def __init__(self,
eq1,
eq2,
regex,
regex2=None,
map_list=None,
align_char=None):
# align equations
if align_char:
difference_vec = \
self.mob_from_char(eq1, eq1.tex_string, align_char).get_center() - \
self.mob_from_char(eq2, eq2.tex_string, align_char).get_center()
else:
difference_vec = eq1.get_center() - eq2.get_center()
eq2.shift(difference_vec)
if regex2 is None:
g1 = self.split_by_regex(eq1, regex)
g2 = self.split_by_regex(eq2, regex)
assert (len(g1.submobjects) == len(g2.submobjects))
trans = ReplacementTransform(g1, g2)
AnimationGroup.__init__(self, trans)
else:
assert (map_list)
g1 = self.split_by_regex(eq1, regex)
g2 = self.split_by_regex(eq2, regex2)
self.g1 = g1
self.g2 = g2
G1 = VGroup()
G2 = VGroup()
F1 = Group()
F2 = Group()
g1_nodes = set(pair[0] for pair in map_list)
g2_nodes = set(pair[1] for pair in map_list)
while map_list:
l1 = [g1.submobjects[map_list[0][0]]]
l2 = [g2.submobjects[map_list[0][1]]]
new_list = []
for i in range(1, len(map_list)):
if map_list[i][0] == map_list[0][0]:
l2.append(g2.submobjects[map_list[i][1]])
elif map_list[i][1] == map_list[0][1]:
l1.append(g1.submobjects[map_list[i][0]])
else:
new_list.append(map_list[i])
map_list = new_list
G1.submobjects.append(VGroup(*l1))
G2.submobjects.append(VGroup(*l2))
for i in range(len(g1.submobjects)):
if i not in g1_nodes:
F1.submobjects.append(g1.submobjects[i])
for i in range(len(g2.submobjects)):
if i not in g2_nodes:
F2.submobjects.append(g2.submobjects[i])
self.g1 = g1
self.g2 = g2
trans = ReplacementTransform(G1, G2)
fadeout = FadeOut(F1)
fadein = FadeIn(F2)
AnimationGroup.__init__(self, trans, fadeout, fadein)
def introduce_bubble(self, *args, **kwargs):
if isinstance(args[0], PiCreature):
pi_creature = args[0]
content = args[1:]
else:
pi_creature = self.get_primary_pi_creature()
content = args
bubble_class = kwargs.pop("bubble_class", SpeechBubble)
target_mode = kwargs.pop(
"target_mode",
"thinking" if bubble_class is ThoughtBubble else "speaking"
)
bubble_kwargs = kwargs.pop("bubble_kwargs", {})
bubble_removal_kwargs = kwargs.pop("bubble_removal_kwargs", {})
added_anims = kwargs.pop("added_anims", [])
anims = []
on_screen_mobjects = self.camera.extract_mobject_family_members(
self.get_mobjects()
)
def has_bubble(pi):
return hasattr(pi, "bubble") and \
pi.bubble is not None and \
pi.bubble in on_screen_mobjects
pi_creatures_with_bubbles = list(filter(has_bubble, self.get_pi_creatures()))
if pi_creature in pi_creatures_with_bubbles:
pi_creatures_with_bubbles.remove(pi_creature)
old_bubble = pi_creature.bubble
bubble = pi_creature.get_bubble(
*content,
bubble_class=bubble_class,
**bubble_kwargs
)
anims += [
ReplacementTransform(old_bubble, bubble),
ReplacementTransform(old_bubble.content, bubble.content),
pi_creature.change_mode, target_mode
]
else:
anims.append(PiCreatureBubbleIntroduction(
pi_creature,
*content,
bubble_class=bubble_class,
bubble_kwargs=bubble_kwargs,
target_mode=target_mode,
**kwargs
))
anims += [
RemovePiCreatureBubble(pi, **bubble_removal_kwargs)
for pi in pi_creatures_with_bubbles
]
anims += added_anims
self.play(*anims, **kwargs)
def solve_the_equations(self):
rects = VGroup(*[
CoverRectangle(
equation[0].get_exponent(), stroke_color = color,
text = str(num), text_color = color
)
for equation, color, num in zip(self.equations, self.colors, self.nums)
])
self.play(DrawBorderThenFill(rects))
self.wait()
sps = VGroup()
for equation, num, color in zip(self.equations, self.nums, self.colors):
sp = TexMobject("x", "^{%d}" % num, "=", "%d" % num)
sp[1::2].set_color(color)
sp.scale(2)
sp.next_to(equation, DOWN, buff = 1)
sps.add(sp)
rss = VGroup()
for num, sp, color in zip(self.nums, sps, self.colors):
rs = TexMobject("x", "=", "%d" % num , "^{{1}\\over{%d}}" % num, "=\\sqrt{2}")
for tex in (rs[2], rs[3][2]):
tex.set_color(color)
rs.match_height(sp).move_to(sp)
rss.add(rs)
tf_anims = []
for sp, rs in zip(sps, rss):
tf_anims.append(ReplacementTransform(sp[0], rs[0]))
tf_anims.append(ReplacementTransform(sp[1], rs[3][2], path_arc = -TAU/4))
tf_anims.append(ReplacementTransform(sp[2], rs[1]))
tf_anims.append(ReplacementTransform(sp[3], rs[2]))
tf_anims.append(Write(rs[3][:2]))
self.play(FadeIn(sps))
self.wait()
self.play(AnimationGroup(*tf_anims), run_time = 2)
self.wait()
self.play(Write(VGroup(*[rs[4:] for rs in rss]), submobject_mode = "all_at_once"))
self.wait()
self.play(FadeOut(rects))
self.wait()
self.rss = rss
def teacher_holds_up(self, mobject, target_mode="raise_right_hand", **kwargs):
mobject.move_to(self.hold_up_spot, DOWN)
mobject.shift_onto_screen()
mobject_copy = mobject.copy()
mobject_copy.shift(DOWN)
mobject_copy.fade(1)
self.play(
ReplacementTransform(mobject_copy, mobject),
self.teacher.change, target_mode,
)
def rhs_could_be_any_number(self):
rhs_list = [
"2", # The journey starts here.
"3", # The first number that pops into your head when you hear "2".
"\\pi", # The good ol' pi.
"\\sqrt{2}", # The (most) famous irrational number.
"42", # The answer to everything.
"17.29", # TAXI.CAB
"-1", # A negative number, because why not?
"e", # The (most) famous mathematical constant.
"\\dfrac{3+\\sqrt{13}}{2}", # The bronze ratio... and a fraction.
"570", # 1/3 of the author.
"\\varphi", # The golden ratio.
"g_{64}", # Gigigigigigigigantic...
"0", # And... stop!
"N",
]
anything_text = TextMobject("等号右边似乎可以放任何数...")
anything_text.set_color(YELLOW)
anything_text.to_edge(UP)
equations = [
VGroup(ExpTower(order = 5), TexMobject("=", rhs).scale(0.8)).scale(2.5)
for rhs in rhs_list
]
init_equation = equations[0]
init_equation.arrange_submobjects(RIGHT, aligned_edge = DOWN)
init_equation.next_to(anything_text, DOWN, buff = self.tower_edge_buff)
init_equation.to_edge(LEFT, buff = self.tower_edge_buff)
for equation in equations:
equation[0].move_to(init_equation[0])
equation[1][0].move_to(init_equation[1][0])
equation[1][1].move_to(init_equation[1][1], aligned_edge = LEFT)
self.play(FadeIn(init_equation))
self.wait()
self.play(Write(anything_text), run_time = 1)
self.play(
ShowCreationThenDestruction(SurroundingRectangle(init_equation[1][1])),
run_time = 2
)
self.wait()
for k, equation in enumerate(equations):
if k > 0 and k != len(equations)-1:
equation[0].move_to(init_equation[0])
equation[1].move_to(init_equation[1], aligned_edge = LEFT)
self.remove(equations[k-1])
self.add(equations[k])
self.wait(1./3)
elif k == len(equations)-1:
self.wait()
self.play(ReplacementTransform(equations[k-1], equations[k]))
self.wait()
self.anything_text = anything_text
self.equation = equations[-1]
def update_mobject(self, new_mob, animate=True):
ret = []
if animate:
ret.extend(
[ReplacementTransform(self.mobject, new_mob, parent=self)])
else:
if hasattr(self, "mobject"):
self.remove(self.mobject)
self.add(new_mob)
self.mobject = new_mob
return ret
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 build_the_tower(self):
highest_order = 6
towers = [
ExpTower(order = k, is_infinite = False)
for k in range(1, highest_order + 1)
]
towers.append(ExpTower(order = highest_order, is_infinite = True))
heights = list(np.linspace(3, 4.5, highest_order + 2))
for tower, height in zip(towers, heights):
tower.set_height(height)
init_tower = towers[0]
final_tower = towers[-1]
self.play(Write(init_tower))
self.wait()
for k, tower in enumerate(towers):
if k < len(towers) - 2:
new_tower = towers[k+1]
new_exponent = new_tower.get_exponent()
new_base = new_tower.get_base()
self.play(
ReplacementTransform(tower, new_exponent),
Write(new_base),
)
self.wait()
else:
xs = final_tower.get_elements()
expdots = final_tower.get_expdots()
sur_rect = SurroundingRectangle(expdots)
self.play(
ReplacementTransform(tower, xs, run_time = 1),
Write(expdots, run_time = 2),
)
self.play(
Indicate(expdots, run_time = 1),
ShowCreationThenDestruction(sur_rect, run_time = 2),
)
self.wait()
break
self.tower = final_tower
self.highest_order = highest_order
def build_the_equation(self):
l_part = self.tower.copy()
r_part = TexMobject("=", "2")
r_part.match_height(l_part.get_base())
equation = VGroup(l_part, r_part)
equation.arrange_submobjects(RIGHT, aligned_edge = DOWN)
self.play(
ReplacementTransform(self.tower, l_part, run_time = 1),
Write(r_part, run_time = 2),
)
self.equation = equation
def update_mobject(self, new_mob, animate=True):
"""
Returns a list of animations of the mobject being updated
"""
ret = []
if animate:
if type(self.mobject) == Line and type(new_mob) == Arrow:
ret.extend([
FadeOut(self.mobject, parent=self),
FadeIn(new_mob, parent=self),
])
else:
ret.extend(
[ReplacementTransform(self.mobject, new_mob, parent=self)])
else:
if hasattr(self, "mobject"):
self.remove(self.mobject)
self.add(new_mob)
self.mobject = new_mob
return ret
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
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()
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)
group = VGroup(pos_axis, time_axis, pos_text, time_text)
group.to_edge(LEFT, buff=2)
self.add(group)
# Some preparations
sequences = [
"UDDDUDUD", "DUUDDDUD", "DDUUUDUD", "UUUDDUDU", "UDDDUDUD"
]
nums = [1, 3, 7, -1, 1]
walks = [
RandomWalk1DArrow(sequence).move_start_to(
pos_axis.number_to_point(0)) for sequence in sequences
]
parts = [walk.split_at(num) for walk, num in zip(walks, nums)]
split_lines = [
DashedLine(TOP, BOTTOM, color = GREY) \
.move_to(time_axis.number_to_point(num+1))
for num in nums
]
zero_words = [
TextMobject("“正点到家” \\\\ $P_%s$" % str((num+1)//2)) \
.next_to(line, LEFT).shift(2.8 * DOWN).set_color(ORANGE)
for num, line in zip(nums, split_lines)
]
nocross_words = [
TextMobject("“不经过家门” \\\\ $Q_%s$" % str(4-(num+1)//2)) \
.next_to(line, RIGHT).shift(2.8 * DOWN).set_color(GREEN)
for num, line in zip(nums, split_lines)
]
for words, direction in zip([zero_words, nocross_words],
[RIGHT, LEFT]):
for word in words:
text, symbol = VGroup(word[:-2]), VGroup(word[-2:])
symbol.scale(1.5)
symbol.next_to(text, DOWN, aligned_edge=direction)
word.add_background_rectangle()
# Demonstrate how to split
self.add(walks[0], split_lines[0], zero_words[0], nocross_words[0])
l = len(walks)
for k in range(l - 1):
cur_walk = walks[k]
cur_line = split_lines[k]
cur_zero_word = zero_words[k]
cur_nocross_word = nocross_words[k]
next_walk = walks[k + 1]
next_line = split_lines[k + 1]
next_zero_word = zero_words[k + 1]
next_nocross_word = nocross_words[k + 1]
part1, part2 = parts[k]
cur_walk.save_state()
self.play(
part1.set_color,
ORANGE,
part2.set_color,
GREEN,
)
self.wait()
self.play(cur_walk.restore)
self.wait()
self.play(
ReplacementTransform(cur_walk, next_walk),
ReplacementTransform(cur_line, next_line),
ReplacementTransform(cur_zero_word, next_zero_word),
ReplacementTransform(cur_nocross_word, next_nocross_word),
)
self.wait()
def show_the_solution(self):
# Prepare for the solution
pre_solve = VGroup(*self.question[::2])
self.play(
ReplacementTransform(pre_solve, self.solve),
FadeOut(self.question[1]),
run_time = 1,
)
self.wait()
# Manipulate LHS
old_l_part, r_part = self.equation
new_l_part = ExpTower(order = self.highest_order+1, is_infinite = True)
new_l_part.match_height(old_l_part)
new_l_part.next_to(r_part, LEFT, aligned_edge = DOWN)
old_rect, new_rect = rects = [
CoverRectangle(part, text = "2")
for part in (old_l_part, new_l_part.get_exponent())
]
old_two, new_two = twos = [
rect.get_text_mob()
for rect in rects
]
self.play(DrawBorderThenFill(old_rect, run_time = 1))
self.wait()
self.play(
ReplacementTransform(old_l_part, new_l_part),
ReplacementTransform(old_rect, new_rect),
)
self.wait()
new_equation = VGroup(new_l_part, r_part, new_rect)
new_equation.generate_target()
new_equation.target.scale(0.8)
new_equation.target.shift(UP)
self.play(MoveToTarget(new_equation))
self.wait()
# A little bit clean-up
source_eq = VGroup(*[
mob.copy()
for mob in (new_l_part.get_base(), new_two, r_part[0], r_part[1])
])
source_eq.generate_target()
target_eq = TexMobject("x", "^2", "=", "2")
target_eq.scale(3).next_to(source_eq, DOWN, buff = 1)
for k, (old_part, new_part) in enumerate(zip(source_eq.target, target_eq)):
old_part.move_to(new_part)
if k == 1:
old_part.scale(0.5)
old_part.shift(RIGHT/4)
self.play(
FadeOut(new_rect),
MoveToTarget(source_eq),
)
self.wait()
# Reveal the final answer
result = TexMobject("x", "=", "\\sqrt", "2")
result.set_height(source_eq.get_height() * 0.7)
result.move_to(source_eq)
self.play(*[
ReplacementTransform(source_eq[m], result[n], path_arc = angle)
for m, n, angle in [(0, 0, 0), (1, 2, -TAU/3), (2, 1, 0), (3, 3, 0)]
])
self.wait()
qed = QEDSymbol()
qed.next_to(result, RIGHT, aligned_edge = DOWN, buff = 1.5)
self.play(FadeIn(qed))
self.wait()