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pretty little coin stacks and sequences

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This commit is contained in:
Ben Hambrecht
2018-04-10 13:56:27 +02:00
parent 9e2ce6ea62
commit 9b35a5daeb
2 changed files with 317 additions and 5 deletions
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320
active_projects/eop/chapter1.py
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@ -1,6 +1,19 @@
from big_ol_pile_of_manim_imports import *
class Coin(VMobject):
COIN_RADIUS = 0.3
COIN_THICKNESS = 0.4 * COIN_RADIUS
COIN_FORESHORTENING = 0.3
COIN_NB_RIDGES = 20
COIN_STROKE_WIDTH = 2
COIN_SEQUENCE_SPACING = 0.1
GRADE_COLOR_1 = COLOR_HEADS = RED
GRADE_COLOR_2 = COLOR_TAILS = BLUE
class PiCreatureCoin(VMobject):
CONFIG = {
"diameter": 0.8,
"thickness": 0.2,
@ -42,7 +55,7 @@ class CoinFlippingPiCreature(PiCreature):
def __init__(self, **kwargs):
coin = Coin() # Line(ORIGIN, 0.4 * RIGHT, stroke_width = 15, color = YELLOW)
coin = PiCreatureCoin() # Line(ORIGIN, 0.4 * RIGHT, stroke_width = 15, color = YELLOW)
PiCreature.__init__(self,**kwargs)
self.coin = coin
self.add(coin)
@ -88,7 +101,7 @@ class FlipCoin(AnimationGroup):
class CoinFlipScene(Scene):
class CoinFlippingPiCreatureScene(Scene):
def construct(self):
@ -101,7 +114,306 @@ class CoinFlipScene(Scene):
class UprightCoin(Circle):
# For use in coin sequences
CONFIG = {
"radius": COIN_RADIUS,
"stroke_width": COIN_STROKE_WIDTH,
"stroke_color": WHITE,
"fill_opacity": 1,
"symbol": "\euro"
}
def __init__(self, **kwargs):
Circle.__init__(self,**kwargs)
self.symbol_mob = TextMobject(self.symbol, stroke_color = self.stroke_color)
self.symbol_mob.scale_to_fit_height(0.5*self.get_height()).move_to(self)
self.add(self.symbol_mob)
class UprightHeads(UprightCoin):
CONFIG = {
"fill_color": COLOR_HEADS,
"symbol": "H",
}
class UprightTails(UprightCoin):
CONFIG = {
"fill_color": COLOR_TAILS,
"symbol": "T",
}
class CoinSequence(VGroup):
CONFIG = {
"sequence": [],
"spacing": COIN_SEQUENCE_SPACING
}
def __init__(self, sequence, **kwargs):
VGroup.__init__(self, **kwargs)
self.sequence = sequence
offset = 0
for symbol in self.sequence:
if symbol == "H":
new_coin = UprightHeads()
elif symbol == "T":
new_coin = UprightTails()
else:
new_coin = UprightCoin(symbol = symbol)
new_coin.shift(offset * RIGHT)
self.add(new_coin)
offset += self.spacing
class FlatCoin(UprightCoin):
# For use in coin stacks
CONFIG = {
"thickness": COIN_THICKNESS,
"foreshortening": COIN_FORESHORTENING,
"nb_ridges": COIN_NB_RIDGES
}
def __init__(self, **kwargs):
UprightCoin.__init__(self, **kwargs)
self.symbol_mob.rotate(TAU/8)
self.stretch_in_place(self.foreshortening, 1)
# draw the edge
control_points1 = self.points[12:25].tolist()
control_points2 = self.copy().shift(self.thickness * DOWN).points[12:25].tolist()
edge_anchors_and_handles = control_points1
edge_anchors_and_handles.append(edge_anchors_and_handles[-1] + self.thickness * DOWN)
edge_anchors_and_handles.append(edge_anchors_and_handles[-1] + self.thickness * UP)
edge_anchors_and_handles += control_points2[::-1] # list concatenation
edge_anchors_and_handles.append(edge_anchors_and_handles[-1] + self.thickness * UP)
edge_anchors_and_handles.append(edge_anchors_and_handles[-1] + self.thickness * DOWN)
edge_anchors_and_handles.append(control_points1[0])
#edge_anchors_and_handles = edge_anchors_and_handles[::-1]
edge = VMobject()
edge.set_points(edge_anchors_and_handles)
edge.set_fill(
color = self.fill_color,
opacity = self.fill_opacity
)
edge.set_stroke(width = self.stroke_width)
self.add(edge)
# draw the ridges
PI = TAU/2
ridge_angles = np.arange(PI/self.nb_ridges,PI,PI/self.nb_ridges)
ridge_positions = 0.5 * 2 * self.radius * np.array([
np.cos(theta) for theta in ridge_angles
])
ridge_color = interpolate_color(self.stroke_color, self.fill_color, 0.7)
for x in ridge_positions:
y = -(1 - (x/self.radius)**2)**0.5 * self.foreshortening * self.radius
ridge = Line(
x * RIGHT + y * UP,
x * RIGHT + y * UP + self.thickness * DOWN,
stroke_color = ridge_color,
stroke_width = self.stroke_width
)
self.add(ridge)
# redraw the unfilled edge to cover the ridge ends
empty_edge = edge.copy()
empty_edge.set_fill(opacity = 0)
self.add(empty_edge)
class FlatHeads(FlatCoin):
CONFIG = {
"fill_color": COLOR_HEADS,
"symbol": "H",
}
class FlatTails(FlatCoin):
CONFIG = {
"fill_color": COLOR_TAILS,
"symbol": "T",
}
class CoinStack(VGroup):
CONFIG = {
"coin_thickness": COIN_THICKNESS,
"size": 5,
"face": FlatCoin,
}
def generate_points(self):
for n in range(self.size):
coin = self.face(thickness = self.coin_thickness)
coin.shift(n * self.coin_thickness * UP)
self.add(coin)
class HeadsStack(CoinStack):
CONFIG = { "face": FlatHeads }
class TailsStack(CoinStack):
CONFIG = { "face": FlatTails }
class TallyStack(VGroup):
def __init__(self,h,t,**kwargs):
self.nb_heads = h
self.nb_tails = t
VGroup.__init__(self,**kwargs)
def generate_points(self):
stack1 = HeadsStack(size = self.nb_heads, coin_thickness = self.coin_thickness)
stack2 = TailsStack(size = self.nb_tails, coin_thickness = self.coin_thickness)
stack2.next_to(stack1, RIGHT, buff = SMALL_BUFF)
self.add(stack1, stack2)
class TestScene(Scene):
def construct(self):
#seq = CoinSequence(["H", "T", "T", "H"])
#self.add(seq)
stack = TallyStack(4,5, coin_thickness = COIN_THICKNESS)
self.add(stack)
self.wait()
class AreaSplittingScene(Scene):
def create_rect_row(self,n):
rects_group = VGroup()
for k in range(n+1):
proportion = float(choose(n,k)) / 2**n
new_rect = Rectangle(
width = proportion * WIDTH,
height = HEIGHT,
fill_color = graded_color(n,k),
fill_opacity = 1
)
new_rect.next_to(rects_group,RIGHT,buff = 0)
rects_group.add(new_rect)
return rects_group
def split_rect_row(self,rect_row):
split_row = VGroup()
for rect in rect_row.submobjects:
half = rect.copy().stretch_in_place(0.5,0)
left_half = half.next_to(rect.get_center(),LEFT,buff = 0)
right_half = half.copy().next_to(rect.get_center(),RIGHT,buff = 0)
split_row.add(left_half, right_half)
return split_row
def rect_center(self,n,i,j):
if n < 0:
raise Exception("wrong indices " + str(n) + ", " + str(i) + ", " + str(j))
if i < 0 or i > n:
raise Exception("wrong indices " + str(n) + ", " + str(i) + ", " + str(j))
if j > choose(n,i) or j < 0:
raise Exception("wrong indices " + str(n) + ", " + str(i) + ", " + str(j))
rect = self.brick_array[n][i]
width = rect.get_width()
left_x = rect.get_center()[0] - width/2
spacing = width / choose(n,i)
x = left_x + (j+0.5) * spacing
return np.array([x,rect.get_center()[1], rect.get_center()[2]])
def construct(self):
# Draw the bricks
brick_wall = VGroup()
rect_row = self.create_rect_row(0)
rect_row.move_to(3.5*UP + 0*HEIGHT*DOWN)
self.add(rect_row)
brick_wall.add(rect_row)
self.brick_array = [[rect_row.submobjects[0]]]
for n in range(NB_ROWS):
# copy and shift
new_rect_row = rect_row.copy()
self.add(new_rect_row)
self.play(new_rect_row.shift,HEIGHT * DOWN)
self.wait()
#split
split_row = self.split_rect_row(new_rect_row)
self.play(FadeIn(split_row))
self.remove(new_rect_row)
self.wait()
# merge
rect_row = self.create_rect_row(n+1)
rect_row.move_to(3.5*UP + (n+1)*HEIGHT*DOWN)
self.play(FadeIn(rect_row))
brick_wall.add(rect_row)
self.remove(split_row)
self.wait()
# add to brick dict
rect_array = []
for rect in rect_row.submobjects:
rect_array.append(rect)
self.brick_array.append(rect_array)
self.play(
brick_wall.set_fill, {"opacity" : 0.2}
)
# Draw the branches
for (n, rect_row_array) in enumerate(self.brick_array):
for (i, rect) in enumerate(rect_row_array):
pos = rect.get_center()
tally = TallyStack(n - i, i)
tally.move_to(pos)
# from the left
lines = VGroup()
if i > 0:
for j in range(choose(n-1,i-1)):
start_pos = self.rect_center(n-1,i-1,j)
end_pos = self.rect_center(n,i,j)
lines.add(Line(start_pos,end_pos, stroke_color = GRADE_COLOR_2))
self.play(
LaggedStart(ShowCreation, lines))
# from the right
lines = VGroup()
if i < n:
for j in range(choose(n-1,i)):
start_pos = self.rect_center(n-1,i,j)
if i != 0:
end_pos = self.rect_center(n,i,choose(n-1,i-1) + j)
else:
end_pos = self.rect_center(n,i,j)
lines.add(Line(start_pos,end_pos, stroke_color = GRADE_COLOR_1))
self.play(
LaggedStart(ShowCreation, lines))
#self.play(FadeIn(tally))

2
active_projects/eop/histograms.py
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@ -1,7 +1,7 @@
from big_ol_pile_of_manim_imports import *
from random import *
def text_range(start,stop,step):
def text_range(start,stop,step): # a range as a list of strings
numbers = np.arange(start,stop,step)
labels = []
for x in numbers: