def get_det_text(
matrix: Matrix,
determinant: int | str | None = None,
background_rect: bool = False,
initial_scale_factor: int = 2
) -> VGroup:
parens = Tex("(", ")")
parens.scale(initial_scale_factor)
parens.stretch_to_fit_height(matrix.get_height())
l_paren, r_paren = parens.split()
l_paren.next_to(matrix, LEFT, buff=0.1)
r_paren.next_to(matrix, RIGHT, buff=0.1)
det = TexText("det")
det.scale(initial_scale_factor)
det.next_to(l_paren, LEFT, buff=0.1)
if background_rect:
det.add_background_rectangle()
det_text = VGroup(det, l_paren, r_paren)
if determinant is not None:
eq = Tex("=")
eq.next_to(r_paren, RIGHT, buff=0.1)
result = Tex(str(determinant))
result.next_to(eq, RIGHT, buff=0.2)
det_text.add(eq, result)
return det_text
def get_dashed_rectangle(self, width, height):
h1 = [ORIGIN, UP * height]
w1 = [UP * height, UP * height + RIGHT * width]
h2 = [UP * height + RIGHT * width, RIGHT * width]
w2 = [RIGHT * width, ORIGIN]
alpha = width / height
divs = self.num_dashes
n_h = int(divs / (2 * (alpha + 1)))
n_w = int(alpha * n_h)
dashedrectangle = VGroup()
for n, l in zip([n_w, n_h], [[w1, w2], [h1, h2]]):
for side in l:
line = VMobject()
line.set_points_as_corners(side)
dashedrectangle.add(
DashedVMobject(
line,
num_dashes=n,
positive_space_ratio=self.positive_space_ratio,
).set_color(self.color).set_style(**self.line_config))
return [
dashedrectangle[0], dashedrectangle[3], dashedrectangle[1],
dashedrectangle[2]
]
def setup_in_uv_space(self):
u_values, v_values = self.get_u_values_and_v_values()
faces = VGroup()
for i in range(len(u_values) - 1):
for j in range(len(v_values) - 1):
u1, u2 = u_values[i:i + 2]
v1, v2 = v_values[j:j + 2]
face = ThreeDVMobject()
face.set_points_as_corners([
[u1, v1, 0],
[u2, v1, 0],
[u2, v2, 0],
[u1, v2, 0],
[u1, v1, 0],
])
faces.add(face)
face.u_index = i
face.v_index = j
face.u1 = u1
face.u2 = u2
face.v1 = v1
face.v2 = v2
faces.set_fill(
color=self.fill_color,
opacity=self.fill_opacity
)
faces.set_stroke(
color=self.stroke_color,
width=self.stroke_width,
opacity=self.stroke_opacity,
)
self.add(*faces)
if self.checkerboard_colors:
self.set_fill_by_checkerboard(*self.checkerboard_colors)
def __init__(self, point, color=YELLOW, **kwargs):
digest_config(self, kwargs)
lines = VGroup()
for angle in np.arange(0, TAU, TAU / self.num_lines):
line = Line(ORIGIN, self.line_length * RIGHT)
line.shift((self.flash_radius - self.line_length) * RIGHT)
line.rotate(angle, about_point=ORIGIN)
lines.add(line)
lines.move_to(point)
lines.set_color(color)
lines.set_stroke(width=3)
line_anims = [
ShowCreationThenDestruction(
line, rate_func=squish_rate_func(smooth, 0, 0.5)
)
for line in lines
]
fade_anims = [
UpdateFromAlphaFunc(
line, lambda m, a: m.set_stroke(
width=self.line_stroke_width * (1 - a)
),
rate_func=squish_rate_func(smooth, 0, 0.75)
)
for line in lines
]
AnimationGroup.__init__(
self, *line_anims + fade_anims, **kwargs
)
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, *text, line_spacing=-1, alignment=None, **config):
self.line_spacing = line_spacing
self.alignment = alignment
VGroup.__init__(self, **config)
lines_str = "\n".join(list(text))
self.lines_text = Text(lines_str, line_spacing=line_spacing, **config)
lines_str_list = lines_str.split("\n")
self.chars = self.gen_chars(lines_str_list)
chars_lines_text_list = VGroup()
char_index_counter = 0
for line_index in range(lines_str_list.__len__()):
chars_lines_text_list.add(
self.lines_text[char_index_counter:char_index_counter +
lines_str_list[line_index].__len__() + 1])
char_index_counter += lines_str_list[line_index].__len__() + 1
self.lines = []
self.lines.append([])
for line_no in range(chars_lines_text_list.__len__()):
self.lines[0].append(chars_lines_text_list[line_no])
self.lines_initial_positions = []
for line_no in range(self.lines[0].__len__()):
self.lines_initial_positions.append(
self.lines[0][line_no].get_center())
self.lines.append([])
self.lines[1].extend(
[self.alignment for _ in range(chars_lines_text_list.__len__())])
VGroup.__init__(
self, *[self.lines[0][i] for i in range(self.lines[0].__len__())],
**config)
self.move_to(np.array([0, 0, 0]))
if self.alignment:
self.set_all_lines_alignments(self.alignment)
def setup_in_uv_space(self):
u_values, v_values = self.get_u_values_and_v_values()
faces = VGroup()
for i in range(len(u_values) - 1):
for j in range(len(v_values) - 1):
u1, u2 = u_values[i:i + 2]
v1, v2 = v_values[j:j + 2]
face = ThreeDVMobject()
face.set_points_as_corners([
[u1, v1, 0],
[u2, v1, 0],
[u2, v2, 0],
[u1, v2, 0],
[u1, v1, 0],
])
faces.add(face)
face.u_index = i
face.v_index = j
face.u1 = u1
face.u2 = u2
face.v1 = v1
face.v2 = v2
faces.set_fill(
color=self.fill_color,
opacity=self.fill_opacity
)
faces.set_stroke(
color=self.stroke_color,
width=self.stroke_width,
opacity=self.stroke_opacity,
)
self.add(*faces)
if self.checkerboard_colors:
self.set_fill_by_checkerboard(*self.checkerboard_colors)
class Shadow_2d(VGroup):
CONFIG = {
'shadow_color': DARK_GRAY,
'shadow_opacity': 0.6,
'blur_width': 0.25,
'layer_num': 40,
'scale_factor': 1,
'shadow_out': True,
'show_basic_shape': True,
'plot_depth':-1,
'rate_func': lambda t: t ** 0.5,
}
def __init__(self, mob_or_points, **kwargs):
VGroup.__init__(self, **kwargs)
if type(mob_or_points) == list:
self.shape = Polygon(*mob_or_points, stroke_width=0, plot_depth=-1)
else:
self.shape = mob_or_points.set_stroke(width=0)
self.shape.set_fill(color=self.shadow_color, opacity=self.shadow_opacity * (1 if self.show_basic_shape else 0)).scale(self.scale_factor)
self.blur_outline = VGroup()
s = (self.shape.get_height() + self.shape.get_width())/2
if self.blur_width > 1e-4:
for i in range(self.layer_num):
layer_i = self.shape.copy().set_stroke(color=self.shadow_color, width=100 * self.blur_width/self.layer_num, opacity=self.shadow_opacity * (1-self.rate_func(i/self.layer_num))).\
set_fill(opacity=0).scale((s + (1 if self.shadow_out else -1) * self.blur_width/self.layer_num * (i+0.5))/ s).set_plot_depth(-2)
self.blur_outline.add(layer_i)
self.add(self.shape, self.blur_outline)
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.set_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.set_height(self.y_axis_label_height)
label.next_to(tick, LEFT, SMALL_BUFF)
labels.add(label)
self.y_axis_labels = labels
self.add(labels)
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.set_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 = Tex(str(np.round(value, 2)))
label.set_height(self.y_axis_label_height)
label.next_to(tick, LEFT, SMALL_BUFF)
labels.add(label)
self.y_axis_labels = labels
self.add(labels)
def add_label(self):
self.id_to_label = [
"0", "H", "He",
"Li", "Be", "B", "C", "N", "O", "F", "Ne",
"Na", "Mg", "Al", "Si", "P", "S", "Cl", "Ar",
"K", "Ca", "Sc", "Ti", "V", "Cr", "Mn", "Fe", "Co", "Ni", "Cu", "Zn", "Ga", "Ge", "As", "Se", "Br", "Kr",
"Rb", "Sr", "Y", "Zr", "Nb", "Mo", "Tc", "Ru", "Rh", "Pd", "Ag", "Cd", "In", "Sn", "Sb", "Te", "I", "Xe",
"Cs", "Ba",
"La", "Ce", "Pr", "Nd", "Pm", "Sm", "Eu", "Gd", "Tb", "Dy", "Ho", "Er", "Tm", "Yb", "Lu",
"Hf", "Ta", "W", "Re", "Os", "Ir", "Pt", "Au", "Hg", "Tl", "Pb", "Bi", "Po", "At", "Rn",
"Fr", "Ra",
"Ac", "Th", "Pa", "U", "Np", "Pu", "Am", "Cm", "Bk", "Cf", "Es", "Fm", "Md", "No", "Lr",
"Rf", "Db", "Sg", "Bh", "Hs", "Mt", "Ds", "Rg", "Cn", "Nh", "Fl", "Mc", "Lv", "Ts", "Og"
]
self.label_to_id = {}
for i, label in enumerate(self.id_to_label):
self.label_to_id[label] = i
labels = VGroup()
for i in range(0, 119):
label = TextMobject(self.id_to_label[i], color=BLACK, background_stroke_width=0)
label.scale(0.5).move_to(self[0][i][1].get_center()).set_shade_in_3d(z_index_as_group=True).shift(OUT * 1e-3)
labels.add(label)
labels[0].set_fill(opacity=0)
for i in [43, 61, *list(range(84, 119))]:
labels[i].set_color(RED)
self.add(labels)
return self
def get_subdivision_braces_and_labels(
self, parts, labels, direction,
buff=SMALL_BUFF,
min_num_quads=1
):
label_mobs = VGroup()
braces = VGroup()
for label, part in zip(labels, parts):
brace = Brace(
part, direction,
min_num_quads=min_num_quads,
buff=buff
)
if isinstance(label, Mobject):
label_mob = label
else:
label_mob = Tex(label)
label_mob.scale(self.default_label_scale_val)
label_mob.next_to(brace, direction, buff)
braces.add(brace)
label_mobs.add(label_mob)
parts.braces = braces
parts.labels = label_mobs
parts.label_kwargs = {
"labels": label_mobs.copy(),
"direction": direction,
"buff": buff,
}
return VGroup(parts.braces, parts.labels)
def get_coordinate_labels(self, *numbers):
# TODO: Should merge this with the code from NumberPlane.get_coordinate_labels
result = VGroup()
if len(numbers) == 0:
numbers = list(range(-int(self.x_radius), int(self.x_radius) + 1))
numbers += [
complex(0, y) for y in range(-int(self.y_radius),
int(self.y_radius) + 1) if y != 0
]
for number in numbers:
# if number == complex(0, 0):
# continue
point = self.number_to_point(number)
num_str = str(number).replace("j", "i")
if num_str.startswith("0"):
num_str = "0"
elif num_str in ["1i", "-1i"]:
num_str = num_str.replace("1", "")
num_mob = TexMobject(num_str)
num_mob.add_background_rectangle()
num_mob.set_height(self.written_coordinate_height)
num_mob.next_to(point, DOWN + LEFT, SMALL_BUFF)
result.add(num_mob)
self.coordinate_labels = result
return result
def get_subdivision_braces_and_labels(
self, parts, labels, direction,
buff=SMALL_BUFF,
min_num_quads=1
):
label_mobs = VGroup()
braces = VGroup()
for label, part in zip(labels, parts):
brace = Brace(
part, direction,
min_num_quads=min_num_quads,
buff=buff
)
if isinstance(label, Mobject):
label_mob = label
else:
label_mob = TexMobject(label)
label_mob.scale(self.default_label_scale_val)
label_mob.next_to(brace, direction, buff)
braces.add(brace)
label_mobs.add(label_mob)
parts.braces = braces
parts.labels = label_mobs
parts.label_kwargs = {
"labels": label_mobs.copy(),
"direction": direction,
"buff": buff,
}
return VGroup(parts.braces, parts.labels)
def add_numbers(self, *numbers, excluding=None, font_size=24, x_values=None, **kwargs):
if x_values is None:
if numbers is not None:
if len(numbers) == 1 and isinstance(numbers[0], list):
x_values = (numbers[0])
if len(numbers) == 1 and numbers[0] is None:
x_values = self.get_tick_range()
elif len(numbers) > 0 and not isinstance(numbers[0], list):
x_values = list(numbers)
else:
x_values =self.get_tick_range()
else:
x_values = self.get_tick_range()
kwargs["font_size"] = font_size
numbers = VGroup()
for x in x_values:
if self.numbers_to_exclude is not None and x in self.numbers_to_exclude:
continue
if excluding is not None and x in excluding:
continue
numbers.add(self.get_number_mobject(x, **kwargs))
self.add(numbers)
self.numbers = numbers
return numbers
'''
def get_tips(self):
result = VGroup()
if hasattr(self, "tip"):
result.add(self.tip)
if hasattr(self, "start_tip"):
result.add(self.start_tip)
return result
def get_words(self, *index):
pre_index = []
pos_index = []
row_parameter = max([self[i].get_height() for i in range(len(self))])
word_parameter = max([self[i].get_width() for i in range(len(self))])
#print(word_parameter)
start = 0
for i in range(len(self) - 1):
distance_letter_between = abs(self[i + 1].get_x() -
self[i].get_x())
distance_row_between = abs(self[i + 1].get_y() - self[i].get_y())
if distance_letter_between > word_parameter:
pre_index.append(start)
pos_index.append(i + 1)
start = i + 1
#print(pre_index)
pre_index.append(pos_index[-1] + 1)
pos_index.append(len(self) - 1)
all_words = VGroup(
*[self[pre:pos + 1] for pre, pos in zip(pre_index, pos_index)])
words = VGroup()
for word in index:
words.add(all_words[word])
if len(index) == 0:
return all_words
else:
return words
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 create_path(self):
path = VGroup()
self.get_path_xyz()
if len(self.path_xyz) > 1:
for i in range(len(self.path_xyz) - 1):
if type(self.trail_color) == str:
path.add(
Line(self.path_xyz[i],
self.path_xyz[i + 1],
stroke_color=self.trail_color,
stroke_opacity=self.rate_func(i /
len(self.path_xyz)),
plot_depth=self.rate_func(2 -
i / len(self.path_xyz)),
stroke_width=self.max_width *
self.rate_func(i / len(self.path_xyz))))
else:
path.add(
Line(self.path_xyz[i],
self.path_xyz[i + 1],
stroke_color=self.colors[i],
stroke_opacity=self.rate_func(i /
len(self.path_xyz)),
plot_depth=self.rate_func(2 -
i / len(self.path_xyz)),
stroke_width=self.max_width *
self.rate_func(i / len(self.path_xyz))))
# print('i = %d' % i)
# # print(self.path_xyz)
# print(self.color)
# print(self.rate_func(i/len(self.path_xyz)))
# print(self.max_width*self.rate_func(i/len(self.path_xyz)))
return path
def get_tips(self):
result = VGroup()
if hasattr(self, "tip"):
result.add(self.tip)
if hasattr(self, "start_tip"):
result.add(self.start_tip)
return result
class DoubleArrow(Arrow):
def init_tip(self):
self.tip = VGroup()
for b in True, False:
t = self.add_tip(add_at_end=b)
t.add_at_end = b
self.tip.add(t)
self.tip.match_style(self.tip[0])
class ComplexPlane(NumberPlane):
CONFIG = {
"color": BLUE,
"line_frequency": 1,
}
def number_to_point(self, number: complex | float) -> np.ndarray:
number = complex(number)
return self.coords_to_point(number.real, number.imag)
def n2p(self, number: complex | float) -> np.ndarray:
return self.number_to_point(number)
def point_to_number(self, point: np.ndarray) -> complex:
x, y = self.point_to_coords(point)
return complex(x, y)
def p2n(self, point: np.ndarray) -> complex:
return self.point_to_number(point)
def get_default_coordinate_values(self,
skip_first: bool = True
) -> list[complex]:
x_numbers = self.get_x_axis().get_tick_range()[1:]
y_numbers = self.get_y_axis().get_tick_range()[1:]
y_numbers = [complex(0, y) for y in y_numbers if y != 0]
return [*x_numbers, *y_numbers]
def add_coordinate_labels(self,
numbers: list[complex] | None = None,
skip_first: bool = True,
**kwargs):
if numbers is None:
numbers = self.get_default_coordinate_values(skip_first)
self.coordinate_labels = VGroup()
for number in numbers:
z = complex(number)
if abs(z.imag) > abs(z.real):
axis = self.get_y_axis()
value = z.imag
kwargs["unit"] = "i"
else:
axis = self.get_x_axis()
value = z.real
number_mob = axis.get_number_mobject(value, **kwargs)
# For i and -i, remove the "1"
if z.imag == 1:
number_mob.remove(number_mob[0])
if z.imag == -1:
number_mob.remove(number_mob[1])
number_mob[0].next_to(number_mob[1],
LEFT,
buff=number_mob[0].get_width() / 4)
self.coordinate_labels.add(number_mob)
self.add(self.coordinate_labels)
return self
def get_transformer(self, **kwargs):
transform_kwargs = dict(self.default_apply_complex_function_kwargs)
transform_kwargs.update(kwargs)
transformer = VGroup()
if hasattr(self, "plane"):
self.prepare_for_transformation(self.plane)
transformer.add(self.plane)
transformer.add(*self.transformable_mobjects)
return transformer, transform_kwargs
def get_submobject_index_labels(mobject, label_height=0.15):
labels = VGroup()
for n, submob in enumerate(mobject):
label = Integer(n)
label.set_height(label_height)
label.move_to(submob)
label.set_stroke(BLACK, 5, background=True)
labels.add(label)
return labels
def get_transformer(self, **kwargs):
transform_kwargs = dict(self.default_apply_complex_function_kwargs)
transform_kwargs.update(kwargs)
transformer = VGroup()
if hasattr(self, "plane"):
self.prepare_for_transformation(self.plane)
transformer.add(self.plane)
transformer.add(*self.transformable_mobjects)
return transformer, transform_kwargs
def add_ticks(self):
ticks = VGroup()
for x in self.get_tick_range():
size = self.tick_size
if x in self.numbers_with_elongated_ticks:
size *= self.longer_tick_multiple
ticks.add(self.get_tick(x, size))
self.add(ticks)
self.ticks = ticks
def add_ticks(self) -> None:
ticks = VGroup()
for x in self.get_tick_range():
size = self.tick_size
if np.isclose(self.numbers_with_elongated_ticks, x).any():
size *= self.longer_tick_multiple
ticks.add(self.get_tick(x, size))
self.add(ticks)
self.ticks = ticks
def get_parts_from_keys(mobject, keys):
if isinstance(keys, str):
keys = [keys]
result = VGroup()
for key in keys:
if not isinstance(key, str):
raise TypeError(key)
result.add(*mobject.get_parts_by_string(key))
return result
def gen_chars(self, lines_str_list):
char_index_counter = 0
chars = VGroup()
for line_no in range(lines_str_list.__len__()):
chars.add(VGroup())
chars[line_no].add(
*self.lines_text.chars[char_index_counter:char_index_counter +
lines_str_list[line_no].__len__() + 1])
char_index_counter += lines_str_list[line_no].__len__() + 1
return chars
def index_labels(mobject: Mobject | np.ndarray,
label_height: float = 0.15) -> VGroup:
labels = VGroup()
for n, submob in enumerate(mobject):
label = Integer(n)
label.set_height(label_height)
label.move_to(submob)
label.set_stroke(BLACK, 5, background=True)
labels.add(label)
return labels
def create_lines(self):
lines = VGroup()
for angle in np.arange(0, TAU, TAU / self.num_lines):
line = Line(ORIGIN, self.line_length * RIGHT)
line.shift((self.flash_radius - self.line_length) * RIGHT)
line.rotate(angle, about_point=ORIGIN)
lines.add(line)
lines.set_stroke(color=self.color, width=self.line_stroke_width)
lines.add_updater(lambda l: l.move_to(self.point))
return lines
def create_boxes(self):
pos = MyBoxes(resolution=(9, 18), bottom_size=self.bottom_size, gap=0.15, box_height=0.4)
boxes = VGroup()
for i in range(0, 119):
box = MyBox(pos=pos[self.id_to_pos[i]].get_center(), bottom_size=self.bottom_size,
box_height=self.box_height, fill_color=self.fill_color)
box.reset_color()
boxes.add(box)
boxes[0].set_fill(opacity=0)
self.add(boxes)
def bar(self,
x,
height,
width=0.8,
align='center',
color=None,
fill_opacity=None,
stroke_width=None,
**kwargs):
if len(x) != len(height):
raise ValueError("'x' and 'height' should be equal sized")
if align == 'center':
align = ORIGIN
elif align == 'edge' or align == 'right':
align = RIGHT
elif align == 'left':
align = LEFT
if color is None:
color = it.cycle([next(self.default_graph_colors_cycle)])
else:
if is_sequence(color):
color = it.cycle(color)
else:
color = it.cycle([color])
if fill_opacity is None:
fill_opacity = self.default_bar_opacity
if stroke_width is None:
stroke_width = self.default_bar_stroke_width
bar_sequence = VGroup()
p_x0, p_y0, p_z0 = self.coords_to_point(0, 0)
for i in range(len(x)):
if is_sequence(width):
bar_width = width[i]
else:
bar_width = width
p_x1, p_y1, p_z1 = self.coords_to_point(x[i], height[i])
p_x2, p_y2, p_z2 = self.coords_to_point(bar_width, 0)
bar_height = p_y1 - p_y0
bar_width = p_x2 - p_x0
bar_center = (p_x1, p_y0, p_z1)
bar = Rectangle(
height=bar_height,
width=bar_width,
color=next(color),
fill_opacity=fill_opacity,
stroke_width=stroke_width,
**kwargs,
).next_to(bar_center, UP + align, buff=0)
bar_sequence.add(bar)
if hasattr(self, "bar_sequences") is False:
self.bar_sequences = VGroup()
self.bar_sequences.add(bar_sequence)
self.add(self.bar_sequences)
return bar_sequence
class Axes(VGroup, CoordinateSystem):
CONFIG = {
"axis_config": {
"include_tip": True,
},
"x_axis_config": {},
"y_axis_config": {
"line_to_number_direction": LEFT,
},
}
def __init__(self, x_range=None, y_range=None, **kwargs):
VGroup.__init__(self, **kwargs)
self.x_axis = self.create_axis(
x_range or self.x_range,
self.x_axis_config,
self.width,
)
self.y_axis = self.create_axis(y_range or self.y_range,
self.y_axis_config, self.height)
self.y_axis.rotate(90 * DEGREES, about_point=ORIGIN)
# Add as a separate group in case various other
# mobjects are added to self, as for example in
# NumberPlane below
self.axes = VGroup(self.x_axis, self.y_axis)
self.add(*self.axes)
self.center()
def create_axis(self, range_terms, axis_config, length):
new_config = merge_dicts_recursively(self.axis_config, axis_config)
new_config["width"] = length
axis = NumberLine(range_terms, **new_config)
axis.shift(-axis.n2p(0))
return axis
def coords_to_point(self, *coords):
origin = self.x_axis.number_to_point(0)
result = np.array(origin)
for axis, coord in zip(self.get_axes(), coords):
result += (axis.number_to_point(coord) - origin)
return result
def point_to_coords(self, point):
return tuple([axis.point_to_number(point) for axis in self.get_axes()])
def get_axes(self):
return self.axes
def add_coordinate_labels(self, x_values=None, y_values=None):
axes = self.get_axes()
self.coordinate_labels = VGroup()
for axis, values in zip(axes, [x_values, y_values]):
numbers = axis.add_numbers(values, excluding=[0])
self.coordinate_labels.add(numbers)
return self.coordinate_labels
def pop_tips(self):
start, end = self.get_start_and_end()
result = VGroup()
if self.has_tip():
result.add(self.tip)
self.remove(self.tip)
if self.has_start_tip():
result.add(self.start_tip)
self.remove(self.start_tip)
self.put_start_and_end_on(start, end)
return result
def get_tips(self):
"""
Returns a VGroup (collection of VMobjects) containing
the TipableVMObject instance's tips.
"""
result = VGroup()
if hasattr(self, "tip"):
result.add(self.tip)
if hasattr(self, "start_tip"):
result.add(self.start_tip)
return result
def pop_tips(self):
start, end = self.get_start_and_end()
result = VGroup()
if self.has_tip():
result.add(self.tip)
self.remove(self.tip)
if self.has_start_tip():
result.add(self.start_tip)
self.remove(self.start_tip)
self.put_start_and_end_on(start, end)
return result
def get_number_mob(self, num):
result = VGroup()
place = 0
max_place = self.max_place
while place < max_place:
digit = TexMobject(str(self.get_place_num(num, place)))
if place >= len(self.digit_place_colors):
self.digit_place_colors += self.digit_place_colors
digit.set_color(self.digit_place_colors[place])
digit.scale(self.num_scale_factor)
digit.next_to(result, LEFT, buff=SMALL_BUFF, aligned_edge=DOWN)
result.add(digit)
place += 1
return result
def get_riemann_rectangles(
self,
graph,
x_min=None,
x_max=None,
dx=0.1,
input_sample_type="left",
stroke_width=1,
stroke_color=BLACK,
fill_opacity=1,
start_color=None,
end_color=None,
show_signed_area=True,
width_scale_factor=1.001
):
x_min = x_min if x_min is not None else self.x_min
x_max = x_max if x_max is not None else self.x_max
if start_color is None:
start_color = self.default_riemann_start_color
if end_color is None:
end_color = self.default_riemann_end_color
rectangles = VGroup()
x_range = np.arange(x_min, x_max, dx)
colors = color_gradient([start_color, end_color], len(x_range))
for x, color in zip(x_range, colors):
if input_sample_type == "left":
sample_input = x
elif input_sample_type == "right":
sample_input = x + dx
elif input_sample_type == "center":
sample_input = x + 0.5 * dx
else:
raise Exception("Invalid input sample type")
graph_point = self.input_to_graph_point(sample_input, graph)
points = VGroup(*list(map(VectorizedPoint, [
self.coords_to_point(x, 0),
self.coords_to_point(x + width_scale_factor * dx, 0),
graph_point
])))
rect = Rectangle()
rect.replace(points, stretch=True)
if graph_point[1] < self.graph_origin[1] and show_signed_area:
fill_color = invert_color(color)
else:
fill_color = color
rect.set_fill(fill_color, opacity=fill_opacity)
rect.set_stroke(stroke_color, width=stroke_width)
rectangles.add(rect)
return rectangles
def get_division_along_dimension(self, p_list, dim, colors, vect):
p_list = self.complete_p_list(p_list)
colors = color_gradient(colors, len(p_list))
last_point = self.get_edge_center(-vect)
parts = VGroup()
for factor, color in zip(p_list, colors):
part = SampleSpace()
part.set_fill(color, 1)
part.replace(self, stretch=True)
part.stretch(factor, dim)
part.move_to(last_point, -vect)
last_point = part.get_edge_center(vect)
parts.add(part)
return parts
def get_number_design(self, value, symbol):
num = int(value)
n_rows = {
2: 2,
3: 3,
4: 2,
5: 2,
6: 3,
7: 3,
8: 3,
9: 4,
10: 4,
}[num]
n_cols = 1 if num in [2, 3] else 2
insertion_indices = {
5: [0],
7: [0],
8: [0, 1],
9: [1],
10: [0, 2],
}.get(num, [])
top = self.get_top() + symbol.get_height() * DOWN
bottom = self.get_bottom() + symbol.get_height() * UP
column_points = [
interpolate(top, bottom, alpha)
for alpha in np.linspace(0, 1, n_rows)
]
design = VGroup(*[
symbol.copy().move_to(point)
for point in column_points
])
if n_cols == 2:
space = 0.2 * self.get_width()
column_copy = design.copy().shift(space * RIGHT)
design.shift(space * LEFT)
design.add(*column_copy)
design.add(*[
symbol.copy().move_to(
center_of_mass(column_points[i:i + 2])
)
for i in insertion_indices
])
for symbol in design:
if symbol.get_center()[1] < self.get_center()[1]:
symbol.rotate_in_place(np.pi)
return design
def get_animation_integral_bounds_change(
self,
graph,
new_t_min,
new_t_max,
fade_close_to_origin=True,
run_time=1.0
):
curr_t_min = self.x_axis.point_to_number(self.area.get_left())
curr_t_max = self.x_axis.point_to_number(self.area.get_right())
if new_t_min is None:
new_t_min = curr_t_min
if new_t_max is None:
new_t_max = curr_t_max
group = VGroup(self.area)
group.add(self.left_v_line)
group.add(self.left_T_label_group)
group.add(self.right_v_line)
group.add(self.right_T_label_group)
def update_group(group, alpha):
area, left_v_line, left_T_label, right_v_line, right_T_label = group
t_min = interpolate(curr_t_min, new_t_min, alpha)
t_max = interpolate(curr_t_max, new_t_max, alpha)
new_area = self.get_area(graph, t_min, t_max)
new_left_v_line = self.get_vertical_line_to_graph(
t_min, graph
)
new_left_v_line.set_color(left_v_line.get_color())
left_T_label.move_to(new_left_v_line.get_bottom(), UP)
new_right_v_line = self.get_vertical_line_to_graph(
t_max, graph
)
new_right_v_line.set_color(right_v_line.get_color())
right_T_label.move_to(new_right_v_line.get_bottom(), UP)
# Fade close to 0
if fade_close_to_origin:
if len(left_T_label) > 0:
left_T_label[0].set_fill(opacity=min(1, np.abs(t_min)))
if len(right_T_label) > 0:
right_T_label[0].set_fill(opacity=min(1, np.abs(t_max)))
Transform(area, new_area).update(1)
Transform(left_v_line, new_left_v_line).update(1)
Transform(right_v_line, new_right_v_line).update(1)
return group
return UpdateFromAlphaFunc(group, update_group, run_time=run_time)
def get_det_text(matrix, determinant=None, background_rect=False, initial_scale_factor=2):
parens = TexMobject("(", ")")
parens.scale(initial_scale_factor)
parens.stretch_to_fit_height(matrix.get_height())
l_paren, r_paren = parens.split()
l_paren.next_to(matrix, LEFT, buff=0.1)
r_paren.next_to(matrix, RIGHT, buff=0.1)
det = TextMobject("det")
det.scale(initial_scale_factor)
det.next_to(l_paren, LEFT, buff=0.1)
if background_rect:
det.add_background_rectangle()
det_text = VGroup(det, l_paren, r_paren)
if determinant is not None:
eq = TexMobject("=")
eq.next_to(r_paren, RIGHT, buff=0.1)
result = TexMobject(str(determinant))
result.next_to(eq, RIGHT, buff=0.2)
det_text.add(eq, result)
return det_text
def __init__(self, focal_point, **kwargs):
digest_config(self, kwargs)
circles = VGroup()
for x in range(self.n_circles):
circle = Circle(
radius=self.big_radius,
stroke_color=BLACK,
stroke_width=0,
)
circle.add_updater(
lambda c: c.move_to(focal_point)
)
circle.save_state()
circle.set_width(self.small_radius * 2)
circle.set_stroke(self.color, self.start_stroke_width)
circles.add(circle)
animations = [
Restore(circle)
for circle in circles
]
super().__init__(*animations, **kwargs)
def add_bars(self, values):
buff = float(self.width) / (2 * len(values) + 1)
bars = VGroup()
for i, value in enumerate(values):
bar = Rectangle(
height=(value / self.max_value) * self.height,
width=buff,
stroke_width=self.bar_stroke_width,
fill_opacity=self.bar_fill_opacity,
)
bar.move_to((2 * i + 1) * buff * RIGHT, DOWN + LEFT)
bars.add(bar)
bars.set_color_by_gradient(*self.bar_colors)
bar_labels = VGroup()
for bar, name in zip(bars, self.bar_names):
label = TexMobject(str(name))
label.scale(self.bar_label_scale_val)
label.next_to(bar, DOWN, SMALL_BUFF)
bar_labels.add(label)
self.add(bars, bar_labels)
self.bars = bars
self.bar_labels = bar_labels
def move_tip_to(self, point):
mover = VGroup(self)
if self.content is not None:
mover.add(self.content)
mover.shift(point - self.get_tip())
return self
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.set_width(max_width)
if labels.get_height() > max_height:
labels.set_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
class CountingScene(Scene):
CONFIG = {
"digit_place_colors": [YELLOW, MAROON_B, RED, GREEN, BLUE, PURPLE_D],
"counting_dot_starting_position": (FRAME_X_RADIUS - 1) * RIGHT + (FRAME_Y_RADIUS - 1) * UP,
"count_dot_starting_radius": 0.5,
"dot_configuration_height": 2,
"ones_configuration_location": UP + 2 * RIGHT,
"num_scale_factor": 2,
"num_start_location": 2 * DOWN,
}
def setup(self):
self.dots = VGroup()
self.number = 0
self.max_place = 0
self.number_mob = VGroup(TexMobject(str(self.number)))
self.number_mob.scale(self.num_scale_factor)
self.number_mob.shift(self.num_start_location)
self.dot_templates = []
self.dot_template_iterators = []
self.curr_configurations = []
self.arrows = VGroup()
self.add(self.number_mob)
def get_template_configuration(self, place):
# This should probably be replaced for non-base-10 counting scenes
down_right = (0.5) * RIGHT + (np.sqrt(3) / 2) * DOWN
result = []
for down_right_steps in range(5):
for left_steps in range(down_right_steps):
result.append(
down_right_steps * down_right + left_steps * LEFT
)
return reversed(result[:self.get_place_max(place)])
def get_dot_template(self, place):
# This should be replaced for non-base-10 counting scenes
dots = VGroup(*[
Dot(
point,
radius=0.25,
fill_opacity=0,
stroke_width=2,
stroke_color=WHITE,
)
for point in self.get_template_configuration(place)
])
dots.set_height(self.dot_configuration_height)
return dots
def add_configuration(self):
new_template = self.get_dot_template(len(self.dot_templates))
new_template.move_to(self.ones_configuration_location)
left_vect = (new_template.get_width() + LARGE_BUFF) * LEFT
new_template.shift(
left_vect * len(self.dot_templates)
)
self.dot_templates.append(new_template)
self.dot_template_iterators.append(
it.cycle(new_template)
)
self.curr_configurations.append(VGroup())
def count(self, max_val, run_time_per_anim=1):
for x in range(max_val):
self.increment(run_time_per_anim)
def increment(self, run_time_per_anim=1):
moving_dot = Dot(
self.counting_dot_starting_position,
radius=self.count_dot_starting_radius,
color=self.digit_place_colors[0],
)
moving_dot.generate_target()
moving_dot.set_fill(opacity=0)
kwargs = {
"run_time": run_time_per_anim
}
continue_rolling_over = True
first_move = True
place = 0
while continue_rolling_over:
added_anims = []
if first_move:
added_anims += self.get_digit_increment_animations()
first_move = False
moving_dot.target.replace(
next(self.dot_template_iterators[place])
)
self.play(MoveToTarget(moving_dot), *added_anims, **kwargs)
self.curr_configurations[place].add(moving_dot)
if len(self.curr_configurations[place].split()) == self.get_place_max(place):
full_configuration = self.curr_configurations[place]
self.curr_configurations[place] = VGroup()
place += 1
center = full_configuration.get_center_of_mass()
radius = 0.6 * max(
full_configuration.get_width(),
full_configuration.get_height(),
)
circle = Circle(
radius=radius,
stroke_width=0,
fill_color=self.digit_place_colors[place],
fill_opacity=0.5,
)
circle.move_to(center)
moving_dot = VGroup(circle, full_configuration)
moving_dot.generate_target()
moving_dot[0].set_fill(opacity=0)
else:
continue_rolling_over = False
def get_digit_increment_animations(self):
result = []
self.number += 1
is_next_digit = self.is_next_digit()
if is_next_digit:
self.max_place += 1
new_number_mob = self.get_number_mob(self.number)
new_number_mob.move_to(self.number_mob, RIGHT)
if is_next_digit:
self.add_configuration()
place = len(new_number_mob.split()) - 1
result.append(FadeIn(self.dot_templates[place]))
arrow = Arrow(
new_number_mob[place].get_top(),
self.dot_templates[place].get_bottom(),
color=self.digit_place_colors[place]
)
self.arrows.add(arrow)
result.append(ShowCreation(arrow))
result.append(Transform(
self.number_mob, new_number_mob,
lag_ratio=0.5
))
return result
def get_number_mob(self, num):
result = VGroup()
place = 0
max_place = self.max_place
while place < max_place:
digit = TexMobject(str(self.get_place_num(num, place)))
if place >= len(self.digit_place_colors):
self.digit_place_colors += self.digit_place_colors
digit.set_color(self.digit_place_colors[place])
digit.scale(self.num_scale_factor)
digit.next_to(result, LEFT, buff=SMALL_BUFF, aligned_edge=DOWN)
result.add(digit)
place += 1
return result
def is_next_digit(self):
return False
def get_place_num(self, num, place):
return 0
def get_place_max(self, place):
return 0
def add_spikes(self):
layers = VGroup()
radii = np.linspace(
self.outer_radius,
self.pupil_radius,
self.n_spike_layers,
endpoint=False,
)
radii[:2] = radii[1::-1] # Swap first two
radii[-1] = interpolate(
radii[-1], self.pupil_radius, 0.25
)
for radius in radii:
tip_angle = self.spike_angle
half_base = radius * np.tan(tip_angle)
triangle, right_half_triangle = [
Polygon(
radius * UP,
half_base * RIGHT,
vertex3,
fill_opacity=1,
stroke_width=0,
)
for vertex3 in (half_base * LEFT, ORIGIN,)
]
left_half_triangle = right_half_triangle.copy()
left_half_triangle.flip(UP, about_point=ORIGIN)
n_spikes = self.n_spikes
full_spikes = [
triangle.copy().rotate(
-angle,
about_point=ORIGIN
)
for angle in np.linspace(
0, TAU, n_spikes, endpoint=False
)
]
index = (3 * n_spikes) // 4
if radius == radii[0]:
layer = VGroup(*full_spikes)
layer.rotate(
-TAU / n_spikes / 2,
about_point=ORIGIN
)
layer.brown_index = index
else:
half_spikes = [
right_half_triangle.copy(),
left_half_triangle.copy().rotate(
90 * DEGREES, about_point=ORIGIN,
),
right_half_triangle.copy().rotate(
90 * DEGREES, about_point=ORIGIN,
),
left_half_triangle.copy()
]
layer = VGroup(*it.chain(
half_spikes[:1],
full_spikes[1:index],
half_spikes[1:3],
full_spikes[index + 1:],
half_spikes[3:],
))
layer.brown_index = index + 1
layers.add(layer)
# Color spikes
blues = self.blue_spike_colors
browns = self.brown_spike_colors
for layer, blue, brown in zip(layers, blues, browns):
index = layer.brown_index
layer[:index].set_color(blue)
layer[index:].set_color(brown)
self.spike_layers = layers
self.add(layers)
