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_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 get_coordinate_labels(self, *numbers):
# TODO: Should merge this with the code from NumberPlane.get_coordinate_labels
result = VGroup()
if len(numbers) == 0:
numbers = 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)
]
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.scale_to_fit_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 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)
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 setup_in_uv_space(self):
u_min = self.u_min
u_max = self.u_max
u_res = self.u_resolution or self.resolution
v_min = self.v_min
v_max = self.v_max
v_res = self.v_resolution or self.resolution
u_values = np.linspace(u_min, u_max, u_res + 1)
v_values = np.linspace(v_min, v_max, v_res + 1)
faces = VGroup()
for u1, u2 in zip(u_values[:-1], u_values[1:]):
for v1, v2 in zip(v_values[:-1], v_values[1:]):
piece = ThreeDVMobject()
piece.set_points_as_corners([
[u1, v1, 0],
[u2, v1, 0],
[u2, v2, 0],
[u1, v2, 0],
[u1, v1, 0],
])
faces.add(piece)
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 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
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 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])
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_words(self):
# Wallis product
product = TexMobject(*(["\\text{Wallis公式：}"] + [
"{%d \\over %d} \\," % (wallis_numer(n), wallis_denom(n))
for n in range(1, 8)
] + ["\\cdots = {\\pi \\over 2}"])).set_color(YELLOW)
rect = SurroundingRectangle(product, color=YELLOW, buff=0.25)
wallis_product = VGroup(product, rect)
wallis_product.set_width(6)
# All those steps
nums = [TextMobject("%d. " % k) for k in [1, 2, 3, 4]]
words = [
TextMobject(word) for word in [
"构造合适的矩形边长",
"同种颜色的矩形的面积之和恒为1",
"整个图形又像一个${1 \\over 4}$圆，半径是",
"比较${1 \\over 4}$圆与矩形的面积",
]
]
formulae = [
TextMobject(formula) for formula in [
"$a_0 = 1,\\, a_n = {1 \\over 2} \cdot {3 \\over 4} \cdots {2n-1 \\over 2n} (n \geq 1)$",
"$a_0 a_n + a_1 a_{n-1} + \\cdots + a_n a_0 = 1$",
"$\\begin{aligned} \
r_n & = a_0 + a_1 + \\cdots + a_{n-1} \\\\ \
& = \\textstyle{3 \\over 2} \cdot {5 \\over 4} \cdots {2n-1 \\over 2n-2} \
\\quad (n \geq 2) \
\\end{aligned}$",
"${1 \\over 4} \\pi {r_n}^2 \\approx n \\quad \\Rightarrow \\quad \\text{Wallis公式}$"
]
]
steps = VGroup()
for num, word, formula in zip(nums, words, formulae):
num.next_to(word, LEFT)
formula.next_to(word, DOWN, aligned_edge=LEFT)
steps.add(VGroup(num, word, formula))
steps.arrange_submobjects(DOWN, buff=0.6, aligned_edge=LEFT)
steps.set_width(6)
steps.next_to(wallis_product, DOWN)
VGroup(wallis_product, steps).center().to_edge(RIGHT, buff=0.15)
# Sep line and QED
sep_line = DashedLine(2 * TOP, 2 * BOTTOM, color=GREY, buff=0.5)
sep_line.next_to(steps, LEFT)
qed = QEDSymbol(height=0.570 / 2)
qed.next_to(steps[-1][-1][-1], RIGHT, aligned_edge=DOWN)
# Add everything
self.add(wallis_product, steps, sep_line, qed)
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 generate_tower_tex_from_texts(self, texts):
tower_tex = VGroup(*[
TexMobject(text)
for text in self.tower_texts
])
if self.is_infinite:
tower_tex.add(ExpDots(**self.expdots_config))
for k, part in enumerate(tower_tex):
part.scale(self.scale_factor**k)
if k > 0:
buff = 0.05 / np.sqrt(k)
part.stretch(self.height_stretch_factor, 1)
part.next_to(tower_tex[k-1], RIGHT+UP, buff = buff)
return tower_tex
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_axis_labels(self, x_label="x", y_label="y"):
x_axis, y_axis = self.get_axes().split()
quads = [
(x_axis, x_label, UP, RIGHT),
(y_axis, y_label, RIGHT, UP),
]
labels = VGroup()
for axis, tex, vect, edge in quads:
label = TexMobject(tex)
label.add_background_rectangle()
label.next_to(axis, vect)
label.to_edge(edge)
labels.add(label)
self.axis_labels = labels
return labels
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 = DecimalNumber(number, **self.decimal_number_config)
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_axis_labels(self, x_label="x", y_label="y"):
x_axis, y_axis = self.get_axes().split()
quads = [
(x_axis, x_label, UP, RIGHT),
(y_axis, y_label, RIGHT, UP),
]
labels = VGroup()
for axis, tex, vect, edge in quads:
label = TexMobject(tex)
label.add_background_rectangle()
label.next_to(axis, vect)
label.to_edge(edge)
labels.add(label)
self.axis_labels = labels
return labels
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_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 __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.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)
LaggedStart.__init__(self, ApplyMethod, circles, lambda c:
(c.restore, ), **kwargs)
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 solve_the_equations(self):
rects = VGroup(*[
CoverRectangle(
equation[0].get_exponent(), stroke_color = color,
text = str(num), text_color = color
)
for equation, color, num in zip(self.equations, self.colors, self.nums)
])
self.play(DrawBorderThenFill(rects))
self.wait()
sps = VGroup()
for equation, num, color in zip(self.equations, self.nums, self.colors):
sp = TexMobject("x", "^{%d}" % num, "=", "%d" % num)
sp[1::2].set_color(color)
sp.scale(2)
sp.next_to(equation, DOWN, buff = 1)
sps.add(sp)
rss = VGroup()
for num, sp, color in zip(self.nums, sps, self.colors):
rs = TexMobject("x", "=", "%d" % num , "^{{1}\\over{%d}}" % num, "=\\sqrt{2}")
for tex in (rs[2], rs[3][2]):
tex.set_color(color)
rs.match_height(sp).move_to(sp)
rss.add(rs)
tf_anims = []
for sp, rs in zip(sps, rss):
tf_anims.append(ReplacementTransform(sp[0], rs[0]))
tf_anims.append(ReplacementTransform(sp[1], rs[3][2], path_arc = -TAU/4))
tf_anims.append(ReplacementTransform(sp[2], rs[1]))
tf_anims.append(ReplacementTransform(sp[3], rs[2]))
tf_anims.append(Write(rs[3][:2]))
self.play(FadeIn(sps))
self.wait()
self.play(AnimationGroup(*tf_anims), run_time = 2)
self.wait()
self.play(Write(VGroup(*[rs[4:] for rs in rss]), submobject_mode = "all_at_once"))
self.wait()
self.play(FadeOut(rects))
self.wait()
self.rss = rss
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.move_to(focal_point)
circle.save_state()
circle.scale_to_fit_width(self.small_radius * 2)
circle.set_stroke(self.color, self.start_stroke_width)
circles.add(circle)
LaggedStart.__init__(
self, ApplyMethod, circles,
lambda c: (c.restore,),
**kwargs
)
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 setup_in_uv_space(self):
res = tuplify(self.resolution)
if len(res) == 1:
u_res = v_res = res[0]
else:
u_res, v_res = res
u_min = self.u_min
u_max = self.u_max
v_min = self.v_min
v_max = self.v_max
u_values = np.linspace(u_min, u_max, u_res + 1)
v_values = np.linspace(v_min, v_max, v_res + 1)
faces = VGroup()
for i in range(u_res):
for j in range(v_res):
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 get_coordinate_labels(self, x_vals=None, y_vals=None):
coordinate_labels = VGroup()
if x_vals is None:
x_vals = list(range(-int(self.x_radius), int(self.x_radius) + 1))
if y_vals is None:
y_vals = list(range(-int(self.y_radius), int(self.y_radius) + 1))
for index, vals in enumerate([x_vals, y_vals]):
num_pair = [0, 0]
for val in vals:
if val == 0:
continue
num_pair[index] = val
point = self.coords_to_point(*num_pair)
num = TexMobject(str(val))
num.add_background_rectangle()
num.set_height(self.written_coordinate_height)
num.next_to(point, DOWN + LEFT, buff=SMALL_BUFF)
coordinate_labels.add(num)
self.coordinate_labels = coordinate_labels
return coordinate_labels
class RandomWalk1DLineAndDot(RandomWalk1D):
CONFIG = {
"dot_color": WHITE,
}
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 get_line_by_number(self, n):
return self.line_group[n]
def get_dots_by_number(self, n):
return VGroup(self.dot_group[n:n + 2])
def get_mob_color_by_number(self, n):
return self.up_color if self.walk_string[
n] == self.up_char else self.down_color
def split_at(self, n):
extra_dot = self.get_dots_by_number(n)[0].copy()
def get_coordinate_labels(self, x_vals=None, y_vals=None):
coordinate_labels = VGroup()
if x_vals is None:
x_vals = range(-int(self.x_radius), int(self.x_radius) + 1)
if y_vals is None:
y_vals = range(-int(self.y_radius), int(self.y_radius) + 1)
for index, vals in enumerate([x_vals, y_vals]):
num_pair = [0, 0]
for val in vals:
if val == 0:
continue
num_pair[index] = val
point = self.coords_to_point(*num_pair)
num = TexMobject(str(val))
num.add_background_rectangle()
num.scale_to_fit_height(
self.written_coordinate_height
)
num.next_to(point, DOWN + LEFT, buff=SMALL_BUFF)
coordinate_labels.add(num)
self.coordinate_labels = coordinate_labels
return coordinate_labels
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 get_animation_integral_bounds_change(self,
graph,
new_t_min,
new_t_max,
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)
if hasattr(self, "right_v_line"):
group.add(self.right_v_line)
else:
group.add(VGroup())
# because update_group expects 3 elements in group
if hasattr(self, "T_label_group"):
group.add(self.T_label_group)
else:
group.add(VGroup())
def update_group(group, alpha):
area, v_line, 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_v_line = self.get_vertical_line_to_graph(t_max, graph)
new_v_line.set_color(v_line.get_color())
T_label.move_to(new_v_line.get_bottom(), UP)
#Fade close to 0
if len(T_label) > 0:
T_label[0].set_fill(opacity=min(1, t_max))
Transform(area, new_area).update(1)
Transform(v_line, new_v_line).update(1)
return group
return UpdateFromAlphaFunc(group, update_group, run_time=run_time)
class Arrow(Line):
CONFIG = {
"tip_length": 0.25,
"tip_width_to_length_ratio": 1,
"max_tip_length_to_length_ratio": 0.35,
"max_stem_width_to_tip_width_ratio": 0.3,
"buff": MED_SMALL_BUFF,
"propagate_style_to_family": False,
"preserve_tip_size_when_scaling": True,
"normal_vector": OUT,
"use_rectangular_stem": True,
"rectangular_stem_width": 0.05,
}
def __init__(self, *args, **kwargs):
points = map(self.pointify, args)
if len(args) == 1:
args = (points[0] + UP + LEFT, points[0])
Line.__init__(self, *args, **kwargs)
self.init_tip()
if self.use_rectangular_stem and not hasattr(self, "rect"):
self.add_rectangular_stem()
self.init_colors()
def init_tip(self):
self.add_tip()
def add_tip(self, add_at_end=True):
tip = VMobject(
close_new_points=True,
mark_paths_closed=True,
fill_color=self.color,
fill_opacity=1,
stroke_color=self.color,
stroke_width=0,
)
tip.add_at_end = add_at_end
self.set_tip_points(tip, add_at_end, preserve_normal=False)
self.add(tip)
if not hasattr(self, 'tip'):
self.tip = VGroup()
self.tip.match_style(tip)
self.tip.add(tip)
return tip
def add_rectangular_stem(self):
self.rect = Rectangle(stroke_width=0,
fill_color=self.tip.get_fill_color(),
fill_opacity=self.tip.get_fill_opacity())
self.add_to_back(self.rect)
self.set_stroke(width=0)
self.set_rectangular_stem_points()
def set_rectangular_stem_points(self):
start, end = self.get_start_and_end()
tip_base_points = self.tip[0].get_anchors()[1:]
tip_base = center_of_mass(tip_base_points)
tbp1, tbp2 = tip_base_points
perp_vect = tbp2 - tbp1
tip_base_width = np.linalg.norm(perp_vect)
if tip_base_width > 0:
perp_vect /= tip_base_width
width = min(
self.rectangular_stem_width,
self.max_stem_width_to_tip_width_ratio * tip_base_width,
)
if hasattr(self, "second_tip"):
start = center_of_mass(self.second_tip.get_anchors()[1:])
self.rect.set_points_as_corners([
tip_base + perp_vect * width / 2,
start + perp_vect * width / 2,
start - perp_vect * width / 2,
tip_base - perp_vect * width / 2,
])
self.stem = self.rect # Alternate name
return self
def set_tip_points(
self,
tip,
add_at_end=True,
tip_length=None,
preserve_normal=True,
):
if tip_length is None:
tip_length = self.tip_length
if preserve_normal:
normal_vector = self.get_normal_vector()
else:
normal_vector = self.normal_vector
line_length = np.linalg.norm(self.points[-1] - self.points[0])
tip_length = min(tip_length,
self.max_tip_length_to_length_ratio * line_length)
indices = (-2, -1) if add_at_end else (1, 0)
pre_end_point, end_point = [
self.get_anchors()[index] for index in indices
]
vect = end_point - pre_end_point
perp_vect = np.cross(vect, normal_vector)
for v in vect, perp_vect:
if np.linalg.norm(v) == 0:
v[0] = 1
v *= tip_length / np.linalg.norm(v)
ratio = self.tip_width_to_length_ratio
tip.set_points_as_corners([
end_point,
end_point - vect + perp_vect * ratio / 2,
end_point - vect - perp_vect * ratio / 2,
])
return self
def get_normal_vector(self):
p0, p1, p2 = self.tip[0].get_anchors()
result = np.cross(p2 - p1, p1 - p0)
norm = np.linalg.norm(result)
if norm == 0:
return self.normal_vector
else:
return result / norm
def reset_normal_vector(self):
self.normal_vector = self.get_normal_vector()
return self
def get_end(self):
if hasattr(self, "tip"):
return self.tip[0].get_anchors()[0]
else:
return Line.get_end(self)
def get_tip(self):
return self.tip
def put_start_and_end_on(self, *args, **kwargs):
Line.put_start_and_end_on(self, *args, **kwargs)
self.set_tip_points(self.tip[0], preserve_normal=False)
self.set_rectangular_stem_points()
return self
def scale(self, scale_factor, **kwargs):
Line.scale(self, scale_factor, **kwargs)
if self.preserve_tip_size_when_scaling:
for t in self.tip:
self.set_tip_points(t, add_at_end=t.add_at_end)
if self.use_rectangular_stem:
self.set_rectangular_stem_points()
return self
def copy(self):
return self.deepcopy()
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
class Arrow(Line):
CONFIG = {
"tip_length": 0.25,
"tip_width_to_length_ratio": 1,
"max_tip_length_to_length_ratio": 0.35,
"max_stem_width_to_tip_width_ratio": 0.3,
"buff": MED_SMALL_BUFF,
"propagate_style_to_family": False,
"preserve_tip_size_when_scaling": True,
"normal_vector": OUT,
"use_rectangular_stem": True,
"rectangular_stem_width": 0.05,
}
def __init__(self, *args, **kwargs):
points = map(self.pointify, args)
if len(args) == 1:
args = (points[0] + UP + LEFT, points[0])
Line.__init__(self, *args, **kwargs)
self.init_tip()
if self.use_rectangular_stem and not hasattr(self, "rect"):
self.add_rectangular_stem()
self.init_colors()
def init_tip(self):
self.add_tip()
def add_tip(self, add_at_end=True):
tip = VMobject(
close_new_points=True,
mark_paths_closed=True,
fill_color=self.color,
fill_opacity=1,
stroke_color=self.color,
stroke_width=0,
)
tip.add_at_end = add_at_end
self.set_tip_points(tip, add_at_end, preserve_normal=False)
self.add(tip)
if not hasattr(self, 'tip'):
self.tip = VGroup()
self.tip.match_style(tip)
self.tip.add(tip)
return tip
def add_rectangular_stem(self):
self.rect = Rectangle(
stroke_width=0,
fill_color=self.tip.get_fill_color(),
fill_opacity=self.tip.get_fill_opacity()
)
self.add_to_back(self.rect)
self.set_stroke(width=0)
self.set_rectangular_stem_points()
def set_rectangular_stem_points(self):
start, end = self.get_start_and_end()
tip_base_points = self.tip[0].get_anchors()[1:]
tip_base = center_of_mass(tip_base_points)
tbp1, tbp2 = tip_base_points
perp_vect = tbp2 - tbp1
tip_base_width = np.linalg.norm(perp_vect)
if tip_base_width > 0:
perp_vect /= tip_base_width
width = min(
self.rectangular_stem_width,
self.max_stem_width_to_tip_width_ratio * tip_base_width,
)
if hasattr(self, "second_tip"):
start = center_of_mass(
self.second_tip.get_anchors()[1:]
)
self.rect.set_points_as_corners([
tip_base + perp_vect * width / 2,
start + perp_vect * width / 2,
start - perp_vect * width / 2,
tip_base - perp_vect * width / 2,
])
self.stem = self.rect # Alternate name
return self
def set_tip_points(
self, tip,
add_at_end=True,
tip_length=None,
preserve_normal=True,
):
if tip_length is None:
tip_length = self.tip_length
if preserve_normal:
normal_vector = self.get_normal_vector()
else:
normal_vector = self.normal_vector
line_length = np.linalg.norm(self.points[-1] - self.points[0])
tip_length = min(
tip_length, self.max_tip_length_to_length_ratio * line_length
)
indices = (-2, -1) if add_at_end else (1, 0)
pre_end_point, end_point = [
self.get_anchors()[index]
for index in indices
]
vect = end_point - pre_end_point
perp_vect = np.cross(vect, normal_vector)
for v in vect, perp_vect:
if np.linalg.norm(v) == 0:
v[0] = 1
v *= tip_length / np.linalg.norm(v)
ratio = self.tip_width_to_length_ratio
tip.set_points_as_corners([
end_point,
end_point - vect + perp_vect * ratio / 2,
end_point - vect - perp_vect * ratio / 2,
])
return self
def get_normal_vector(self):
p0, p1, p2 = self.tip[0].get_anchors()
result = np.cross(p2 - p1, p1 - p0)
norm = np.linalg.norm(result)
if norm == 0:
return self.normal_vector
else:
return result / norm
def reset_normal_vector(self):
self.normal_vector = self.get_normal_vector()
return self
def get_end(self):
if hasattr(self, "tip"):
return self.tip[0].get_anchors()[0]
else:
return Line.get_end(self)
def get_tip(self):
return self.tip
def put_start_and_end_on(self, *args, **kwargs):
Line.put_start_and_end_on(self, *args, **kwargs)
self.set_tip_points(self.tip[0], preserve_normal=False)
self.set_rectangular_stem_points()
return self
def scale(self, scale_factor, **kwargs):
Line.scale(self, scale_factor, **kwargs)
if self.preserve_tip_size_when_scaling:
for t in self.tip:
self.set_tip_points(t, add_at_end=t.add_at_end)
if self.use_rectangular_stem:
self.set_rectangular_stem_points()
return self
def copy(self):
return self.deepcopy()
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.scale_to_fit_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(
self.dot_template_iterators[place].next()
)
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,
submobject_mode="lagged_start"
))
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 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 RandomWalk1DArrow(RandomWalk1D):
CONFIG = {
"up_color": BLUE,
"down_color": RED,
}
def generate_points(self):
self.arrow_group = VGroup()
vertices = self.generate_vertices_from_string(self.walk_string)
for k in range(len(vertices) - 1):
arrow = Arrow(vertices[k],
vertices[k + 1],
color=self.get_arrow_color_by_number(k),
buff=0)
self.arrow_group.add(arrow)
self.add(self.arrow_group)
self.horizontally_center()
def get_length(self):
return len(self.arrow_group)
def get_arrow_by_number(self, n):
return self.arrow_group[n]
def get_arrow_color_by_number(self, n):
return self.up_color if self.walk_string[
n] == self.up_char else self.down_color
def split_at(self, n):
if n < 0:
return VGroup(), self.arrow_group
else:
return VGroup(self.arrow_group[:n + 1]), VGroup(
self.arrow_group[n + 1:])
def get_arrow_starting_point(self, n):
arrow = self.get_arrow_by_number(n)
return arrow.get_start()
def get_arrow_end_point(self, n):
arrow = self.get_arrow_by_number(n)
return arrow.get_end()
def get_starting_point(self):
return self.get_arrow_starting_point(0)
def get_end_point(self):
return self.get_arrow_end_point(-1)
def move_start_to(self, position):
self.shift(position - self.get_starting_point())
return self
def get_flip_arrows_animation(self, n, color=None):
arrows = [self.get_arrow_by_number(k) for k in range(n + 1)]
for arrow in arrows:
arrow.generate_target()
arrow.target.rotate(np.pi)
if color is not None:
arrow.target.set_color(color)
return AnimationGroup(*[MoveToTarget(arrow) for arrow in arrows])
