def __init__(self, **kwargs):
SVGMobject.__init__(self, **kwargs)
self.scale_to_fit_height(self.height)
self.set_stroke(color=WHITE, width=0)
self.set_fill(self.color, opacity=1)
from for_3b1b_videos.pi_creature import Randolph
randy = Randolph(mode="happy")
randy.scale_to_fit_height(0.6 * self.get_height())
randy.stretch(0.8, 0)
randy.look(RIGHT)
randy.move_to(self)
randy.shift(0.07 * self.height * (RIGHT + UP))
self.randy = self.pi_creature = randy
self.add_to_back(randy)
orientation_line = Line(self.get_left(), self.get_right())
orientation_line.set_stroke(width=0)
self.add(orientation_line)
self.orientation_line = orientation_line
for light, color in zip(self.get_lights(), self.light_colors):
light.set_fill(color, 1)
light.is_subpath = False
self.add_treds_to_tires()
def __init__(self, **kwargs):
SVGMobject.__init__(self, **kwargs)
self.scale_to_fit_height(self.height)
self.set_stroke(color = WHITE, width = 0)
self.set_fill(self.color, opacity = 1)
from for_3b1b_videos.pi_creature import Randolph
randy = Randolph(mode = "happy")
randy.scale_to_fit_height(0.6*self.get_height())
randy.stretch(0.8, 0)
randy.look(RIGHT)
randy.move_to(self)
randy.shift(0.07*self.height*(RIGHT+UP))
self.randy = self.pi_creature = randy
self.add_to_back(randy)
orientation_line = Line(self.get_left(), self.get_right())
orientation_line.set_stroke(width = 0)
self.add(orientation_line)
self.orientation_line = orientation_line
for light, color in zip(self.get_lights(), self.light_colors):
light.set_fill(color, 1)
light.is_subpath = False
self.add_treds_to_tires()
def __init__(self, mobject, **kwargs):
VGroup.__init__(self,
Line(UP + LEFT, DOWN + RIGHT),
Line(UP + RIGHT, DOWN + LEFT),
)
self.replace(mobject, stretch=True)
self.set_stroke(self.stroke_color, self.stroke_width)
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 __init__(self, **kwargs):
circle = Circle()
ticks = []
for x in range(12):
alpha = x / 12.
point = complex_to_R3(np.exp(2 * np.pi * alpha * complex(0, 1)))
length = 0.2 if x % 3 == 0 else 0.1
ticks.append(Line(point, (1 - length) * point))
self.hour_hand = Line(ORIGIN, 0.3 * UP)
self.minute_hand = Line(ORIGIN, 0.6 * UP)
# for hand in self.hour_hand, self.minute_hand:
# #Balance out where the center is
# hand.add(VectorizedPoint(-hand.get_end()))
VGroup.__init__(self, circle, self.hour_hand, self.minute_hand, *ticks)
def add_treds_to_tires(self):
for tire in self.get_tires():
radius = tire.get_width() / 2
center = tire.get_center()
tred = Line(0.9 * radius * RIGHT,
1.4 * radius * RIGHT,
stroke_width=2,
color=BLACK)
tred.rotate_in_place(np.pi / 4)
for theta in np.arange(0, 2 * np.pi, np.pi / 4):
new_tred = tred.copy()
new_tred.rotate(theta, about_point=ORIGIN)
new_tred.shift(center)
tire.add(new_tred)
return self
def generate_points(self):
start_angle = np.pi/2 + self.arc_angle/2
end_angle = np.pi/2 - self.arc_angle/2
self.add(Arc(
start_angle = start_angle,
angle = -self.arc_angle
))
tick_angle_range = np.linspace(start_angle, end_angle, self.num_ticks)
for index, angle in enumerate(tick_angle_range):
vect = rotate_vector(RIGHT, angle)
tick = Line((1-self.tick_length)*vect, vect)
label = TexMobject(str(10*index))
label.scale_to_fit_height(self.tick_length)
label.shift((1+self.tick_length)*vect)
self.add(tick, label)
needle = Polygon(
LEFT, UP, RIGHT,
stroke_width = 0,
fill_opacity = 1,
fill_color = self.needle_color
)
needle.stretch_to_fit_width(self.needle_width)
needle.stretch_to_fit_height(self.needle_height)
needle.rotate(start_angle - np.pi/2, about_point = ORIGIN)
self.add(needle)
self.needle = needle
self.center_offset = self.get_center()
def add_treds_to_tires(self):
for tire in self.get_tires():
radius = tire.get_width() / 2
center = tire.get_center()
tred = Line(
0.9 * radius * RIGHT, 1.4 * radius * RIGHT,
stroke_width=2,
color=BLACK
)
tred.rotate_in_place(np.pi / 4)
for theta in np.arange(0, 2 * np.pi, np.pi / 4):
new_tred = tred.copy()
new_tred.rotate(theta, about_point=ORIGIN)
new_tred.shift(center)
tire.add(new_tred)
return self
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 generate_points(self):
if self.x_radius is None:
center_to_edge = (FRAME_X_RADIUS + abs(self.center_point[0]))
self.x_radius = center_to_edge / self.x_unit_size
if self.y_radius is None:
center_to_edge = (FRAME_Y_RADIUS + abs(self.center_point[1]))
self.y_radius = center_to_edge / self.y_unit_size
self.axes = VMobject()
self.main_lines = VMobject()
self.secondary_lines = VMobject()
tuples = [
(
self.x_radius,
self.x_line_frequency,
self.y_radius * DOWN,
self.y_radius * UP,
RIGHT
),
(
self.y_radius,
self.y_line_frequency,
self.x_radius * LEFT,
self.x_radius * RIGHT,
UP,
),
]
for radius, freq, start, end, unit in tuples:
main_range = np.arange(0, radius, freq)
step = freq / float(freq + self.secondary_line_ratio)
for v in np.arange(0, radius, step):
line1 = Line(start + v * unit, end + v * unit)
line2 = Line(start - v * unit, end - v * unit)
if v == 0:
self.axes.add(line1)
elif v in main_range:
self.main_lines.add(line1, line2)
else:
self.secondary_lines.add(line1, line2)
self.add(self.secondary_lines, self.main_lines, self.axes)
self.stretch(self.x_unit_size, 0)
self.stretch(self.y_unit_size, 1)
self.shift(self.center_point)
# Put x_axis before y_axis
y_axis, x_axis = self.axes.split()
self.axes = VMobject(x_axis, y_axis)
def generate_points(self):
self.main_line = Line(self.x_min * RIGHT, self.x_max * RIGHT)
self.tick_marks = VGroup()
self.add(self.main_line, self.tick_marks)
rounding_value = int(-np.log10(0.1 * self.tick_frequency))
rounded_numbers_with_elongated_ticks = np.round(
self.numbers_with_elongated_ticks, rounding_value)
for x in self.get_tick_numbers():
rounded_x = np.round(x, rounding_value)
if rounded_x in rounded_numbers_with_elongated_ticks:
tick_size_used = self.longer_tick_multiple * self.tick_size
else:
tick_size_used = self.tick_size
self.add_tick(x, tick_size_used)
self.stretch(self.unit_size, 0)
self.shift(-self.number_to_point(self.number_at_center))
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 generate_points(self):
body = Cube(side_length=1)
for dim, scale_factor in enumerate(self.body_dimensions):
body.stretch(scale_factor, dim=dim)
body.scale_to_fit_width(self.width)
body.set_fill(self.shaded_body_color, opacity=1)
body.sort_submobjects(lambda p: p[2])
body[-1].set_fill(self.body_color)
keyboard = VGroup(*[
VGroup(*[
Square(**self.key_color_kwargs)
for x in range(12 - y % 2)
]).arrange_submobjects(RIGHT, buff=SMALL_BUFF)
for y in range(4)
]).arrange_submobjects(DOWN, buff=MED_SMALL_BUFF)
keyboard.stretch_to_fit_width(
self.keyboard_width_to_body_width * body.get_width(),
)
keyboard.stretch_to_fit_height(
self.keyboard_height_to_body_height * body.get_height(),
)
keyboard.next_to(body, OUT, buff=0.1 * SMALL_BUFF)
keyboard.shift(MED_SMALL_BUFF * UP)
body.add(keyboard)
screen_plate = body.copy()
screen_plate.stretch(self.screen_thickness /
self.body_dimensions[2], dim=2)
screen = Rectangle(
stroke_width=0,
fill_color=BLACK,
fill_opacity=1,
)
screen.replace(screen_plate, stretch=True)
screen.scale_in_place(self.screen_width_to_screen_plate_width)
screen.next_to(screen_plate, OUT, buff=0.1 * SMALL_BUFF)
screen_plate.add(screen)
screen_plate.next_to(body, UP, buff=0)
screen_plate.rotate(
self.open_angle, RIGHT,
about_point=screen_plate.get_bottom()
)
self.screen_plate = screen_plate
self.screen = screen
axis = Line(
body.get_corner(UP + LEFT + OUT),
body.get_corner(UP + RIGHT + OUT),
color=BLACK,
stroke_width=2
)
self.axis = axis
self.add(body, screen_plate, axis)
self.rotate(5 * np.pi / 12, LEFT, about_point=ORIGIN)
self.rotate(np.pi / 6, DOWN, about_point=ORIGIN)
def __init__(self, *text_parts, **kwargs):
TextMobject.__init__(self, *text_parts, **kwargs)
self.scale(self.scale_factor)
self.to_edge(UP)
if self.include_underline:
underline = Line(LEFT, RIGHT)
underline.next_to(self, DOWN, buff=self.underline_buff)
if self.match_underline_width_to_text:
underline.match_width(self)
else:
underline.set_width(self.underline_width)
self.add(underline)
self.underline = underline
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 get_tick(self, x, size=None):
if size is None:
size = self.tick_size
result = Line(size * DOWN, size * UP)
result.rotate(self.main_line.get_angle())
result.move_to(self.number_to_point(x))
return result
def scroll_through_patrons(self):
logo_box = Square(side_length=2.5)
logo_box.to_corner(DOWN + LEFT, buff=MED_LARGE_BUFF)
total_width = FRAME_X_RADIUS - logo_box.get_right()[0]
black_rect = Rectangle(
fill_color=BLACK,
fill_opacity=1,
stroke_width=0,
width=FRAME_WIDTH,
height=0.6 * FRAME_HEIGHT,
)
black_rect.to_edge(UP, buff=0)
line = DashedLine(FRAME_X_RADIUS * LEFT, FRAME_X_RADIUS * RIGHT)
line.move_to(ORIGIN)
self.add(line)
thanks = TextMobject("Funded by the community, with special thanks to:")
thanks.scale(0.9)
thanks.next_to(black_rect.get_bottom(), UP, SMALL_BUFF)
thanks.set_color(YELLOW)
underline = Line(LEFT, RIGHT)
underline.scale_to_fit_width(thanks.get_width() + MED_SMALL_BUFF)
underline.next_to(thanks, DOWN, SMALL_BUFF)
thanks.add(underline)
self.add(thanks)
patrons = VGroup(*map(TextMobject, self.specific_patrons))
patrons.scale(self.patron_scale_val)
for patron in patrons:
if patron.get_width() > self.max_patron_width:
patron.scale_to_fit_width(self.max_patron_width)
columns = VGroup(*[
VGroup(*patrons[i::self.n_patron_columns])
for i in range(self.n_patron_columns)
])
for column in columns:
for n, name in enumerate(column):
name.shift(n * self.name_y_spacing * DOWN)
columns.arrange_submobjects(
RIGHT, buff=LARGE_BUFF,
aligned_edge=UP,
)
columns.scale_to_fit_width(total_width - 1)
columns.next_to(black_rect, DOWN, 3 * LARGE_BUFF)
columns.to_edge(RIGHT)
thanks.align_to(columns, alignment_vect=RIGHT)
self.play(
columns.move_to, 2 * DOWN, DOWN,
columns.to_edge, RIGHT,
Animation(black_rect),
Animation(line),
Animation(thanks),
rate_func=None,
run_time=self.run_time,
)
def generate_points(self):
self.line_group = VGroup()
self.dot_group = VGroup()
vertices = self.generate_vertices_from_string(self.walk_string)
for k in range(len(vertices) - 1):
line = Line(vertices[k],
vertices[k + 1],
color=self.get_mob_color_by_number(k))
dot = Dot(vertices[k], color=self.dot_color)
self.line_group.add(line)
self.dot_group.add(dot)
self.dot_group.add(Dot(vertices[-1], color=self.dot_color))
self.add(self.line_group, self.dot_group)
self.horizontally_center()
def __init__(self, text, **kwargs):
TextMobject.__init__(self, text, **kwargs)
self.scale(self.scale_factor)
self.to_edge(UP)
if self.include_underline:
underline = Line(LEFT, RIGHT)
underline.next_to(self, DOWN, buff=self.underline_buff)
if self.match_underline_width_to_text:
underline.match_width(self)
else:
underline.scale_to_fit_width(self.underline_width)
self.add(underline)
self.underline = underline
def generate_points(self):
outer_rect = Rectangle(
width=self.diameter,
height=self.thickness,
fill_color=self.fill_color,
fill_opacity=self.fill_opacity,
stroke_color=self.stroke_color,
stroke_width=0, # self.stroke_width
)
self.add(outer_rect)
PI = TAU / 2
ridge_angles = np.arange(PI / self.nb_ridges, PI, PI / self.nb_ridges)
ridge_positions = 0.5 * self.diameter * np.array(
[np.cos(theta) for theta in ridge_angles])
ridge_color = interpolate_color(BLACK, self.stroke_color, 0.5)
for x in ridge_positions:
ridge = Line(x * RIGHT + 0.5 * self.thickness * DOWN,
x * RIGHT + 0.5 * self.thickness * UP,
stroke_color=ridge_color,
stroke_width=self.stroke_width)
self.add(ridge)
def get_secant_slope_group(
self,
x,
graph,
dx=None,
dx_line_color=None,
df_line_color=None,
dx_label=None,
df_label=None,
include_secant_line=True,
secant_line_color=None,
secant_line_length=10,
):
"""
Resulting group is of the form VGroup(
dx_line,
df_line,
dx_label, (if applicable)
df_label, (if applicable)
secant_line, (if applicable)
)
with attributes of those names.
"""
kwargs = locals()
kwargs.pop("self")
group = VGroup()
group.kwargs = kwargs
dx = dx or float(self.x_max - self.x_min) / 10
dx_line_color = dx_line_color or self.default_input_color
df_line_color = df_line_color or graph.get_color()
p1 = self.input_to_graph_point(x, graph)
p2 = self.input_to_graph_point(x + dx, graph)
interim_point = p2[0] * RIGHT + p1[1] * UP
group.dx_line = Line(p1, interim_point, color=dx_line_color)
group.df_line = Line(interim_point, p2, color=df_line_color)
group.add(group.dx_line, group.df_line)
labels = VGroup()
if dx_label is not None:
group.dx_label = TexMobject(dx_label)
labels.add(group.dx_label)
group.add(group.dx_label)
if df_label is not None:
group.df_label = TexMobject(df_label)
labels.add(group.df_label)
group.add(group.df_label)
if len(labels) > 0:
max_width = 0.8 * group.dx_line.get_width()
max_height = 0.8 * group.df_line.get_height()
if labels.get_width() > max_width:
labels.scale_to_fit_width(max_width)
if labels.get_height() > max_height:
labels.scale_to_fit_height(max_height)
if dx_label is not None:
group.dx_label.next_to(group.dx_line,
np.sign(dx) * DOWN,
buff=group.dx_label.get_height() / 2)
group.dx_label.set_color(group.dx_line.get_color())
if df_label is not None:
group.df_label.next_to(group.df_line,
np.sign(dx) * RIGHT,
buff=group.df_label.get_height() / 2)
group.df_label.set_color(group.df_line.get_color())
if include_secant_line:
secant_line_color = secant_line_color or self.default_derivative_color
group.secant_line = Line(p1, p2, color=secant_line_color)
group.secant_line.scale_in_place(secant_line_length /
group.secant_line.get_length())
group.add(group.secant_line)
return group
def generate_mobject(self, dic, labels_dict):
# Create a dictionary with all attributes to create a new Mobject.
# Unspecified values will be filled from the current Mobject if it
# exists, and with default values if not.
if "stroke_width" not in dic:
if hasattr(self, "mobject"):
dic["stroke_width"] = self.mobject.stroke_width
else:
print("Attempted to initialize Edge without stroke_width")
breakpoint(context=7)
if "rectangular_stem_width" not in dic:
if hasattr(self, "mobject"):
dic["rectangular_stem_width"] = \
self.mobject.rectangular_stem_width
else:
print("Attempted to initialize Edge without "
"rectangular_stem_width")
breakpoint(context=7)
if "scale_factor" not in dic:
if hasattr(self, "mobject"):
dic["scale_factor"] = self.mobject.scale_factor
else:
print("Attempted to initialize Edge without scale_factor")
breakpoint(context=7)
if "color" not in dic:
if hasattr(self, "mobject"):
dic["color"] = self.mobject.color
if "directed" not in dic:
if hasattr(self, "mobject") and self.mobject.directed:
dic["directed"] = self.mobject.directed
else:
dic["directed"] = False
if "curved" not in dic:
if hasattr(self, "mobject") and self.mobject.curved:
dic["curved"] = self.mobject.curved
else:
dic["curved"] = False
# where along the edge the label is placed
if "label_location" not in dic:
if hasattr(self, "mobject") and self.mobject.label_location:
dic["label_location"] = self.mobject.label_location
else:
dic["label_location"] = 0.5
# which side of the edge on which the label is placed
if "label_side" not in dic:
if hasattr(self, "mobject") and self.mobject.label_side:
dic["label_side"] = self.mobject.label_side
else:
dic["label_side"] = Side.CLOCKWISE
normalized_vec = self.end_node.mobject.get_center() - \
self.start_node.mobject.get_center()
normalized_vec = normalized_vec / numpy.linalg.norm(normalized_vec)
normal_vec = rotate_vector(normalized_vec, numpy.pi / 2)
if dic["directed"]:
mob = Arrow(self.start_node.mobject.get_center() + normalized_vec *
(self.start_node.mobject.radius - 0.0),
self.end_node.mobject.get_center() - normalized_vec *
(self.end_node.mobject.radius - 0.0),
buff=0,
**dic)
else:
mob = Line(
self.start_node.mobject.get_center() +
normalized_vec * self.start_node.mobject.radius,
self.end_node.mobject.get_center() -
normalized_vec * self.end_node.mobject.radius, **dic)
if dic["curved"]:
start, end = mob.get_start_and_end()
midpoint = (start + end) / 2
def f(x):
return x - 0.1 * normal_vec * \
(numpy.linalg.norm(start - midpoint) -
numpy.linalg.norm(x - midpoint))
mob.shift(-0.05 * normal_vec).apply_function(f)
return mob
def construct(self):
colors = ["#FF0000", "#FF8000", "#FFFF00", "#00FF00", "#0080FF"]
wallis_rects_4 = WallisRectangles(
order=5,
rect_colors=colors,
)
vert_lines = VGroup(*[
Line(3.5*UP, 3.5*DOWN, color = GREY, stroke_width = 3) \
.next_to(wallis_rects_4.get_rectangle(0, k), direction, buff = 0)
for k, direction in zip(list(range(5))+[4], [LEFT]*5+[RIGHT])
])
horiz_lines = VGroup(*[
Line(3.5*LEFT, 3.5*RIGHT, color = GREY, stroke_width = 3) \
.next_to(wallis_rects_4.get_rectangle(k, 0), direction, buff = 0)
for k, direction in zip(list(range(5))+[4], [DOWN]*5+[UP])
])
for vert_line in vert_lines:
vert_line.vertically_center()
for horiz_line in horiz_lines:
horiz_line.horizontally_center()
vert_labels = VGroup(*[
TexMobject("a_%d" % k) \
.move_to((vert_lines[k].get_center() + vert_lines[k+1].get_center())/2) \
.shift(3.5*DOWN)
for k in range(5)
])
horiz_labels = VGroup(*[
TexMobject("a_%d" % k) \
.move_to((horiz_lines[k].get_center() + horiz_lines[k+1].get_center())/2) \
.shift(3.5*LEFT)
for k in range(5)
])
area_texs = VGroup()
factors = [1.25, 1, 0.9, 0.7, 0.6]
for p in range(5):
for q in range(5 - p):
rect = wallis_rects_4.get_rectangle(p, q)
tex = TexMobject("{a_%d} {a_%d}" % (q, p))
tex.scale(factors[p + q])
tex.move_to(rect)
area_texs.add(tex)
figure = VGroup()
figure.add(wallis_rects_4, vert_lines, horiz_lines, vert_labels,
horiz_labels, area_texs)
figure.to_edge(LEFT)
self.add(figure)
tex_list = VGroup()
for p in range(5):
formula_string = (
" + ".join(["a_%d a_%d" % (q, p - q)
for q in range(p + 1)]) + "=1")
formula = TexMobject(formula_string)
tex_list.add(formula)
# tex_list.add(TexMobject("\\vdots"))
tex_factors = np.linspace(1, 0.7, 5)
for tex, color, factor in zip(tex_list, colors, tex_factors):
tex.set_color(color)
tex.scale(factor)
tex_list.arrange_submobjects(DOWN, aligned_edge=LEFT)
tex_list.to_edge(RIGHT)
self.add(tex_list)
self.wait()
def construct(self):
# Chart on the left
colors = [WHITE, ORANGE, GREEN]
titles = VGroup(*[
TexMobject(text).set_color(color)
for text, color in zip(["n", "p_n", "q_n"], colors)
])
contents = VGroup(*[
VGroup(*[
TexMobject("%d" % num) for num in
[k, central_binomial_coeff(k),
central_binomial_coeff(k)]
]) for k in range(8)
])
titles.arrange_submobjects(RIGHT, buff=1)
for num, line in enumerate(contents):
for k, element in enumerate(line):
buff = 0.6 + 0.8 * num
element.next_to(titles[k], DOWN, aligned_edge=LEFT, buff=buff)
element.set_color(colors[k])
sep_line = Line(ORIGIN, 4.5 * RIGHT, stroke_width=5)
sep_line.next_to(titles, DOWN)
chart = VGroup(titles, contents, sep_line)
chart.set_height(7)
chart.center().to_edge(LEFT)
self.add(chart)
# Figures on the right
std_zero_pos_axis = NumberLine(x_min=-2,
x_max=2,
color=GREY,
unit_size=0.25,
tick_size=0.05)
std_zero_pos_axis.rotate(np.pi / 2)
std_nocross_pos_axis = NumberLine(x_min=-4,
x_max=4,
color=GREY,
unit_size=0.25,
tick_size=0.05)
std_nocross_pos_axis.rotate(np.pi / 2)
std_time_axis = NumberLine(x_min=0,
x_max=5.5,
color=GREY,
unit_size=0.25,
tick_size=0.05)
std_zero_axes = VGroup(std_zero_pos_axis, std_time_axis)
std_nocross_axes = VGroup(std_nocross_pos_axis, std_time_axis)
zero_walks = VGroup()
for sequence in ["UUDD", "UDUD", "UDDU", "DDUU", "DUDU", "DUUD"]:
axes = std_zero_axes.copy()
zero_walk = RandomWalk1DArrow(sequence, step_size=0.25)
zero_walk.move_start_to(axes[0].number_to_point(0))
zero_walks.add(VGroup(axes, zero_walk))
zero_walks.arrange_submobjects_in_grid(2, 3, buff=0.5)
zero_rect = SurroundingRectangle(zero_walks, color=ORANGE, buff=0.4)
zero_walks.add(zero_rect)
nocross_walks = VGroup()
for sequence in ["DDDD", "DDUD", "DDDU", "UUUU", "UUDU", "UUUD"]:
axes = std_nocross_axes.copy()
nocross_walk = RandomWalk1DArrow(sequence, step_size=0.25)
nocross_walk.move_start_to(axes[0].number_to_point(0))
nocross_walks.add(VGroup(axes, nocross_walk))
nocross_walks.arrange_submobjects_in_grid(2, 3, buff=0.5)
nocross_rect = SurroundingRectangle(nocross_walks,
color=GREEN,
buff=0.4)
nocross_walks.add(nocross_rect)
relation = TexMobject("p_2", "=", "q_2", "=", "6")
relation[0].set_color(ORANGE)
relation[2].set_color(GREEN)
relation.scale(1.5)
figure = VGroup(zero_walks, relation, nocross_walks)
figure.arrange_submobjects(DOWN)
figure.set_height(7)
figure.center().to_edge(RIGHT)
self.add(figure)
self.wait()
class NumberLine(VMobject):
CONFIG = {
"color": LIGHT_GREY,
"x_min": -FRAME_X_RADIUS,
"x_max": FRAME_X_RADIUS,
"unit_size": 1,
"tick_size": 0.1,
"tick_frequency": 1,
"leftmost_tick": None, # Defaults to value near x_min s.t. 0 is a tick
"numbers_with_elongated_ticks": [0],
"include_numbers": False,
"numbers_to_show": None,
"longer_tick_multiple": 2,
"number_at_center": 0,
"number_scale_val": 0.75,
"label_direction": DOWN,
"line_to_number_buff": MED_SMALL_BUFF,
"include_tip": False,
"propagate_style_to_family": True,
}
def __init__(self, **kwargs):
digest_config(self, kwargs)
if self.leftmost_tick is None:
tf = self.tick_frequency
self.leftmost_tick = tf * np.ceil(self.x_min / tf)
VMobject.__init__(self, **kwargs)
if self.include_tip:
self.add_tip()
if self.include_numbers:
self.add_numbers()
def generate_points(self):
self.main_line = Line(self.x_min * RIGHT, self.x_max * RIGHT)
self.tick_marks = VGroup()
self.add(self.main_line, self.tick_marks)
rounding_value = int(-np.log10(0.1 * self.tick_frequency))
rounded_numbers_with_elongated_ticks = np.round(
self.numbers_with_elongated_ticks, rounding_value)
for x in self.get_tick_numbers():
rounded_x = np.round(x, rounding_value)
if rounded_x in rounded_numbers_with_elongated_ticks:
tick_size_used = self.longer_tick_multiple * self.tick_size
else:
tick_size_used = self.tick_size
self.add_tick(x, tick_size_used)
self.stretch(self.unit_size, 0)
self.shift(-self.number_to_point(self.number_at_center))
def add_tick(self, x, size=None):
self.tick_marks.add(self.get_tick(x, size))
return self
def get_tick(self, x, size=None):
if size is None:
size = self.tick_size
result = Line(size * DOWN, size * UP)
result.rotate(self.main_line.get_angle())
result.move_to(self.number_to_point(x))
return result
def get_tick_marks(self):
return self.tick_marks
def get_tick_numbers(self):
epsilon = 0.001
return np.arange(self.leftmost_tick, self.x_max + epsilon,
self.tick_frequency)
def number_to_point(self, number):
alpha = float(number - self.x_min) / (self.x_max - self.x_min)
return interpolate(self.main_line.get_start(),
self.main_line.get_end(), alpha)
def point_to_number(self, point):
left_point, right_point = self.main_line.get_start_and_end()
full_vect = right_point - left_point
def distance_from_left(p):
return np.dot(p - left_point,
full_vect) / np.linalg.norm(full_vect)
return interpolate(
self.x_min, self.x_max,
distance_from_left(point) / distance_from_left(right_point))
def default_numbers_to_display(self):
if self.numbers_to_show is not None:
return self.numbers_to_show
return np.arange(int(self.leftmost_tick), int(self.x_max) + 1)
def get_number_mobjects(self, *numbers, **kwargs):
# TODO, handle decimals
if len(numbers) == 0:
numbers = self.default_numbers_to_display()
if "force_integers" in kwargs and kwargs["force_integers"]:
numbers = list(map(int, numbers))
result = VGroup()
for number in numbers:
mob = TexMobject(str(number))
mob.scale(self.number_scale_val)
mob.next_to(
self.number_to_point(number),
self.label_direction,
self.line_to_number_buff,
)
result.add(mob)
return result
def get_labels(self):
return self.get_number_mobjects()
def add_numbers(self, *numbers, **kwargs):
self.numbers = self.get_number_mobjects(*numbers, **kwargs)
self.add(self.numbers)
return self
def add_tip(self):
start, end = self.main_line.get_start_and_end()
vect = (end - start) / np.linalg.norm(end - start)
arrow = Arrow(start, end + MED_SMALL_BUFF * vect, buff=0)
tip = arrow.tip
tip.set_color(self.color)
self.tip = tip
self.add(tip)
def add_axes(self):
x_axis = Line(self.tick_width * LEFT / 2, self.width * RIGHT)
y_axis = Line(MED_LARGE_BUFF * DOWN, self.height * UP)
ticks = VGroup()
heights = np.linspace(0, self.height, self.n_ticks + 1)
values = np.linspace(0, self.max_value, self.n_ticks + 1)
for y, value in zip(heights, values):
tick = Line(LEFT, RIGHT)
tick.scale_to_fit_width(self.tick_width)
tick.move_to(y * UP)
ticks.add(tick)
y_axis.add(ticks)
self.add(x_axis, y_axis)
self.x_axis, self.y_axis = x_axis, y_axis
if self.label_y_axis:
labels = VGroup()
for tick, value in zip(ticks, values):
label = TexMobject(str(np.round(value, 2)))
label.scale_to_fit_height(self.y_axis_label_height)
label.next_to(tick, LEFT, SMALL_BUFF)
labels.add(label)
self.y_axis_labels = labels
self.add(labels)
