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 topics.characters 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()
class TransformOverIncreasingOrders(SpaceFillingCurveScene):
def setup(self, CurveClass):
sample = CurveClass(order = 1)
self.curve = Line(3*LEFT, 3*RIGHT)
self.curve.gradient_highlight(
sample.start_color,
sample.end_color
)
self.CurveClass = CurveClass
self.order = 0
def construct(self, CurveClass, max_order):
self.setup(CurveClass)
while self.order < max_order:
self.increase_order()
self.dither()
def increase_order(self, *other_anims):
self.order += 1
new_curve = self.CurveClass(order = self.order)
self.play(
Transform(self.curve, new_curve),
*other_anims,
run_time = 3/np.sqrt(self.order)
)
class TransformOverIncreasingOrders(SpaceFillingCurveScene):
def setup(self, CurveClass):
sample = CurveClass(order = 1)
self.curve = Line(3*LEFT, 3*RIGHT)
self.curve.gradient_highlight(
sample.start_color,
sample.end_color
)
self.CurveClass = CurveClass
self.order = 0
def construct(self, CurveClass, max_order):
self.setup(CurveClass)
while self.order < max_order:
self.increase_order()
self.dither()
def increase_order(self, *other_anims):
self.order += 1
new_curve = self.CurveClass(order = self.order)
self.play(
Transform(self.curve, new_curve),
*other_anims,
run_time = 3/np.sqrt(self.order)
)
def construct(self):
curve = HilbertCurve(order = 6)
curve.highlight(WHITE)
colored_curve = curve.copy()
colored_curve.thin_out(3)
lion = ImageMobject("lion", invert = False)
lion.replace(curve, stretch = True)
sparce_lion = lion.copy()
sparce_lion.thin_out(100)
distance_matrix = cdist(colored_curve.points, sparce_lion.points)
closest_point_indices = np.apply_along_axis(
np.argmin, 1, distance_matrix
)
colored_curve.rgbas = sparce_lion.rgbas[closest_point_indices]
line = Line(5*LEFT, 5*RIGHT)
Mobject.align_data(line, colored_curve)
line.rgbas = colored_curve.rgbas
self.add(lion)
self.play(ShowCreation(curve, run_time = 3))
self.play(
FadeOut(lion),
Transform(curve, colored_curve),
run_time = 3
)
self.wait()
self.play(Transform(curve, line, run_time = 5))
self.wait()
def generate_points(self):
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.space_unit_to_x_unit, 0)
self.stretch(self.space_unit_to_y_unit, 1)
#Put x_axis before y_axis
y_axis, x_axis = self.axes.split()
self.axes = VMobject(x_axis, y_axis)
def construct(self):
curve = HilbertCurve(order = 6)
curve.highlight(WHITE)
colored_curve = curve.copy()
colored_curve.thin_out(3)
lion = ImageMobject("lion", invert = False)
lion.replace(curve, stretch = True)
sparce_lion = lion.copy()
sparce_lion.thin_out(100)
distance_matrix = cdist(colored_curve.points, sparce_lion.points)
closest_point_indices = np.apply_along_axis(
np.argmin, 1, distance_matrix
)
colored_curve.rgbs = sparce_lion.rgbs[closest_point_indices]
line = Line(5*LEFT, 5*RIGHT)
Mobject.align_data(line, colored_curve)
line.rgbs = colored_curve.rgbs
self.add(lion)
self.play(ShowCreation(curve, run_time = 3))
self.play(
FadeOut(lion),
Transform(curve, colored_curve),
run_time = 3
)
self.dither()
self.play(Transform(curve, line, run_time = 5))
self.dither()
def construct(self):
grid = get_grid()
grid.sort_points(np.linalg.norm)
freq_line = get_freq_line()
freq_line.sort_points(lambda p : p[0])
red, blue = Color(RED), Color(BLUE)
freq_line.gradient_highlight(red, blue)
colors = [
Color(rgb = interpolate(
np.array(red.rgb),
np.array(blue.rgb),
alpha
))
for alpha in np.arange(4)/3.
]
string = Line(3*LEFT, 3*RIGHT, color = colors[1])
vibration = Vibrate(string)
vibration_copy = vibration.copy()
vibration_copy.mobject.stroke_width = 1
sub_vibrations = [
Vibrate(
string.copy().shift((n-1)*UP).highlight(colors[n]),
overtones = 1,
spatial_period = 6./(n+1),
temporal_period = 1./(n+1),
amplitude = 0.5/(n+1)
)
for n in range(4)
]
words = TexMobject("&\\vdots \\\\ \\text{thousands }& \\text{of frequencies} \\\\ &\\vdots")
words.to_edge(UP, buff = 0.1)
self.add(grid)
self.dither()
self.play(DelayByOrder(ApplyMethod(
grid.gradient_highlight, red, blue
)))
self.play(Transform(grid, freq_line))
self.dither()
self.play(
ShimmerIn(
words,
rate_func = squish_rate_func(smooth, 0, 0.2)
),
*sub_vibrations,
run_time = 5
)
self.play(
*[
TransformAnimations(
sub_vib, vibration
)
for sub_vib in sub_vibrations
]+[FadeOut(words)]
)
self.clear()
self.add(freq_line)
self.play(vibration)
def setup(self, CurveClass):
sample = CurveClass(order = 1)
self.curve = Line(3*LEFT, 3*RIGHT)
self.curve.gradient_highlight(
sample.start_color,
sample.end_color
)
self.CurveClass = CurveClass
self.order = 0
def construct(self, order):
if order == 2:
result_tex = "(0.125, 0.75)"
elif order == 3:
result_tex = "(0.0758, 0.6875)"
phc, arg, result = TexMobject([
"\\text{PHC}_%d"%order,
"(0.3)",
"= %s"%result_tex
]).to_edge(UP).split()
function = TextMobject("Function", size = "\\normal")
function.shift(phc.get_center()+DOWN+2*LEFT)
function_arrow = Arrow(function, phc)
line = Line(5*LEFT, 5*RIGHT)
curve = HilbertCurve(order = order)
line.match_colors(curve)
grid = Grid(2**order, 2**order)
grid.fade()
for mob in curve, grid:
mob.scale(0.7)
index = int(0.3*line.get_num_points())
dot1 = Dot(line.points[index])
arrow1 = Arrow(arg, dot1, buff = 0.1)
dot2 = Dot(curve.points[index])
arrow2 = Arrow(result.get_bottom(), dot2, buff = 0.1)
self.add(phc)
self.play(
ShimmerIn(function),
ShowCreation(function_arrow)
)
self.dither()
self.remove(function_arrow, function)
self.play(ShowCreation(line))
self.dither()
self.play(
ShimmerIn(arg),
ShowCreation(arrow1),
ShowCreation(dot1)
)
self.dither()
self.remove(arrow1)
self.play(
FadeIn(grid),
Transform(line, curve),
Transform(dot1, dot2),
run_time = 2
)
self.dither()
self.play(
ShimmerIn(result),
ShowCreation(arrow2)
)
self.dither()
def construct(self, order):
if order == 2:
result_tex = "(0.125, 0.75)"
elif order == 3:
result_tex = "(0.0758, 0.6875)"
phc, arg, result = TexMobject([
"\\text{PHC}_%d"%order,
"(0.3)",
"= %s"%result_tex
]).to_edge(UP).split()
function = TextMobject("Function", size = "\\normal")
function.shift(phc.get_center()+DOWN+2*LEFT)
function_arrow = Arrow(function, phc)
line = Line(5*LEFT, 5*RIGHT)
curve = HilbertCurve(order = order)
line.match_colors(curve)
grid = Grid(2**order, 2**order)
grid.fade()
for mob in curve, grid:
mob.scale(0.7)
index = int(0.3*line.get_num_points())
dot1 = Dot(line.points[index])
arrow1 = Arrow(arg, dot1, buff = 0.1)
dot2 = Dot(curve.points[index])
arrow2 = Arrow(result.get_bottom(), dot2, buff = 0.1)
self.add(phc)
self.play(
ShimmerIn(function),
ShowCreation(function_arrow)
)
self.wait()
self.remove(function_arrow, function)
self.play(ShowCreation(line))
self.wait()
self.play(
ShimmerIn(arg),
ShowCreation(arrow1),
ShowCreation(dot1)
)
self.wait()
self.remove(arrow1)
self.play(
FadeIn(grid),
Transform(line, curve),
Transform(dot1, dot2),
run_time = 2
)
self.wait()
self.play(
ShimmerIn(result),
ShowCreation(arrow2)
)
self.wait()
def generate_points(self):
self.main_line = Line(self.x_min * RIGHT, self.x_max * RIGHT)
self.tick_marks = VMobject()
self.add(self.main_line, self.tick_marks)
for x in self.get_tick_numbers():
self.add_tick(x, self.tick_size)
for x in self.numbers_with_elongated_ticks:
self.add_tick(x, self.longer_tick_multiple * self.tick_size)
self.stretch(self.space_unit_to_num, 0)
self.shift(-self.number_to_point(self.number_at_center))
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.highlight(X_COLOR)
y_line.highlight(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
self.play(Write(array, run_time=1))
self.dither()
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.dither()
if clean_up:
self.clear()
self.add(*starting_mobjects)
def construct(self, order):
start_color, end_color = RED, GREEN
curve = HilbertCurve(order = order)
line = Line(5*LEFT, 5*RIGHT)
for mob in curve, line:
mob.gradient_highlight(start_color, end_color)
freq_line = get_freq_line()
freq_line.replace(line, stretch = True)
unit = 6./(2**order) #sidelength of pixel
up = unit*UP
right = unit*RIGHT
lower_left = 3*(LEFT+DOWN)
squares = Mobject(*[
Square(
side_length = unit,
color = WHITE
).shift(x*right+y*up)
for x, y in it.product(range(2**order), range(2**order))
])
squares.center()
targets = Mobject()
for square in squares.submobjects:
center = square.get_center()
distances = np.apply_along_axis(
lambda p : np.linalg.norm(p-center),
1,
curve.points
)
index_along_curve = np.argmin(distances)
fraction_along_curve = index_along_curve/float(curve.get_num_points())
target = square.copy().center().scale(0.8/(2**order))
line_index = int(fraction_along_curve*line.get_num_points())
target.shift(line.points[line_index])
targets.add(target)
self.add(squares)
self.play(ShowCreation(
curve,
run_time = 5,
rate_func = None
))
self.dither()
self.play(
Transform(curve, line),
Transform(squares, targets),
run_time = 3
)
self.dither()
self.play(ShowCreation(freq_line))
self.dither()
def construct(self, max_order):
sample = self.curve_class(order = 1)
curve = Line(sample.radius*LEFT, sample.radius*RIGHT)
curve.gradient_highlight(
sample.start_color,
sample.end_color
)
for order in range(1, max_order):
new_curve = self.curve_class(order = order)
self.play(
Transform(curve, new_curve),
run_time = 3/np.sqrt(order),
)
self.dither()
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)
for x in self.get_tick_numbers():
if x in self.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_lines(self, left, right):
line_kwargs = {
"color": BLUE,
"stroke_width": 2,
}
left_rows = [VMobject(*row) for row in left.get_mob_matrix()]
h_lines = VMobject()
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 = [
VMobject(*col) for col in np.transpose(right.get_mob_matrix())
]
v_lines = VMobject()
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 construct(self):
big_grid_dim = 20.
small_grid_dim = 6.
big_grid = Grid(64, 64, height=big_grid_dim, width=big_grid_dim)
big_grid.to_corner(UP + RIGHT, buff=2)
small_grid = big_grid.copy()
small_grid.scale(small_grid_dim / big_grid_dim)
small_grid.center()
pixel = MobjectFromRegion(
region_from_polygon_vertices(
*0.2 *
np.array([RIGHT + DOWN, RIGHT + UP, LEFT + UP, LEFT + DOWN])))
pixel.set_color(WHITE)
pixel_width = big_grid.width / big_grid.columns
pixel.scale_to_fit_width(pixel_width)
pixel.to_corner(UP + RIGHT, buff=2)
pixel.shift(5 * pixel_width * (2 * LEFT + DOWN))
freq_line = get_freq_line()
dot = Dot()
dot.shift(freq_line.get_center() + 2 * RIGHT)
string = Line(LEFT, RIGHT, color=GREEN)
arrow = Arrow(dot, string.get_center())
vibration_config = {
"overtones": 1,
"spatial_period": 2,
}
vibration, loud_vibration, quiet_vibration = [
Vibrate(string.copy(), amplitude=a, **vibration_config)
for a in [0.5, 1., 0.25]
]
self.add(small_grid)
self.dither()
self.play(Transform(small_grid, big_grid))
self.play(FadeIn(pixel))
self.dither()
self.play(FadeOut(small_grid), ShowCreation(freq_line))
self.remove(small_grid)
self.play(Transform(pixel, dot), )
self.dither()
self.play(ShowCreation(arrow))
self.play(loud_vibration)
self.play(TransformAnimations(loud_vibration, quiet_vibration),
ApplyMethod(dot.fade, 0.9))
self.clear()
self.add(freq_line, dot, arrow)
self.play(quiet_vibration)
def construct(self):
words = TextMobject("Order 2 Pseudo-Hilbert Curve")
words.to_edge(UP, buff=0.3)
words.highlight(GREEN)
grid2 = Grid(2, 2)
grid4 = Grid(4, 4, point_thickness=2)
# order_1_curve = HilbertCurve(order = 1)
# squaggle_curve = order_1_curve.copy().apply_function(
# lambda (x, y, z) : (x + np.cos(3*y), y + np.sin(3*x), z)
# )
# squaggle_curve.show()
mini_curves = [
HilbertCurve(order=1).scale(0.5).shift(1.5 * vect)
for vect in [LEFT + DOWN, LEFT + UP, RIGHT + UP, RIGHT + DOWN]
]
last_curve = mini_curves[0]
naive_curve = Mobject(last_curve)
for mini_curve in mini_curves[1:]:
line = Line(last_curve.points[-1], mini_curve.points[0])
naive_curve.add(line, mini_curve)
last_curve = mini_curve
naive_curve.ingest_sub_mobjects()
naive_curve.gradient_highlight(RED, GREEN)
order_2_curve = HilbertCurve(order=2)
self.add(words, grid2)
self.dither()
self.play(ShowCreation(grid4))
self.play(*[ShowCreation(mini_curve) for mini_curve in mini_curves])
self.dither()
self.play(ShowCreation(naive_curve, run_time=5))
self.remove(*mini_curves)
self.dither()
self.play(Transform(naive_curve, order_2_curve))
self.dither()
def __init__(self, source, target):
matching_line = Line(0.5 * DOWN, 0.5 * UP)
def matched_objects(source, target):
matched = VGroup(source.copy(), matching_line.copy(),
target.copy())
matched.arrange_submobjects(direction=DOWN)
return matched
final_mobj = VGroup(
*(matched_objects(s, t)
for (s, t) in zip(source.submobjects, target.submobjects)))
self.buff = 2 * DEFAULT_MOBJECT_TO_MOBJECT_BUFFER
final_mobj.arrange_submobjects(buff=self.buff)
final_mobj.center()
def match_animation(source, target, matched):
return AnimationGroup(Transform(source, matched.submobjects[0]),
ShowCreation(matched.submobjects[1]),
Transform(target, matched.submobjects[2]))
self.match_animations = [
match_animation(s, t, m) for (s, t, m) in zip(
source.submobjects, target.submobjects, final_mobj.submobjects)
]
self.matching = VGroup(*[mob[1] for mob in final_mobj])
def add_tick(self, x, size):
self.tick_marks.add(
Line(
x * RIGHT + size * DOWN,
x * RIGHT + size * UP,
))
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)
self.add(needle)
self.needle = needle
self.center_offset = self.get_center()
def get_circles_and_points(self, min_input, max_input):
input_left, input_right = [
self.interval.number_to_point(num)
for num in min_input, max_input
]
input_circle = Circle(
radius = np.linalg.norm(input_left-input_right)/2,
color = WHITE
)
input_circle.shift((input_left+input_right)/2)
input_points = Line(
input_left, input_right,
color = self.input_color
)
output_points = Mobject(color = self.output_color)
n = self.output.get_num_points()
output_points.add_points(
self.output.points[int(min_input*n):int(max_input*n)]
)
output_center = output_points.points[int(0.5*output_points.get_num_points())]
max_distance = np.linalg.norm(output_center-output_points.points[-1])
output_circle = Circle(
radius = max_distance,
color = WHITE
)
output_circle.shift(output_center)
return (
input_circle,
input_points,
output_circle,
output_points
)
def __init__(self, camera):
VMobject.__init__(self)
stroke = 20
factor = sum(PRODUCTION_QUALITY_CAMERA_CONFIG["pixel_shape"]) / sum(
camera.pixel_shape)
stroke /= factor
self.add(Circle())
h1, h2, x = 1, 1.5, 0.5
y = -np.sqrt(1 - x**2) + h1
self.add(Line([-x, y, 0], [-x, y - h1, 0]))
self.add(Line([0, 1, 0], [0, 1 - h2, 0]))
self.add(Line([x, y, 0], [x, y - h1, 0]))
self.set_stroke(color="#00ffff", width=stroke)
self.to_corner(RIGHT + DOWN)
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.highlight(X_COLOR)
y_line.highlight(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
self.play(Write(array, run_time = 1))
self.dither()
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.dither()
if clean_up:
self.clear()
self.add(*starting_mobjects)
def generate_points(self):
if self.x_radius is None:
center_to_edge = (SPACE_WIDTH + abs(self.center_point[0]))
self.x_radius = center_to_edge / self.x_unit_size
if self.y_radius is None:
center_to_edge = (SPACE_HEIGHT + 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 setup(self, CurveClass):
sample = CurveClass(order = 1)
self.curve = Line(3*LEFT, 3*RIGHT)
self.curve.gradient_highlight(
sample.start_color,
sample.end_color
)
self.CurveClass = CurveClass
self.order = 0
def generate_points(self):
self.main_line = Line(self.x_min*RIGHT, self.x_max*RIGHT)
self.tick_marks = VMobject()
self.add(self.main_line, self.tick_marks)
for x in self.get_tick_numbers():
self.add_tick(x, self.tick_size)
for x in self.numbers_with_elongated_ticks:
self.add_tick(x, self.longer_tick_multiple*self.tick_size)
self.stretch(self.unit_size, 0)
self.shift(-self.number_to_point(self.number_at_center))
def generate_points(self):
complex_power = 0.9
radius = self.initial_width / 2
circle = Circle(radius=radius)
circle.scale(1.0 / radius)
circle.apply_complex_function(lambda z: z**complex_power)
circle.scale(radius)
boundary_point_as_complex = radius * complex(-1)**complex_power
boundary_points = [[
boundary_point_as_complex.real,
unit * boundary_point_as_complex.imag, 0
] for unit in -1, 1]
tip = radius * (1.5 * LEFT + UP)
self.little_line = Line(boundary_points[0], tip)
self.circle = circle
self.add(circle, self.little_line, Line(boundary_points[1], tip))
self.highlight("white")
self.rotate(np.pi / 2)
self.stretch_to_fit_height(self.initial_height)
def zoom_in_on(self, number, zoom_factor, run_time=2.0):
unit_length_to_spatial_width = self.number_line.unit_length_to_spatial_width * zoom_factor
radius = SPACE_WIDTH / unit_length_to_spatial_width
tick_frequency = 10**(np.floor(np.log10(radius)))
left_tick = tick_frequency * (np.ceil(
(number - radius) / tick_frequency))
new_number_line = NumberLine(
numerical_radius=radius,
unit_length_to_spatial_width=unit_length_to_spatial_width,
tick_frequency=tick_frequency,
leftmost_tick=left_tick,
number_at_center=number)
new_displayed_numbers = new_number_line.default_numbers_to_display()
new_number_mobs = new_number_line.get_number_mobjects(
*new_displayed_numbers)
transforms = []
additional_mobjects = []
squished_new_line = new_number_line.copy()
squished_new_line.scale(1.0 / zoom_factor)
squished_new_line.shift(self.number_line.number_to_point(number))
squished_new_line.points[:, 1] = self.number_line.number_to_point(0)[1]
transforms.append(Transform(squished_new_line, new_number_line))
for mob, num in zip(new_number_mobs, new_displayed_numbers):
point = Point(self.number_line.number_to_point(num))
point.shift(new_number_line.get_vertical_number_offset())
transforms.append(Transform(point, mob))
for mob in self.mobjects:
if mob == self.number_line:
new_mob = mob.copy()
new_mob.shift(-self.number_line.number_to_point(number))
new_mob.stretch(zoom_factor, 0)
transforms.append(Transform(mob, new_mob))
continue
mob_center = mob.get_center()
number_under_center = self.number_line.point_to_number(mob_center)
new_point = new_number_line.number_to_point(number_under_center)
new_point += mob_center[1] * UP
if mob in self.number_mobs:
transforms.append(Transform(mob, Point(new_point)))
else:
transforms.append(
ApplyMethod(mob.shift, new_point - mob_center))
additional_mobjects.append(mob)
line_to_hide_pixelation = Line(self.number_line.get_left(),
self.number_line.get_right(),
color=self.number_line.get_color())
self.add(line_to_hide_pixelation)
self.play(*transforms, run_time=run_time)
self.clear()
self.number_line = new_number_line
self.displayed_numbers = new_displayed_numbers
self.number_mobs = new_number_mobs
self.add(self.number_line, *self.number_mobs)
self.add(*additional_mobjects)
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)
self.rotate(np.pi/6, DOWN)
def add_lines(self, left, right):
line_kwargs = {
"color" : BLUE,
"stroke_width" : 2,
}
left_rows = [
VMobject(*row) for row in left.get_mob_matrix()
]
h_lines = VMobject()
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 = [
VMobject(*col) for col in np.transpose(right.get_mob_matrix())
]
v_lines = VMobject()
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.dither()
self.show_frame()
def construct(self):
grid = Grid(64, 64)
space_region = Region()
space_mobject = MobjectFromRegion(space_region, DARK_GREY)
curve = PeanoCurve(order = 5).replace(space_mobject)
line = Line(5*LEFT, 5*RIGHT)
line.gradient_highlight(curve.start_color, curve.end_color)
for mob in grid, space_mobject:
mob.sort_points(np.linalg.norm)
infinitely = TextMobject("Infinitely")
detailed = TextMobject("detailed")
extending = TextMobject("extending")
detailed.next_to(infinitely, RIGHT)
extending.next_to(infinitely, RIGHT)
Mobject(extending, infinitely, detailed).center()
arrows = Mobject(*[
Arrow(2*p, 4*p)
for theta in np.arange(np.pi/6, 2*np.pi, np.pi/3)
for p in [rotate_vector(RIGHT, theta)]
])
self.add(grid)
self.wait()
self.play(Transform(grid, space_mobject, run_time = 5))
self.remove(grid)
self.highlight_region(space_region, DARK_GREY)
self.wait()
self.add(infinitely, detailed)
self.wait()
self.play(DelayByOrder(Transform(detailed, extending)))
self.play(ShowCreation(arrows))
self.wait()
self.clear()
self.highlight_region(space_region, DARK_GREY)
self.play(ShowCreation(line))
self.play(Transform(line, curve, run_time = 5))
def construct(self):
grid = Grid(64, 64)
space_region = Region()
space_mobject = MobjectFromRegion(space_region, DARK_GREY)
curve = PeanoCurve(order = 5).replace(space_mobject)
line = Line(5*LEFT, 5*RIGHT)
line.gradient_highlight(curve.start_color, curve.end_color)
for mob in grid, space_mobject:
mob.sort_points(np.linalg.norm)
infinitely = TextMobject("Infinitely")
detailed = TextMobject("detailed")
extending = TextMobject("extending")
detailed.next_to(infinitely, RIGHT)
extending.next_to(infinitely, RIGHT)
Mobject(extending, infinitely, detailed).center()
arrows = Mobject(*[
Arrow(2*p, 4*p)
for theta in np.arange(np.pi/6, 2*np.pi, np.pi/3)
for p in [rotate_vector(RIGHT, theta)]
])
self.add(grid)
self.dither()
self.play(Transform(grid, space_mobject, run_time = 5))
self.remove(grid)
self.highlight_region(space_region, DARK_GREY)
self.dither()
self.add(infinitely, detailed)
self.dither()
self.play(DelayByOrder(Transform(detailed, extending)))
self.play(ShowCreation(arrows))
self.dither()
self.clear()
self.highlight_region(space_region, DARK_GREY)
self.play(ShowCreation(line))
self.play(Transform(line, curve, run_time = 5))
def label_spaces(self):
input_space = TextMobject("Input Space")
input_space.to_edge(UP)
input_space.shift(LEFT * SPACE_WIDTH / 2)
output_space = TextMobject("Output Space")
output_space.to_edge(UP)
output_space.shift(RIGHT * SPACE_WIDTH / 2)
line = Line(UP * SPACE_HEIGHT, DOWN * SPACE_HEIGHT, color=WHITE)
self.play(
ShimmerIn(input_space),
ShimmerIn(output_space),
ShowCreation(line),
ShowCreation(self.interval),
)
self.dither()
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.highlight(X_COLOR)
y_line.highlight(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.dither()
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.dither()
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 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.highlight(X_COLOR)
y_line.highlight(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.dither()
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.dither()
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 construct(self):
def special_rotate(mob):
mob.rotate(0.9*np.pi/2, RIGHT)
mob.rotate(-np.pi/4, UP)
return mob
plane = NumberPlane()
copies = [
special_rotate(plane.copy().shift(u*n*OUT))
for n in range(1, 3)
for u in -1, 1
]
line = Line(4*IN, 4*OUT)
self.add(plane)
self.play(*[
ApplyFunction(special_rotate, mob, run_time = 3)
for mob in plane, line
])
self.dither()
for copy in copies:
self.play(Transform(plane.copy(), copy))
self.dither()
def construct(self):
big_grid_dim = 20.
small_grid_dim = 6.
big_grid = Grid(64, 64, height = big_grid_dim, width = big_grid_dim)
big_grid.to_corner(UP+RIGHT, buff = 2)
small_grid = big_grid.copy()
small_grid.scale(small_grid_dim/big_grid_dim)
small_grid.center()
pixel = MobjectFromRegion(
region_from_polygon_vertices(*0.2*np.array([
RIGHT+DOWN,
RIGHT+UP,
LEFT+UP,
LEFT+DOWN
]))
)
pixel.set_color(WHITE)
pixel_width = big_grid.width/big_grid.columns
pixel.scale_to_fit_width(pixel_width)
pixel.to_corner(UP+RIGHT, buff = 2)
pixel.shift(5*pixel_width*(2*LEFT+DOWN))
freq_line = get_freq_line()
dot = Dot()
dot.shift(freq_line.get_center() + 2*RIGHT)
string = Line(LEFT, RIGHT, color = GREEN)
arrow = Arrow(dot, string.get_center())
vibration_config = {
"overtones" : 1,
"spatial_period" : 2,
}
vibration, loud_vibration, quiet_vibration = [
Vibrate(string.copy(), amplitude = a, **vibration_config)
for a in [0.5, 1., 0.25]
]
self.add(small_grid)
self.dither()
self.play(
Transform(small_grid, big_grid)
)
self.play(FadeIn(pixel))
self.dither()
self.play(
FadeOut(small_grid),
ShowCreation(freq_line)
)
self.remove(small_grid)
self.play(
Transform(pixel, dot),
)
self.dither()
self.play(ShowCreation(arrow))
self.play(loud_vibration)
self.play(
TransformAnimations(loud_vibration, quiet_vibration),
ApplyMethod(dot.fade, 0.9)
)
self.clear()
self.add(freq_line, dot, arrow)
self.play(quiet_vibration)
class NumberLine(VMobject):
CONFIG = {
"color" : BLUE,
"x_min" : -SPACE_WIDTH,
"x_max" : SPACE_WIDTH,
"space_unit_to_num" : 1,
"tick_size" : 0.1,
"tick_frequency" : 0.5,
"leftmost_tick" : None, #Defaults to ceil(x_min)
"numbers_with_elongated_ticks" : [0],
"longer_tick_multiple" : 2,
"number_at_center" : 0,
"propogate_style_to_family" : True
}
def __init__(self, **kwargs):
digest_config(self, kwargs)
if self.leftmost_tick is None:
self.leftmost_tick = np.ceil(self.x_min)
VMobject.__init__(self, **kwargs)
def generate_points(self):
self.main_line = Line(self.x_min*RIGHT, self.x_max*RIGHT)
self.tick_marks = VMobject()
self.add(self.main_line, self.tick_marks)
for x in self.get_tick_numbers():
self.add_tick(x, self.tick_size)
for x in self.numbers_with_elongated_ticks:
self.add_tick(x, self.longer_tick_multiple*self.tick_size)
self.stretch(self.space_unit_to_num, 0)
self.shift(-self.number_to_point(self.number_at_center))
def add_tick(self, x, size):
self.tick_marks.add(Line(
x*RIGHT+size*DOWN,
x*RIGHT+size*UP,
))
return self
def get_tick_marks(self):
return self.tick_marks
def get_tick_numbers(self):
return np.arange(self.leftmost_tick, self.x_max, self.tick_frequency)
def number_to_point(self, number):
return interpolate(
self.main_line.get_left(),
self.main_line.get_right(),
float(number-self.x_min)/(self.x_max - self.x_min)
)
def point_to_number(self, point):
dist_from_left = (point[0]-self.main_line.get_left()[0])
num_dist_from_left = num_dist_from_left/self.space_unit_to_num
return self.x_min + dist_from_left
def default_numbers_to_display(self):
return self.get_tick_numbers()[::2]
def get_vertical_number_offset(self, direction = DOWN):
return 4*direction*self.tick_size
def get_number_mobjects(self, *numbers, **kwargs):
#TODO, handle decimals
if len(numbers) == 0:
numbers = self.default_numbers_to_display()
result = []
for number in numbers:
mob = TexMobject(str(int(number)))
mob.scale_to_fit_height(2*self.tick_size)
mob.shift(
self.number_to_point(number),
self.get_vertical_number_offset(**kwargs)
)
result.append(mob)
return result
def add_numbers(self, *numbers, **kwargs):
self.numbers = self.get_number_mobjects(
*numbers, **kwargs
)
self.add(*self.numbers)
return self
class NumberLine(VMobject):
CONFIG = {
"color" : BLUE,
"x_min" : -SPACE_WIDTH,
"x_max" : SPACE_WIDTH,
"unit_size" : 1,
"tick_size" : 0.1,
"tick_frequency" : 1,
"leftmost_tick" : None, #Defaults to ceil(x_min)
"numbers_with_elongated_ticks" : [0],
"numbers_to_show" : None,
"longer_tick_multiple" : 2,
"number_at_center" : 0,
"propogate_style_to_family" : True
}
def __init__(self, **kwargs):
digest_config(self, kwargs)
if self.leftmost_tick is None:
self.leftmost_tick = np.ceil(self.x_min)
VMobject.__init__(self, **kwargs)
def generate_points(self):
self.main_line = Line(self.x_min*RIGHT, self.x_max*RIGHT)
self.tick_marks = VMobject()
self.add(self.main_line, self.tick_marks)
for x in self.get_tick_numbers():
self.add_tick(x, self.tick_size)
for x in self.numbers_with_elongated_ticks:
self.add_tick(x, self.longer_tick_multiple*self.tick_size)
self.stretch(self.unit_size, 0)
self.shift(-self.number_to_point(self.number_at_center))
def add_tick(self, x, size):
self.tick_marks.add(Line(
x*RIGHT+size*DOWN,
x*RIGHT+size*UP,
))
return self
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(self.leftmost_tick, self.x_max, 1)
def get_vertical_number_offset(self, direction = DOWN):
return 4*direction*self.tick_size
def get_number_mobjects(self, *numbers, **kwargs):
#TODO, handle decimals
if len(numbers) == 0:
numbers = self.default_numbers_to_display()
result = VGroup()
for number in numbers:
mob = TexMobject(str(int(number)))
mob.scale_to_fit_height(3*self.tick_size)
mob.shift(
self.number_to_point(number),
self.get_vertical_number_offset(**kwargs)
)
result.add(mob)
return result
def add_numbers(self, *numbers, **kwargs):
self.numbers = self.get_number_mobjects(
*numbers, **kwargs
)
self.add(*self.numbers)
return self
