def coords_to_vector(self,
vector,
coords_start=2 * RIGHT + 2 * UP,
clean_up=True):
starting_mobjects = list(self.mobjects)
array = Matrix(vector)
array.shift(coords_start)
arrow = Vector(vector)
x_line = Line(ORIGIN, vector[0] * RIGHT)
y_line = Line(x_line.get_end(), arrow.get_end())
x_line.set_color(X_COLOR)
y_line.set_color(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
self.play(Write(array, run_time=1))
self.wait()
self.play(
ApplyFunction(
lambda x: self.position_x_coordinate(x, x_line, vector),
x_coord))
self.play(ShowCreation(x_line))
self.play(
ApplyFunction(
lambda y: self.position_y_coordinate(y, y_line, vector),
y_coord), FadeOut(array.get_brackets()))
y_coord, brackets = self.get_mobjects_from_last_animation()
self.play(ShowCreation(y_line))
self.play(ShowCreation(arrow))
self.wait()
if clean_up:
self.clear()
self.add(*starting_mobjects)
def add_lines(self, left, right):
line_kwargs = {
"color": BLUE,
"stroke_width": 2,
}
left_rows = [VGroup(*row) for row in left.get_mob_matrix()]
h_lines = VGroup()
for row in left_rows[:-1]:
h_line = Line(row.get_left(), row.get_right(), **line_kwargs)
h_line.next_to(row, DOWN, buff=left.v_buff / 2.)
h_lines.add(h_line)
right_cols = [
VGroup(*col) for col in np.transpose(right.get_mob_matrix())
]
v_lines = VGroup()
for col in right_cols[:-1]:
v_line = Line(col.get_top(), col.get_bottom(), **line_kwargs)
v_line.next_to(col, RIGHT, buff=right.h_buff / 2.)
v_lines.add(v_line)
self.play(ShowCreation(h_lines))
self.play(ShowCreation(v_lines))
self.wait()
self.show_frame()
def construct(self):
# Setup
pos_axis = NumberLine(x_min=-3.5, x_max=3.5, color=WHITE)
pos_axis.rotate(np.pi / 2)
pos_axis.add_tip()
time_axis = NumberLine(x_min=0, x_max=9.5, color=WHITE)
time_axis.add_tip()
house = House()
house.rotate(np.pi / 2)
house.place_on(pos_axis.number_to_point(0))
zero_drunk = Drunk(direction=UP, color=self.zero_color)
zero_drunk.step_on(pos_axis.number_to_point(0))
neg_drunk = Drunk(direction=UP, color=self.neg_color)
neg_drunk.step_on(pos_axis.number_to_point(0))
group = VGroup(house, VGroup(pos_axis, time_axis), zero_drunk,
neg_drunk)
group.to_edge(LEFT)
pos_text = TextMobject("位置")
pos_text.next_to(pos_axis.number_to_point(3.5), LEFT)
time_text = TextMobject("时间")
time_text.next_to(time_axis.number_to_point(9.5), DOWN)
self.add(group, pos_text, time_text)
old_zero_drunk = zero_drunk.copy()
old_neg_drunk = neg_drunk.copy()
# Start Wandering
zero_sequence = "UUUDDDDU"
zero_walk = RandomWalk1DArrow(
zero_sequence,
up_color=self.zero_color,
down_color=self.zero_color,
)
zero_walk.move_start_to(pos_axis.number_to_point(0))
neg_sequence = "DDUDDUDU"
neg_walk = RandomWalk1DArrow(
neg_sequence,
up_color=self.neg_color,
down_color=self.neg_color,
)
neg_walk.move_start_to(pos_axis.number_to_point(0))
for k, (zero_char,
neg_char) in enumerate(zip(zero_sequence, neg_sequence)):
zero_increment = 1 if zero_char == "U" else -1
neg_increment = 1 if neg_char == "U" else -1
zero_arrow = zero_walk.get_arrow_by_number(k)
neg_arrow = neg_walk.get_arrow_by_number(k)
self.play(DrunkWander(zero_drunk, zero_increment, direction=UP),
DrunkWander(neg_drunk, neg_increment, direction=UP),
ShowCreation(zero_arrow), ShowCreation(neg_arrow))
self.wait()
# Reset
self.play(
Transform(zero_drunk, old_zero_drunk),
Transform(neg_drunk, old_neg_drunk),
FadeOut(zero_walk),
FadeOut(neg_walk),
)
self.wait()
def vector_to_coords(self, vector, integer_labels=True, clean_up=True):
starting_mobjects = list(self.mobjects)
show_creation = False
if isinstance(vector, Arrow):
arrow = vector
vector = arrow.get_end()[:2]
else:
arrow = Vector(vector)
show_creation = True
array = vector_coordinate_label(arrow, integer_labels=integer_labels)
x_line = Line(ORIGIN, vector[0] * RIGHT)
y_line = Line(x_line.get_end(), arrow.get_end())
x_line.set_color(X_COLOR)
y_line.set_color(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
x_coord_start = self.position_x_coordinate(
x_coord.copy(), x_line, vector
)
y_coord_start = self.position_y_coordinate(
y_coord.copy(), y_line, vector
)
brackets = array.get_brackets()
if show_creation:
self.play(ShowCreation(arrow))
self.play(
ShowCreation(x_line),
Write(x_coord_start),
run_time=1
)
self.play(
ShowCreation(y_line),
Write(y_coord_start),
run_time=1
)
self.wait()
self.play(
Transform(x_coord_start, x_coord, submobject_mode="all_at_once"),
Transform(y_coord_start, y_coord, submobject_mode="all_at_once"),
Write(brackets, run_time=1),
)
self.wait()
self.remove(x_coord_start, y_coord_start, brackets)
self.add(array)
if clean_up:
self.clear()
self.add(*starting_mobjects)
return array, x_line, y_line
def add_vector(self, vector, color=YELLOW, animate=True, **kwargs):
if not isinstance(vector, Arrow):
vector = Vector(vector, color=color, **kwargs)
if animate:
self.play(ShowCreation(vector))
self.add(vector)
return vector
def add_T_label(self,
x_val,
side=RIGHT,
label=None,
color=WHITE,
animated=False,
**kwargs):
triangle = RegularPolygon(n=3, start_angle=np.pi / 2)
triangle.scale_to_fit_height(MED_SMALL_BUFF)
triangle.move_to(self.coords_to_point(x_val, 0), UP)
triangle.set_fill(color, 1)
triangle.set_stroke(width=0)
if label == None:
T_label = TexMobject(self.variable_point_label, fill_color=color)
else:
T_label = TexMobject(label, fill_color=color)
T_label.next_to(triangle, DOWN)
v_line = self.get_vertical_line_to_graph(x_val,
self.v_graph,
color=YELLOW)
if animated:
self.play(DrawBorderThenFill(triangle), ShowCreation(v_line),
Write(T_label, run_time=1), **kwargs)
if np.all(side == LEFT):
self.left_T_label_group = VGroup(T_label, triangle)
self.left_v_line = v_line
self.add(self.left_T_label_group, self.left_v_line)
elif np.all(side == RIGHT):
self.right_T_label_group = VGroup(T_label, triangle)
self.right_v_line = v_line
self.add(self.right_T_label_group, self.right_v_line)
def update_labels(self, new_labels, **kwargs):
assert (type(new_labels) == OrderedDict)
# make sure labels are different
for old_label in self.labels.values():
for new_label in new_labels.values():
assert (id(old_label) != id(new_label))
anims = []
# delete
for key, val in new_labels.items():
if val is None:
anims.append(Uncreate(self.labels[key]))
self.remove(self.labels[key])
del new_labels[key]
del self.labels[key]
# scale
for label in new_labels.values():
if type(label) == Arrow:
continue # TODO
scale_factor = self.get_label_scale_factor(label, len(new_labels))
label.scale(scale_factor)
# place
new_labels = self.place_labels(new_labels, **kwargs)
# animate
if "animate" not in kwargs or kwargs["animate"]:
for name in new_labels.keys():
if name in self.labels:
anims.extend([
ReplacementTransform(self.labels[name],
new_labels[name],
parent=self)
])
else:
anims.extend([ShowCreation(new_labels[name])])
self.add(new_labels[name])
for name in self.labels:
if name not in new_labels:
anims.extend([Uncreate(self.labels[name])])
self.remove(self.labels[name])
else:
for name in new_labels.keys():
if name not in self.labels:
self.add(new_labels[name])
else:
self.add(new_labels[name])
self.remove(self.labels[name])
for name in self.labels:
if name not in new_labels:
self.remove(self.labels[name])
self.labels = new_labels
return anims
def construct(self):
# Setup
self.set_camera_orientation(phi = np.pi/3, theta = 3*np.pi/4)
self.begin_ambient_camera_rotation(np.pi/50)
# Part 1: Increasing the order
for order in range(1, self.max_order+1):
if order == 1:
fractal = HilbertCurve3D(order = 1)
self.play(ShowCreation(fractal), run_time = 2)
cur_order = fractal.order
else:
new_fractal = HilbertCurve3D(order = cur_order + 1)
self.play(Transform(fractal, new_fractal))
cur_order = new_fractal.order
self.wait(2)
self.wait(5)
self.play(FadeOut(fractal))
self.wait(3)
# Part 2: Show one-touch construction
self.play(ShowCreation(fractal, run_time = 60))
self.wait(5)
# Part 3: Decreasing the order till it vanishes
for k in reversed(range(1, self.max_order)):
new_fractal = HilbertCurve3D(order = cur_order - 1)
self.play(Transform(fractal, new_fractal))
cur_order = new_fractal.order
self.wait(2)
self.play(Uncreate(fractal), run_time = 1)
# The end
self.stop_ambient_camera_rotation()
self.set_camera_orientation(phi = 0, theta = -np.pi/2)
author = TextMobject("@Solara570")
author.scale(1.5)
author.to_corner(RIGHT+DOWN)
self.play(FadeIn(author), run_time = 1)
self.wait(2)
def add_unit_square(self, color=YELLOW, opacity=0.3, animate=False):
square = Square(color=color, side_length=1)
square.shift(-square.get_corner(DOWN + LEFT))
if animate:
added_anims = map(Animation, self.moving_vectors)
self.play(ShowCreation(square), *added_anims)
self.play(square.set_fill, color, opacity, *added_anims)
else:
square.set_fill(color, opacity)
self.add_transformable_mobject(square)
self.bring_to_front(*self.moving_vectors)
self.square = square
return self
def get_digit_increment_animations(self):
result = []
self.number += 1
is_next_digit = self.is_next_digit()
if is_next_digit: self.max_place += 1
new_number_mob = self.get_number_mob(self.number)
new_number_mob.move_to(self.number_mob, RIGHT)
if is_next_digit:
self.add_configuration()
place = len(new_number_mob.split()) - 1
result.append(FadeIn(self.dot_templates[place]))
arrow = Arrow(new_number_mob[place].get_top(),
self.dot_templates[place].get_bottom(),
color=self.digit_place_colors[place])
self.arrows.add(arrow)
result.append(ShowCreation(arrow))
result.append(
Transform(self.number_mob,
new_number_mob,
submobject_mode="lagged_start"))
return result
def place_cursors(self, indices=None, block=None):
"""
place cursors on the blocks denoted by indices if it was passed,
otherwise the blocks denoted by self.cursor_indices
"""
if indices is None and len(self.cursor_indices) == 0:
raise Exception("no indices to use")
elif indices is None:
indices = self.cursor_indices
if block is None:
cur_block = self
else:
cur_block = block
cursors = []
for block_idx in indices:
cur_block = cur_block.submobjects[block_idx]
cursor = TexMobject("\\blacktriangleright")
cursor.next_to(cur_block[0], LEFT)
cursors.append(cursor)
self.cursors.extend(cursors)
return [ShowCreation(Group(*cursors))]
def construct(self):
# Setup
pos_axis = NumberLine(x_min=-3.5, x_max=3.5, color=WHITE)
pos_axis.rotate(np.pi / 2)
pos_axis.add_tip()
time_axis = NumberLine(x_min=0, x_max=9.5, color=WHITE)
time_axis.add_tip()
house = House()
house.rotate(np.pi / 2)
house.place_on(pos_axis.number_to_point(0))
drunk = Drunk(direction=UP)
drunk.step_on(pos_axis.number_to_point(0))
group = VGroup(house, VGroup(pos_axis, time_axis), drunk)
group.to_edge(LEFT)
pos_text = TextMobject("位置")
pos_text.next_to(pos_axis.number_to_point(3.5), LEFT)
time_text = TextMobject("时间")
time_text.next_to(time_axis.number_to_point(9.5), DOWN)
self.add(group, pos_text, time_text)
old_drunk = drunk.copy()
# Start Wandering
sequence = "UDUDDDUD"
random_walk = RandomWalk1DArrow(sequence)
random_walk.move_start_to(pos_axis.number_to_point(0))
for k, walk_char in enumerate(sequence):
increment = 1 if walk_char == "U" else -1
arrow = random_walk.get_arrow_by_number(k)
self.play(
DrunkWander(drunk, increment, direction=UP),
ShowCreation(arrow),
)
self.wait()
# Reset
self.play(Transform(drunk, old_drunk), FadeOut(random_walk))
self.wait()
def add_axes(self, animate=False, color=WHITE, **kwargs):
axes = Axes(color=color, tick_frequency=1)
if animate:
self.play(ShowCreation(axes, submobject_mode="one_at_a_time"))
self.add(axes)
return axes
def add_plane(self, animate=False, **kwargs):
plane = NumberPlane(**kwargs)
if animate:
self.play(ShowCreation(plane, submobject_mode="lagged_start"))
self.add(plane)
return plane
def construct(self):
# Setup
axes_group = self.axes_group
pos_axis, time_axis = axes_group[:2]
title_pq = self.title_pq
walk_q = self.walk_q
parts_q = self.parts_q
l_arrow = self.l_arrow
self.add(axes_group, title_pq, walk_q, l_arrow)
walk_q_copy = walk_q.copy()
# Q_4 -> P_4
steps_qp = VGroup(*[
TextMobject(text) for text in [
"1. 找到路径终点的位置坐标$h$", "2. 找到最晚一次穿过$\\frac{h}{2}$的时刻",
"3. 在这个时刻上进行分割", "4. 将第一段水平翻转", "5. 拼接两个片段"
]
])
for step in steps_qp:
step.set_color(YELLOW)
step.add_background_rectangle()
step1_qp, step2_qp, step3_qp, step4_qp, step5_qp = steps_qp
# 1. Find the endpoint
step1_qp.next_to(time_axis.number_to_point(4.5), UP)
end_horiz_line = DashedLine(LEFT_SIDE, RIGHT_SIDE, color=YELLOW)
end_horiz_line.move_to(pos_axis.number_to_point(-4))
end_horiz_line.horizontally_center()
end_brace_line = DashedLine(time_axis.number_to_point(8),
walk_q.get_end_point())
end_brace = Brace(end_brace_line, direction=RIGHT, color=YELLOW)
h = TexMobject("h").set_color(YELLOW)
end_brace.put_at_tip(h)
self.play(Write(step1_qp), ShowCreation(end_horiz_line), run_time=1)
self.play(GrowFromCenter(end_brace), GrowFromCenter(h))
self.wait(1.5)
self.play(FadeOut(step1_qp))
# 2. Find the last time it GOES THROUGH half its final value
half_point = walk_q.get_arrow_end_point(3)
step2_qp.next_to(time_axis.number_to_point(4.5), UP)
half_horiz_line = end_horiz_line.copy().shift(2 * UP)
half_brace_line = DashedLine(time_axis.number_to_point(4), half_point)
half_brace = Brace(half_brace_line, direction=RIGHT, color=YELLOW)
half_h = TexMobject("\\frac{h}{2}").set_color(YELLOW)
half_brace.put_at_tip(half_h)
half_dot = Dot(half_point, color=YELLOW)
self.play(FadeIn(step2_qp), run_time=1)
self.wait(0.5)
self.play(
ReplacementTransform(end_brace, half_brace),
ReplacementTransform(end_horiz_line, half_horiz_line),
ReplacementTransform(h, half_h[0]),
Write(half_h[1:]),
)
self.play(DrawBorderThenFill(half_dot))
self.wait(1.5)
self.play(
FadeOut(VGroup(step2_qp, half_horiz_line, half_brace, half_h)))
# 3. Split
vert_line = DashedLine(2.5 * UP, 2.5 * DOWN, color=YELLOW)
vert_line.move_to(half_point)
step3_qp.next_to(vert_line, UP)
left_part_q, right_part_q = parts_q
self.play(ShowCreation(vert_line), Write(step3_qp), run_time=1)
self.play(
FadeOut(half_dot),
left_part_q.shift,
0.5 * DOWN + 0.5 * LEFT,
right_part_q.shift,
0.5 * UP + 0.5 * RIGHT,
)
self.wait(1.5)
self.play(FadeOut(vert_line), FadeOut(step3_qp))
# 4. Flip the first segment horizontally
flip_axis = DashedLine(2 * UP, 2 * DOWN, color=GREY)
flip_axis.move_to(left_part_q)
step4_qp.next_to(flip_axis, DOWN)
self.play(
ShowCreation(flip_axis),
Write(step4_qp),
run_time=1,
)
self.play(
left_part_q.flip,
Animation(flip_axis),
)
self.wait(1.5)
self.play(FadeOut(step4_qp), FadeOut(flip_axis))
# 5. Put the pieces together
step5_qp.shift(2.5 * DOWN)
flip_arrow_anims = walk_q.get_flip_arrows_animation(3, color=ORANGE)
self.play(Write(step5_qp), run_time=1)
self.wait(0.5)
self.play(flip_arrow_anims, right_part_q.set_color, ORANGE)
self.wait(0.5)
self.play(
left_part_q.shift,
2.5 * UP + 0.5 * RIGHT,
right_part_q.shift,
3.5 * UP + 0.5 * LEFT,
Animation(step5_qp),
)
self.wait(0.5)
self.play(FadeOut(step5_qp))
self.wait(1.5)
# Now Reset
self.play(FadeOut(walk_q))
self.play(FadeIn(walk_q_copy))
self.wait()
def construct(self):
# Setup
axes_group = self.axes_group
title_pq = self.title_pq
walk_p = self.walk_p
parts_p = self.parts_p
r_arrow = self.r_arrow
self.add(axes_group, title_pq, walk_p, r_arrow)
walk_p_copy = walk_p.copy()
# P_4 -> Q_4
steps_pq = VGroup(*[
TextMobject(text) for text in [
"1. 第一步是沿着正方向走的", "2. 找到第一次到达最大值的时刻", "3. 在这个时刻上进行分割",
"4. 将第一段水平翻转", "5. 拼接两个片段"
]
])
for step in steps_pq:
step.set_color(YELLOW)
step.add_background_rectangle()
step1_pq, step2_pq, step3_pq, step4_pq, step5_pq = steps_pq
# 1. Check the first step of the walk
step1_circle = Circle(color=YELLOW)
first_arrow = walk_p.get_arrow_by_number(0)
step1_circle.surround(first_arrow)
step1_pq.next_to(step1_circle, RIGHT + DOWN)
self.play(ShowCreation(step1_circle), Write(step1_pq), run_time=1)
self.wait(1.5)
self.play(FadeOut(step1_circle), FadeOut(step1_pq))
# 2. Find the first time it reaches the maximum
peak = walk_p.get_arrow_end_point(3)
horiz_line = DashedLine(2.5 * LEFT, 2.5 * RIGHT, color=YELLOW)
horiz_line.move_to(peak)
dot = Dot(color=YELLOW)
dot.move_to(peak)
step2_pq.next_to(horiz_line, UP)
self.play(ShowCreation(horiz_line),
DrawBorderThenFill(dot),
Write(step2_pq),
run_time=1)
self.wait(1.5)
self.play(FadeOut(horiz_line), FadeOut(step2_pq))
# 3. Split
vert_line = DashedLine(2.5 * UP, 2.5 * DOWN, color=YELLOW)
vert_line.move_to(peak)
step3_pq.next_to(vert_line, DOWN)
left_part_p, right_part_p = parts_p
self.play(ShowCreation(vert_line), Write(step3_pq), run_time=1)
self.play(
FadeOut(dot),
left_part_p.shift,
0.5 * DOWN + 0.5 * LEFT,
right_part_p.shift,
DOWN + 0.5 * RIGHT,
)
self.wait(1.5)
self.play(FadeOut(vert_line), FadeOut(step3_pq))
# 4. Flip the first segment horizontally
flip_axis = DashedLine(2 * UP, 2 * DOWN, color=GREY)
flip_axis.move_to(left_part_p)
step4_pq.next_to(flip_axis, DOWN)
self.play(
ShowCreation(flip_axis),
Write(step4_pq),
run_time=1,
)
self.play(
left_part_p.flip,
Animation(flip_axis),
)
self.wait(1.5)
self.play(FadeOut(step4_pq), FadeOut(flip_axis))
# 5. Put the pieces together
step5_pq.move_to(dot)
flip_arrow_anims = walk_p.get_flip_arrows_animation(3, color=GREEN)
self.play(Write(step5_pq), run_time=1)
self.wait(0.5)
self.play(flip_arrow_anims, right_part_p.set_color, GREEN)
self.wait(0.5)
self.play(
left_part_p.shift,
1.5 * DOWN + 0.5 * RIGHT,
right_part_p.shift,
3 * DOWN + 0.5 * LEFT,
Animation(step5_pq),
)
self.wait(0.5)
self.play(FadeOut(step5_pq))
self.wait(1.5)
# Now Reset
self.play(FadeOut(walk_p))
self.play(FadeIn(walk_p_copy))
self.wait()