mirror of
https://github.com/3b1b/manim.git
synced 2025-07-28 12:32:36 +08:00
middle of massive restructure, everything still broken
This commit is contained in:
Grant Sanderson
493
old_projects/counting_in_binary.py
Normal file
493
old_projects/counting_in_binary.py
Normal file
@ -0,0 +1,493 @@
|
||||
#!/usr/bin/env python
|
||||
|
||||
import numpy as np
|
||||
import itertools as it
|
||||
from copy import deepcopy
|
||||
import sys
|
||||
|
||||
|
||||
from animation import *
|
||||
from mobject import *
|
||||
from constants import *
|
||||
from region import *
|
||||
from scene import Scene, SceneFromVideo
|
||||
from script_wrapper import command_line_create_scene
|
||||
|
||||
MOVIE_PREFIX = "counting_in_binary/"
|
||||
BASE_HAND_FILE = os.path.join(MOVIE_DIR, MOVIE_PREFIX, "Base.mp4")
|
||||
FORCED_FRAME_DURATION = 0.02
|
||||
TIME_RANGE = (0, 42)
|
||||
INITIAL_PADDING = 27
|
||||
NUM_GOOD_FRAMES = 1223
|
||||
|
||||
ALGORITHM_TEXT = [
|
||||
"""
|
||||
\\begin{flushleft}
|
||||
Turn up the rightmost finger that is down.
|
||||
""", """
|
||||
Turn down all fingers to its right.
|
||||
\\end{flushleft}
|
||||
"""
|
||||
]
|
||||
FINGER_WORDS = [
|
||||
"Thumb",
|
||||
"Index Finger",
|
||||
"Middle Finger",
|
||||
"Ring Finger",
|
||||
"Pinky",
|
||||
]
|
||||
|
||||
COUNT_TO_FRAME_NUM = {
|
||||
0 : 0,
|
||||
1 : 27,
|
||||
2 : 76,
|
||||
3 : 110,
|
||||
4 : 163,
|
||||
5 : 189,
|
||||
6 : 226,
|
||||
7 : 264,
|
||||
8 : 318,
|
||||
9 : 356,
|
||||
10 : 384,
|
||||
11 : 423,
|
||||
12 : 457,
|
||||
13 : 513,
|
||||
14 : 528,
|
||||
15 : 590,
|
||||
16 : 620,
|
||||
17 : 671,
|
||||
18 : 691,
|
||||
19 : 740,
|
||||
20 : 781,
|
||||
21 : 810,
|
||||
22 : 855,
|
||||
23 : 881,
|
||||
24 : 940,
|
||||
25 : 970,
|
||||
26 : 1014,
|
||||
27 : 1055,
|
||||
28 : 1092,
|
||||
29 : 1143,
|
||||
30 : 1184,
|
||||
31 : 1219,
|
||||
}
|
||||
|
||||
COUNT_TO_TIP_POS = {
|
||||
0 : [5.0, 0.5, 0.0],
|
||||
1 : [3.1, 2.5, 0.0],
|
||||
2 : [1.5, 2.3, 0.0],
|
||||
3 : [0.7, 2.0, 0.0],
|
||||
4 : [0.0, 1.0, 0.0],
|
||||
}
|
||||
|
||||
def finger_tip_power_of_2(finger_no):
|
||||
return tex_mobject(str(2**finger_no)).shift(COUNT_TO_TIP_POS[finger_no])
|
||||
|
||||
class Hand(ImageMobject):
|
||||
STARTING_BOTTOM_RIGHT = [4.61111111e+00, -3.98888889e+00, 9.80454690e-16]
|
||||
def __init__(self, num, small = False, **kwargs):
|
||||
Mobject2D.__init__(self, **kwargs)
|
||||
path = os.path.join(
|
||||
MOVIE_DIR, MOVIE_PREFIX, "images", "Hand%d.png"%num
|
||||
)
|
||||
invert = False
|
||||
if not self.read_in_cached_attrs(path, invert):
|
||||
ImageMobject.__init__(self, path, invert = invert)
|
||||
center = self.get_center()
|
||||
self.center()
|
||||
self.rotate(np.pi, axis = RIGHT+UP)
|
||||
self.sort_points(lambda p : np.log(complex(*p[:2])).imag)
|
||||
self.rotate(np.pi, axis = RIGHT+UP)
|
||||
self.shift(center)
|
||||
self.cache_attrs(path, invert = False)
|
||||
self.shift(self.STARTING_BOTTOM_RIGHT-self.get_boundary_point(DOWN+RIGHT))
|
||||
if small:
|
||||
self.shrink()
|
||||
|
||||
def shrink(self):
|
||||
self.scale_in_place(0.8).to_edge(DOWN, buff = 0.0)
|
||||
|
||||
# def highlight_thumb(self, color = "yellow"):
|
||||
# self.highlight(
|
||||
# color = color,
|
||||
# condition = lambda p : p[0] > 4.5 and p[1] > -1.5
|
||||
# )
|
||||
|
||||
def get_algorithm():
|
||||
return text_mobject(ALGORITHM_TEXT)
|
||||
|
||||
def get_finger_colors():
|
||||
return list(Color("yellow").range_to("red", 5))
|
||||
|
||||
def five_char_binary(num):
|
||||
result = bin(num)[2:]
|
||||
return (5-len(result))*"0" + result
|
||||
|
||||
def read_reversed_binary(string):
|
||||
return sum([
|
||||
2**count if char == '1' else 0
|
||||
for count, char in zip(it.count(), string)
|
||||
])
|
||||
|
||||
class LeftHand(Hand):
|
||||
def __init__(self, num, **kwargs):
|
||||
Hand.__init__(
|
||||
self,
|
||||
read_reversed_binary(five_char_binary(num)),
|
||||
**kwargs
|
||||
)
|
||||
self.rotate(np.pi, UP)
|
||||
self.shift(LEFT)
|
||||
|
||||
def get_hand_map(which_hand = "right"):
|
||||
if which_hand == "right":
|
||||
Class = Hand
|
||||
elif which_hand == "left":
|
||||
Class = LeftHand
|
||||
else:
|
||||
print "Bad arg, bro"
|
||||
return
|
||||
return dict([
|
||||
(num, Class(num, small=True))
|
||||
for num in range(32)
|
||||
])
|
||||
|
||||
class OverHand(SceneFromVideo):
|
||||
def construct(self):
|
||||
SceneFromVideo.construct(self, BASE_HAND_FILE)
|
||||
self.frame_duration = FORCED_FRAME_DURATION
|
||||
self.frames = self.frames[:NUM_GOOD_FRAMES]
|
||||
|
||||
|
||||
class SaveEachNumber(OverHand):
|
||||
def construct(self):
|
||||
OverHand.construct(self)
|
||||
for count in COUNT_TO_FRAME_NUM:
|
||||
path = os.path.join(
|
||||
MOVIE_DIR, MOVIE_PREFIX, "images",
|
||||
"Hand%d.png"%count
|
||||
)
|
||||
Image.fromarray(self.frames[COUNT_TO_FRAME_NUM[count]]).save(path)
|
||||
|
||||
def write_to_movie(self, name = None):
|
||||
print "Why bother writing to movie..."
|
||||
|
||||
class ShowCounting(OverHand):
|
||||
def construct(self):
|
||||
OverHand.construct(self)
|
||||
self.frames = INITIAL_PADDING*[self.frames[0]] + self.frames
|
||||
num_frames = len(self.frames)
|
||||
self.frames = [
|
||||
disp.paint_mobject(
|
||||
self.get_counting_mob(32*count // num_frames),
|
||||
frame
|
||||
)
|
||||
for frame, count in zip(self.frames, it.count())
|
||||
]
|
||||
|
||||
def get_counting_mob(self, count):
|
||||
mob = tex_mobject(str(count))
|
||||
mob.scale(2)
|
||||
mob.shift(LEFT)
|
||||
mob.to_edge(UP, buff = 0.1)
|
||||
return mob
|
||||
|
||||
|
||||
class ShowFrameNum(OverHand):
|
||||
def construct(self):
|
||||
OverHand.construct(self)
|
||||
for frame, count in zip(self.frames, it.count()):
|
||||
print count, "of", len(self.frames)
|
||||
mob = CompoundMobject(*[
|
||||
tex_mobject(char).shift(0.3*x*RIGHT)
|
||||
for char, x, in zip(str(count), it.count())
|
||||
])
|
||||
self.frames[count] = disp.paint_mobject(
|
||||
mob.to_corner(UP+LEFT),
|
||||
frame
|
||||
)
|
||||
|
||||
class CountTo1023(Scene):
|
||||
def construct(self):
|
||||
rh_map = get_hand_map("right")
|
||||
lh_map = get_hand_map("left")
|
||||
def get_num(count):
|
||||
return CompoundMobject(*[
|
||||
tex_mobject(char).shift(0.35*x*RIGHT)
|
||||
for char, x, in zip(str(count), it.count())
|
||||
]).center().to_edge(UP)
|
||||
self.frames = [
|
||||
disp.paint_mobject(CompoundMobject(
|
||||
rh_map[count%32], lh_map[count//32], get_num(count)
|
||||
))
|
||||
for count in range(2**10)
|
||||
]
|
||||
|
||||
class Introduction(Scene):
|
||||
def construct(self):
|
||||
words = text_mobject("""
|
||||
First, let's see how to count
|
||||
to 31 on just one hand...
|
||||
""")
|
||||
hand = Hand(0)
|
||||
for mob in words, hand:
|
||||
mob.sort_points(lambda p : p[0])
|
||||
|
||||
self.add(words)
|
||||
self.dither()
|
||||
self.play(DelayByOrder(Transform(words, hand)))
|
||||
self.dither()
|
||||
|
||||
|
||||
class ShowReadingRule(Scene):
|
||||
def construct(self):
|
||||
sample_counts = [6, 17, 27, 31]
|
||||
question = text_mobject("""
|
||||
How do you recognize what number a given configuration represents?
|
||||
""", size = "\\Huge").scale(0.75).to_corner(UP+LEFT)
|
||||
answer = text_mobject([
|
||||
"Think of each finger as representing a power of 2, ",
|
||||
"then add up the numbers represented by the standing fingers."
|
||||
], size = "\\Huge").scale(0.75).to_corner(UP+LEFT).split()
|
||||
self.add(question)
|
||||
for count in sample_counts:
|
||||
hand = Hand(count, small = True)
|
||||
self.add(hand)
|
||||
self.dither()
|
||||
self.remove(hand)
|
||||
self.add(hand)
|
||||
self.dither()
|
||||
self.remove(question)
|
||||
self.add(answer[0])
|
||||
counts = map(finger_tip_power_of_2, range(5))
|
||||
for count in counts:
|
||||
self.play(SpinInFromNothing(count, run_time = 0.3))
|
||||
self.dither()
|
||||
self.play(ShimmerIn(answer[1]))
|
||||
for count in sample_counts:
|
||||
self.clear()
|
||||
self.add(*answer)
|
||||
self.read_sample(count)
|
||||
|
||||
def read_sample(self, num):
|
||||
hand = Hand(num, small = True)
|
||||
bool_arr = [c == '1' for c in five_char_binary(num)]
|
||||
counts = [4-count for count in range(5) if bool_arr[count]]
|
||||
count_mobs = map(finger_tip_power_of_2, counts)
|
||||
if num in [6, 27]:
|
||||
count_mobs[1].shift(0.2*DOWN + 0.2*LEFT)
|
||||
if num in [6, 17]:
|
||||
hand.shift(0.8*LEFT)
|
||||
sum_mobs = tex_mobject(
|
||||
" + ".join([str(2**c) for c in counts]).split(" ") + ["=%d"%num]
|
||||
).to_corner(UP+RIGHT).split()
|
||||
self.add(hand, *count_mobs)
|
||||
self.dither()
|
||||
self.play(*[
|
||||
Transform(count_mobs[n/2], sum_mobs[n])
|
||||
if n%2 == 0 and n/2 < len(counts)
|
||||
else FadeIn(sum_mobs[n])
|
||||
for n in range(len(sum_mobs))
|
||||
])
|
||||
self.dither(2.0)
|
||||
|
||||
|
||||
class ShowIncrementRule(Scene):
|
||||
def construct(self):
|
||||
#First count from 18 to 22
|
||||
def to_left(words):
|
||||
return "\\begin{flushleft}" + words + "\\end{flushleft}"
|
||||
phrases = [
|
||||
text_mobject(to_left(words), size = "\\Huge").scale(0.75).to_corner(UP+LEFT)
|
||||
for words in [
|
||||
"But while you're counting, you don't need to think about powers of 2.",
|
||||
"Can you see the pattern for incrementing?",
|
||||
"If the thumb is down, turn it up.",
|
||||
"If the thumb is up, but the forefinger is down, flip them both.",
|
||||
"If the thumb and forefinger are up, but the middle finger is down, flip all three.",
|
||||
"In general, flip all of the fingers up to the rightmost one which is down.",
|
||||
"After practicing for a minute or two, you're mind starts doing it automatically.",
|
||||
"Question: Why does this rule for incrementation work?",
|
||||
]
|
||||
]
|
||||
ranges = [
|
||||
(0, 14, False),
|
||||
(14, 28, False),
|
||||
(12, 13, True),
|
||||
(29, 31, True),
|
||||
(27, 29, True),
|
||||
(23, 24, True),
|
||||
(14, 20, False),
|
||||
(20, 26, False)
|
||||
]
|
||||
oh = OverHand()
|
||||
for phrase, (start, end, pause) in zip(phrases, ranges):
|
||||
if pause:
|
||||
self.background = oh.frames[COUNT_TO_FRAME_NUM[start]]
|
||||
self.add(phrase)
|
||||
self.play(ShimmerIn(self.get_arrow_set(start)))
|
||||
self.dither()
|
||||
self.clear()
|
||||
self.reset_background()
|
||||
self.frames += [
|
||||
disp.paint_mobject(phrase, frame)
|
||||
for frame in oh.frames[COUNT_TO_FRAME_NUM[start]:COUNT_TO_FRAME_NUM[end]]
|
||||
]
|
||||
if pause:
|
||||
self.frames += [self.frames[-1]]*int(1.0/self.frame_duration)
|
||||
|
||||
def get_arrow_set(self, num):
|
||||
arrow = tex_mobject("\\downarrow", size = "\\Huge")
|
||||
arrow.highlight("green")
|
||||
arrow.shift(-arrow.get_bottom())
|
||||
if num == 12:
|
||||
tips = [(4, 1, 0)]
|
||||
elif num == 29:
|
||||
tips = [
|
||||
(6, 1.5, 0),
|
||||
(3, 1.5, 0),
|
||||
]
|
||||
elif num == 27:
|
||||
tips = [
|
||||
(5.5, 1.5, 0),
|
||||
(2.75, 3.5, 0),
|
||||
(2, 1.0, 0),
|
||||
]
|
||||
elif num == 23:
|
||||
tips = [
|
||||
(6, 1, 0),
|
||||
(3.25, 3.5, 0),
|
||||
(2.25, 3.5, 0),
|
||||
(1.5, 0.75, 0),
|
||||
]
|
||||
return CompoundMobject(*[
|
||||
deepcopy(arrow).shift(tip)
|
||||
for tip in tips
|
||||
])
|
||||
|
||||
|
||||
class MindFindsShortcuts(Scene):
|
||||
def construct(self):
|
||||
words1 = text_mobject("""
|
||||
Before long, your mind starts to recognize certain
|
||||
patterns without needing to perform the addition.
|
||||
""", size = "\\Huge").scale(0.75).to_corner(LEFT+UP)
|
||||
words2 = text_mobject("""
|
||||
Which makes it faster to recognize other patterns...
|
||||
""", size = "\\Huge").scale(0.75).to_corner(LEFT+UP)
|
||||
|
||||
hand = Hand(7).scale(0.5).center().shift(DOWN+2*LEFT)
|
||||
sum421 = tex_mobject("4+2+1").shift(DOWN+2*RIGHT)
|
||||
seven = tex_mobject("7").shift(DOWN+6*RIGHT)
|
||||
compound = CompoundMobject(
|
||||
Arrow(hand, sum421),
|
||||
sum421,
|
||||
Arrow(sum421, seven)
|
||||
)
|
||||
self.add(
|
||||
words1,
|
||||
hand,
|
||||
compound,
|
||||
seven
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
Transform(compound, Arrow(hand, seven).highlight("yellow")),
|
||||
ShimmerIn(text_mobject("Directly recognize").shift(1.5*DOWN+2*RIGHT))
|
||||
)
|
||||
self.dither()
|
||||
|
||||
self.clear()
|
||||
hands = dict([
|
||||
(num, Hand(num).center().scale(0.5).shift(DOWN))
|
||||
for num in [23, 16, 7]
|
||||
])
|
||||
hands[23].shift(5*LEFT)
|
||||
hands[16].shift(LEFT)
|
||||
hands[7].shift(3*RIGHT)
|
||||
for num in 7, 16:
|
||||
hands[num].add(tex_mobject(str(num)).shift(hands[num].get_top()+0.5*UP))
|
||||
plus = tex_mobject("+").shift(DOWN + RIGHT)
|
||||
equals = tex_mobject("=").shift(DOWN + 2.5*LEFT)
|
||||
equals23 = tex_mobject("=23").shift(DOWN + 5.5*RIGHT)
|
||||
|
||||
self.add(words2, hands[23])
|
||||
self.dither()
|
||||
self.play(
|
||||
Transform(
|
||||
deepcopy(hands[16]).highlight("black").center().shift(hands[23].get_center()),
|
||||
hands[16]
|
||||
),
|
||||
Transform(
|
||||
deepcopy(hands[7]).highlight("black").center().shift(hands[23].get_center()),
|
||||
hands[7]
|
||||
),
|
||||
Animation(hands[23]),
|
||||
FadeIn(equals),
|
||||
FadeIn(plus)
|
||||
)
|
||||
self.dither()
|
||||
self.play(ShimmerIn(equals23))
|
||||
self.dither()
|
||||
|
||||
|
||||
class CountingExampleSentence(ShowCounting):
|
||||
def construct(self):
|
||||
words = "As an example, this is me counting the number of words in this sentence on just one hand!"
|
||||
self.words = text_mobject(words.split(), size = "\\Huge").scale(0.7).to_corner(UP+LEFT, buff = 0.25).split()
|
||||
ShowCounting.construct(self)
|
||||
|
||||
def get_counting_mob(self, num):
|
||||
return CompoundMobject(*self.words[:num])
|
||||
|
||||
class FinishCountingExampleSentence(Scene):
|
||||
def construct(self):
|
||||
words = "As an example, this is me counting the number of words in this sentence on just one hand!"
|
||||
words = text_mobject(words, size = "\\Huge").scale(0.7).to_corner(UP+LEFT, buff = 0.25)
|
||||
hand = Hand(18)
|
||||
sixteen = tex_mobject("16").shift([0, 2.25, 0])
|
||||
two = tex_mobject("2").shift([3, 3.65, 0])
|
||||
eightteen = tex_mobject("18").shift([1.5, 2.5, 0])
|
||||
eightteen.sort_points()
|
||||
comp = CompoundMobject(sixteen, two)
|
||||
self.add(hand, comp, words)
|
||||
self.dither()
|
||||
self.play(Transform(comp, eightteen))
|
||||
self.dither()
|
||||
|
||||
class Question(Scene):
|
||||
def construct(self):
|
||||
self.add(text_mobject("Left to ponder: Why does this rule for incrementing work?"))
|
||||
|
||||
|
||||
class TwoHandStatement(Scene):
|
||||
def construct(self):
|
||||
self.add(text_mobject(
|
||||
"With 10 fingers, you can count up to $2^{10} - 1 = 1023$..."
|
||||
))
|
||||
|
||||
class WithToes(Scene):
|
||||
def construct(self):
|
||||
words = text_mobject([
|
||||
"If you were dexterous enough to use your toes as well,",
|
||||
"you could count to 1,048,575"
|
||||
]).split()
|
||||
self.add(words[0])
|
||||
self.dither()
|
||||
self.play(ShimmerIn(words[1]))
|
||||
self.dither()
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
command_line_create_scene(MOVIE_PREFIX)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user