowCreation(plane, run_time = 3))
self.play(Write(triplet))
# self.play(ShowCreation(triplet.arrow))
self.wait(3)
for tup, eq, to_draw in (pair, circle_eq, circle), (triplet, sphere_eq, VMobject()):
for mob in tup, eq:
mob.xyz = VGroup(*[sm for sm in map(mob.get_part_by_tex, "xyz") if sm is not None])
self.play(
ReplacementTransform(tup.xyz, eq.xyz),
FadeOut(VGroup(*[sm for sm in tup if sm not in tup.xyz])),
)
self.play(
Write(VGroup(*[sm for sm in eq if sm not in eq.xyz])),
ShowCreation(to_draw)
)
self.wait(3)
class SphereForming(ExternallyAnimatedScene):
pass
class PreviousVideos(Scene):
def construct(self):
titles = VGroup(*list(map(TextMobject, [
"Pi hiding in prime regularities",
"Visualizing all possible pythagorean triples",
"Borsuk-Ulam theorem",
])))
titles.to_edge(UP, buff = MED_SMALL_BUFF)
screen = ScreenRectangle(height = 6)
screen.next_to(titles, DOWN)
title = titles[0]
self.add(title, screen)
self.wait(2)
for new_title in titles[1:]:
self.play(Transform(title, new_title))
self.wait(2)
class TODOTease(TODOStub):
CONFIG = {
"message" : "Tease"
}
class AskAboutLongerLists(TeacherStudentsScene):
def construct(self):
question = TextMobject(
"What about \\\\",
"$(x_1, x_2, x_3, x_4)?$"
)
tup = question[1]
alt_tups = list(map(TextMobject, [
"$(x_1, x_2, x_3, x_4, x_5)?$",
"$(x_1, x_2, \\dots, x_{99}, x_{100})?$"
]))
self.student_says(question, run_time = 1)
self.wait()
for alt_tup in alt_tups:
alt_tup.move_to(tup)
self.play(Transform(tup, alt_tup))
self.wait()
self.wait()
self.play(
RemovePiCreatureBubble(self.students[1]),
self.teacher.change, "raise_right_hand"
)
self.change_student_modes(
*["confused"]*3,
look_at_arg = self.teacher.get_top() + 2*UP
)
self.play(self.teacher.look, UP)
self.wait(5)
self.student_says(
"I...don't see it.",
target_mode = "maybe",
student_index = 0
)
self.wait(3)
class FourDCubeRotation(ExternallyAnimatedScene):
pass
class HypersphereRotation(ExternallyAnimatedScene):
pass
class FourDSurfaceRotating(ExternallyAnimatedScene):
pass
class Professionals(PiCreatureScene):
def construct(self):
self.introduce_characters()
self.add_equation()
self.analogies()
def introduce_characters(self):
titles = VGroup(*list(map(TextMobject, [
"Mathematician",
"Computer scientist",
"Physicist",
])))
self.remove(*self.pi_creatures)
for title, pi in zip(titles, self.pi_creatures):
title.next_to(pi, DOWN)
self.play(
Animation(VectorizedPoint(pi.eyes.get_center())),
FadeIn(pi),
Write(title, run_time = 1),
)
self.wait()
def add_equation(self):
quaternion = TexMobject(
"\\frac{1}{2}", "+",
"0", "\\textbf{i}", "+",
"\\frac{\\sqrt{6}}{4}", "\\textbf{j}", "+",
"\\frac{\\sqrt{6}}{4}", "\\textbf{k}",
)
quaternion.scale(0.7)
quaternion.next_to(self.mathy, UP)
quaternion.set_color_by_tex_to_color_map({
"i" : RED,
"j" : GREEN,
"k" : BLUE,
})
array = TexMobject("[a_1, a_2, \\dots, a_{100}]")
array.next_to(self.compy, UP)
kets = TexMobject(
"\\alpha",
"|\\!\\uparrow\\rangle + ",
"\\beta",
"|\\!\\downarrow\\rangle"
)
kets.set_color_by_tex_to_color_map({
"\\alpha" : GREEN,
"\\beta" : RED,
})
kets.next_to(self.physy, UP)
terms = VGroup(quaternion, array, kets)
for term, pi in zip(terms, self.pi_creatures):
self.play(
Write(term, run_time = 1),
pi.change, "pondering", term
)
self.wait(2)
self.terms = terms
def analogies(self):
examples = VGroup()
plane = ComplexPlane(
x_radius = 2.5,
y_radius = 1.5,
)
plane.add_coordinates()
plane.add(Circle(color = YELLOW))
plane.scale(0.75)
examples.add(plane)
examples.add(Circle())
examples.arrange(RIGHT, buff = 2)
examples.to_edge(UP, buff = LARGE_BUFF)
labels = VGroup(*list(map(TextMobject, ["2D", "3D"])))
title = TextMobject("Fly by instruments")
title.scale(1.5)
title.to_edge(UP)
for label, example in zip(labels, examples):
label.next_to(example, DOWN)
self.play(
ShowCreation(example),
Write(label, run_time = 1)
)
example.add(label)
self.wait()
self.wait()
self.play(
FadeOut(examples),
self.terms.shift, UP,
Write(title, run_time = 2)
)
self.play(*[
ApplyMethod(
pi.change, mode, self.terms.get_left(),
run_time = 2,
rate_func = squish_rate_func(smooth, a, a+0.5)
)
for pi, mode, a in zip(
self.pi_creatures,
["confused", "sassy", "erm"],
np.linspace(0, 0.5, len(self.pi_creatures))
)
])
self.wait()
self.play(Animation(self.terms[-1]))
self.wait(2)
######
def create_pi_creatures(self):
self.mathy = Mathematician()
self.physy = PiCreature(color = PINK)
self.compy = PiCreature(color = PURPLE)
pi_creatures = VGroup(self.mathy, self.compy, self.physy)
for pi in pi_creatures:
pi.scale(0.7)
pi_creatures.arrange(RIGHT, buff = 3)
pi_creatures.to_edge(DOWN, buff = LARGE_BUFF)
return pi_creatures
class OfferAHybrid(SliderScene):
CONFIG = {
"n_sliders" : 3,
}
def construct(self):
self.remove(self.sliders)
titles = self.get_titles()
h_line = Line(LEFT, RIGHT).scale(FRAME_X_RADIUS)
h_line.next_to(titles, DOWN)
v_lines = VGroup(*[
Line(UP, DOWN).scale(FRAME_Y_RADIUS)
for x in range(2)
])
v_lines.generate_target()
for line, vect in zip(v_lines.target, [LEFT, RIGHT]):
line.shift(vect*FRAME_X_RADIUS/3)
equation = TexMobject("x^2 + y^2 + z^2 = 1")
equation.generate_target()
equation.shift(FRAME_X_RADIUS*LEFT/2)
equation.target.shift(FRAME_WIDTH*LEFT/3)
self.add(titles, h_line, v_lines, equation)
self.wait()
self.play(*list(map(MoveToTarget, [titles, v_lines, equation])))
self.play(Write(self.sliders, run_time = 1))
self.initialize_ambiant_slider_movement()
self.wait(10)
self.wind_down_ambient_movement()
self.wait()
def get_titles(self):
titles = VGroup(*list(map(TextMobject, [
"Analytic", "Hybrid", "Geometric"
])))
titles.to_edge(UP)
titles[1].set_color(BLUE)
titles.generate_target()
titles[1].scale_in_place(0.001)
titles[0].shift(FRAME_X_RADIUS*LEFT/2)
titles.target[0].shift(FRAME_WIDTH*LEFT/3)
titles[2].shift(FRAME_X_RADIUS*RIGHT/2)
titles.target[2].shift(FRAME_WIDTH*RIGHT/3)
return titles
class TODOBoxExample(TODOStub):
CONFIG = {
"message" : "Box Example"
}
class RotatingSphereWithWanderingPoint(ExternallyAnimatedScene):
pass
class DismissProjection(PiCreatureScene):
CONFIG = {
"screen_rect_color" : WHITE,
"example_vect" : np.array([0.52, 0.26, 0.53, 0.60]),
}
def construct(self):
self.remove(self.pi_creature)
self.show_all_spheres()
self.discuss_4d_sphere_definition()
self.talk_through_animation()
self.transition_to_next_scene()
def show_all_spheres(self):
equations = VGroup(*list(map(TexMobject, [
"x^2 + y^2 = 1",
"x^2 + y^2 + z^2 = 1",
"x^2 + y^2 + z^2 + w^2 = 1",
])))
colors = [YELLOW, GREEN, BLUE]
for equation, edge, color in zip(equations, [LEFT, ORIGIN, RIGHT], colors):
equation.set_color(color)
equation.shift(3*UP)
equation.to_edge(edge)
equations[1].shift(LEFT)
spheres = VGroup(
self.get_circle(equations[0]),
self.get_sphere_screen(equations[1], DOWN),
self.get_sphere_screen(equations[2], DOWN),
)
for equation, sphere in zip(equations, spheres):
self.play(
Write(equation),
LaggedStartMap(ShowCreation, sphere),
)
self.wait()
self.equations = equations
self.spheres = spheres
def get_circle(self, equation):
result = VGroup(
NumberPlane(
x_radius = 2.5,
y_radius = 2,
).fade(0.4),
Circle(color = YELLOW, radius = 1),
)
result.scale(0.7)
result.next_to(equation, DOWN)
return result
def get_sphere_screen(self, equation, vect):
square = Rectangle()
square.set_width(equation.get_width())
square.stretch_to_fit_height(3)
square.next_to(equation, vect)
square.set_color(self.screen_rect_color)
return square
def discuss_4d_sphere_definition(self):
sphere = self.spheres[-1]
equation = self.equations[-1]
sphere_words = TextMobject("``4-dimensional sphere''")
sphere_words.next_to(sphere, DOWN+LEFT, buff = LARGE_BUFF)
arrow = Arrow(
sphere_words.get_right(), sphere.get_bottom(),
path_arc = np.pi/3,
color = BLUE
)
descriptor = TexMobject(
"\\text{Just lists of numbers like }",
"(%.02f \\,, %.02f \\,, %.02f \\,, %.02f \\,)"%tuple(self.example_vect)
)
descriptor[1].set_color(BLUE)
descriptor.next_to(sphere_words, DOWN)
dot = Dot(descriptor[1].get_top())
dot.set_fill(WHITE, opacity = 0.75)
self.play(
Write(sphere_words),
ShowCreation(
arrow,
rate_func = squish_rate_func(smooth, 0.5, 1)
),
run_time = 3,
)
self.wait()
self.play(Write(descriptor, run_time = 2))
self.wait()
self.play(
dot.move_to, equation.get_left(),
dot.set_fill, None, 0,
path_arc = -np.pi/12
)
self.wait(2)
self.sphere_words = sphere_words
self.sphere_arrow = arrow
self.descriptor = descriptor
def talk_through_animation(self):
sphere = self.spheres[-1]
morty = self.pi_creature
alt_dims = VGroup(*list(map(TextMobject, ["5D", "6D", "7D"])))
alt_dims.next_to(morty.eyes, UP, SMALL_BUFF)
alt_dim = alt_dims[0]
self.play(FadeIn(morty))
self.play(morty.change, "raise_right_hand", sphere)
self.wait(3)
self.play(morty.change, "confused", sphere)
self.wait(3)
self.play(
morty.change, "erm", alt_dims,
FadeIn(alt_dim)
)
for new_alt_dim in alt_dims[1:]:
self.wait()
self.play(Transform(alt_dim, new_alt_dim))
self.wait()
self.play(morty.change, "concerned_musician")
self.play(FadeOut(alt_dim))
self.wait()
self.play(morty.change, "angry", sphere)
self.wait(2)
def transition_to_next_scene(self):
equation = self.equations[-1]
self.equations.remove(equation)
tup = self.descriptor[1]
self.descriptor.remove(tup)
equation.generate_target()
equation.target.center().to_edge(UP)
tup.generate_target()
tup.target.next_to(equation.target, DOWN)
tup.target.set_color(WHITE)
self.play(LaggedStartMap(FadeOut, VGroup(*[
self.equations, self.spheres,
self.sphere_words, self.sphere_arrow,
self.descriptor,
self.pi_creature
])))
self.play(*list(map(MoveToTarget, [equation, tup])))
self.wait()
###
def create_pi_creature(self):
return Mortimer().scale(0.8).to_corner(DOWN+RIGHT)
class RotatingSphere(ExternallyAnimatedScene):
pass
class Introduce4DSliders(SliderScene):
CONFIG = {
"slider_config" : {
"include_real_estate_ticks" : False,
"numbers_with_elongated_ticks" : [-1, 0, 1],
"tick_frequency" : 0.25,
"tick_size" : 0.05,
"dial_color" : YELLOW,
},
"slider_spacing" : LARGE_BUFF,
}
def construct(self):
self.match_last_scene()
self.introduce_sliders()
self.ask_about_constraint()
def match_last_scene(self):
self.start_vect = DismissProjection.CONFIG["example_vect"]
self.remove(self.sliders)
equation = TexMobject("x^2 + y^2 + z^2 + w^2 = 1")
x, y, z, w = self.start_vect
tup = TexMobject(
"(", "%.02f \\,"%x,
",", "%.02f \\,"%y,
",", "%.02f \\,"%z,