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
def update_func(group, alpha):
dx = interpolate(start_dx, target_dx, alpha)
x = interpolate(start_x, target_x, alpha)
kwargs = dict(secant_slope_group.kwargs)
kwargs["dx"] = dx
kwargs["x"] = x
new_group = self.get_secant_slope_group(**kwargs)
Transform(group, new_group).update(1)
return group
def update_submobject(self, submobject, starting_sumobject, alpha):
submobject.points[:, :] = starting_sumobject.points
submobject.scale(interpolate(1, self.scale_value,
there_and_back(alpha)),
about_point=self.scale_about_point)
submobject.rotate(wiggle(alpha, self.n_wiggles) * self.rotation_angle,
about_point=self.rotate_about_point)
def fade_to_no_recurse(self, color, alpha):
if self.get_num_points() > 0:
start = color_to_rgb(self.get_color())
end = color_to_rgb(color)
new_rgb = interpolate(start, end, alpha)
self.set_color(Color(rgb=new_rgb), family=False)
return self
def straight_path(start_points, end_points, alpha):
"""
Same function as interpolate, but renamed to reflect
intent of being used to determine how a set of points move
to another set. For instance, it should be a specific case
of path_along_arc
"""
return interpolate(start_points, end_points, alpha)
def set_points_as_corners(self, points):
if len(points) <= 1:
return self
points = np.array(points)
self.set_anchors_and_handles(
points, *[
interpolate(points[:-1], points[1:], alpha)
for alpha in (1. / 3, 2. / 3)
])
return self
def set_colors_by_radial_gradient(self, center=None, radius=1, inner_color=WHITE, outer_color=BLACK):
start_rgba, end_rgba = list(map(color_to_rgba, [start_color, end_color]))
if center is None:
center = self.get_center()
for mob in self.family_members_with_points():
num_points = mob.get_num_points()
t = min(1, np.abs(mob.get_center() - center) / radius)
mob.rgbas = np.array(
[interpolate(start_rgba, end_rgba, t)] * num_points
)
return self
def add_line(self, start, end, color=None):
start, end = list(map(np.array, [start, end]))
length = get_norm(end - start)
if length == 0:
points = [start]
else:
epsilon = self.epsilon / length
points = [
interpolate(start, end, t)
for t in np.arange(0, 1, epsilon)
]
self.add_points(points, color=color)
def color_gradient(reference_colors, length_of_output):
if length_of_output == 0:
return reference_colors[0]
rgbs = list(map(color_to_rgb, reference_colors))
alphas = np.linspace(0, (len(rgbs) - 1), length_of_output)
floors = alphas.astype('int')
alphas_mod1 = alphas % 1
# End edge case
alphas_mod1[-1] = 1
floors[-1] = len(rgbs) - 2
return [
rgb_to_color(interpolate(rgbs[i], rgbs[i + 1], alpha))
for i, alpha in zip(floors, alphas_mod1)
]
def set_color_by_gradient(self, *colors):
self.rgbas = np.array(list(map(
color_to_rgba,
color_gradient(colors, len(self.points))
)))
return self
start_rgba, end_rgba = list(map(color_to_rgba, [start_color, end_color]))
for mob in self.family_members_with_points():
num_points = mob.get_num_points()
mob.rgbas = np.array([
interpolate(start_rgba, end_rgba, alpha)
for alpha in np.arange(num_points) / float(num_points)
])
return self
def interpolate_color(self, mobject1, mobject2, alpha):
attrs = [
"fill_rgbas",
"stroke_rgbas",
"background_stroke_rgbas",
"stroke_width",
"background_stroke_width",
"sheen_direction",
"sheen",
]
for attr in attrs:
setattr(
self, attr,
interpolate(getattr(mobject1, attr), getattr(mobject2, attr),
alpha))
if alpha == 1.0:
setattr(self, attr, getattr(mobject2, attr))
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 fractalification_iteration(vmobject,
dimension=1.05,
num_inserted_anchors_range=list(range(1, 4))):
num_points = vmobject.get_num_points()
if num_points > 0:
# original_anchors = vmobject.get_anchors()
original_anchors = [
vmobject.point_from_proportion(x)
for x in np.linspace(0, 1 - 1. / num_points, num_points)
]
new_anchors = []
for p1, p2, in zip(original_anchors, original_anchors[1:]):
num_inserts = random.choice(num_inserted_anchors_range)
inserted_points = [
interpolate(p1, p2, alpha)
for alpha in np.linspace(0, 1, num_inserts + 2)[1:-1]
]
mass_scaling_factor = 1. / (num_inserts + 1)
length_scaling_factor = mass_scaling_factor**(1. / dimension)
target_length = get_norm(p1 - p2) * length_scaling_factor
curr_length = get_norm(p1 - p2) * mass_scaling_factor
# offset^2 + curr_length^2 = target_length^2
offset_len = np.sqrt(target_length**2 - curr_length**2)
unit_vect = (p1 - p2) / get_norm(p1 - p2)
offset_unit_vect = rotate_vector(unit_vect, np.pi / 2)
inserted_points = [
point + u * offset_len * offset_unit_vect
for u, point in zip(it.cycle([-1, 1]), inserted_points)
]
new_anchors += [p1] + inserted_points
new_anchors.append(original_anchors[-1])
vmobject.set_points_as_corners(new_anchors)
vmobject.submobjects = [
fractalification_iteration(submob, dimension,
num_inserted_anchors_range)
for submob in vmobject.submobjects
]
return vmobject
def update_submobject(self, submobject, starting_submobject, alpha):
submobject.pointwise_become_partial(starting_submobject, 0,
min(2 * alpha, 1))
if alpha < 0.5:
if self.stroke_color:
color = self.stroke_color
elif starting_submobject.stroke_width > 0:
color = starting_submobject.get_stroke_color()
else:
color = starting_submobject.get_color()
submobject.set_stroke(color, width=self.stroke_width)
submobject.set_fill(opacity=0)
else:
if not self.reached_halfway_point_before:
self.reached_halfway_point_before = True
submobject.points = np.array(starting_submobject.points)
width, opacity = [
interpolate(start, end, 2 * alpha - 1)
for start, end in [(self.stroke_width,
starting_submobject.get_stroke_width()),
(0, starting_submobject.get_fill_opacity())]
]
submobject.set_stroke(width=width)
submobject.set_fill(opacity=opacity)
def update_submobject(self, submobject, starting_submobject, alpha):
submobject.set_stroke(opacity=interpolate(
0, starting_submobject.get_stroke_opacity(), alpha))
submobject.set_fill(opacity=interpolate(
0, starting_submobject.get_fill_opacity(), alpha))
def fade_to(self, color, alpha):
self.rgbas = interpolate(self.rgbas, color_to_rgba(color), alpha)
for mob in self.submobjects:
mob.fade_to(color, alpha)
return self
def interpolate_color(self, mobject1, mobject2, alpha):
assert (mobject1.pixel_array.shape == mobject2.pixel_array.shape)
self.pixel_array = interpolate(mobject1.pixel_array,
mobject2.pixel_array,
alpha).astype(self.pixel_array_dtype)
def interpolate_color(self, mobject1, mobject2, alpha):
self.rgbas = interpolate(
mobject1.rgbas, mobject2.rgbas, alpha
)
def parameterized_function(alpha):
x = interpolate(x_min, x_max, alpha)
y = func(x)
if not np.isfinite(y):
y = self.y_max
return self.coords_to_point(x, y)
def interpolate_color(color1, color2, alpha):
rgb = interpolate(color_to_rgb(color1), color_to_rgb(color2), alpha)
return rgb_to_color(rgb)
def random_bright_color():
color = random_color()
curr_rgb = color_to_rgb(color)
new_rgb = interpolate(curr_rgb, np.ones(len(curr_rgb)), 0.5)
return Color(rgb=new_rgb)
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)
