def generate_dual_graph(self):
point_at_infinity = np.array([np.inf] * 3)
cycles = self.graph.region_cycles
self.dual_points = [
center_of_mass([self.points[index] for index in cycle])
for cycle in cycles
]
self.dual_vertices = [
Dot(point).set_color("green") for point in self.dual_points
]
self.dual_vertices[-1] = Circle().scale(FRAME_X_RADIUS +
FRAME_Y_RADIUS)
self.dual_points[-1] = point_at_infinity
self.dual_edges = []
for pair in self.graph.edges:
dual_point_pair = []
for cycle in cycles:
if not (pair[0] in cycle and pair[1] in cycle):
continue
index1, index2 = cycle.index(pair[0]), cycle.index(pair[1])
if abs(index1 - index2) in [1, len(cycle) - 1]:
dual_point_pair.append(
self.dual_points[cycles.index(cycle)])
assert (len(dual_point_pair) == 2)
for i in 0, 1:
if all(dual_point_pair[i] == point_at_infinity):
new_point = np.array(dual_point_pair[1 - i])
vect = center_of_mass([
self.points[pair[0]], self.points[pair[1]]
]) - new_point
new_point += FRAME_X_RADIUS * vect / np.linalg.norm(vect)
dual_point_pair[i] = new_point
self.dual_edges.append(Line(*dual_point_pair).set_color())
def set_rectangular_stem_points(self):
start, end = self.get_start_and_end()
tip_base_points = self.tip[0].get_anchors()[1:3]
tip_base = center_of_mass(tip_base_points)
tbp1, tbp2 = tip_base_points
perp_vect = tbp2 - tbp1
tip_base_width = get_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_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 generate_dual_graph(self):
point_at_infinity = np.array([np.inf] * 3)
cycles = self.graph.region_cycles
self.dual_points = [
center_of_mass([
self.points[index]
for index in cycle
])
for cycle in cycles
]
self.dual_vertices = [
Dot(point).set_color("green")
for point in self.dual_points
]
self.dual_vertices[-1] = Circle().scale(FRAME_X_RADIUS +
FRAME_Y_RADIUS)
self.dual_points[-1] = point_at_infinity
self.dual_edges = []
for pair in self.graph.edges:
dual_point_pair = []
for cycle in cycles:
if not (pair[0] in cycle and pair[1] in cycle):
continue
index1, index2 = cycle.index(pair[0]), cycle.index(pair[1])
if abs(index1 - index2) in [1, len(cycle) - 1]:
dual_point_pair.append(
self.dual_points[cycles.index(cycle)]
)
assert(len(dual_point_pair) == 2)
for i in 0, 1:
if all(dual_point_pair[i] == point_at_infinity):
new_point = np.array(dual_point_pair[1 - i])
vect = center_of_mass([
self.points[pair[0]],
self.points[pair[1]]
]) - new_point
new_point += FRAME_X_RADIUS * vect / np.linalg.norm(vect)
dual_point_pair[i] = new_point
self.dual_edges.append(
Line(*dual_point_pair).set_color()
)
def transform_points_pre_display(self, mobject, points):
fixed_orientation = mobject in self.fixed_orientation_mobjects
fixed_in_frame = mobject in self.fixed_in_frame_mobjects
if fixed_in_frame:
return points
if fixed_orientation:
center = center_of_mass(points)
new_center = self.project_point(center)
return points + (new_center - center)
else:
return self.project_points(points)
def get_anchor_points(self):
step = float(self.radius) * self.start_step
step /= (self.scale_factor**self.order)
curr = np.zeros(3)
result = [curr]
for letter in self.get_command_string():
if letter is "+":
step = rotate(step, self.angle)
elif letter is "-":
step = rotate(step, -self.angle)
else:
curr = curr + step
result.append(curr)
return np.array(result) - center_of_mass(result)
def get_anchor_points(self):
step = float(self.radius) * self.start_step
step /= (self.scale_factor**self.order)
curr = np.zeros(3)
result = [curr]
for letter in self.get_command_string():
if letter is "+":
step = rotate(step, self.angle)
elif letter is "-":
step = rotate(step, -self.angle)
else:
curr = curr + step
result.append(curr)
return np.array(result) - center_of_mass(result)
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
