def calc_new_agc_info(agc1, agc2, agc3, known_agc=None):
k1, k2, k3 = [agc.get_curvature() for agc in (agc1, agc2, agc3)]
z1, z2, z3 = [agc.get_complex_center() for agc in (agc1, agc2, agc3)]
sum_k = k1 + k2 + k3
sum_kz = k1 * z1 + k2 * z2 + k3 * z3
if known_agc is not None:
kc = known_agc.get_curvature()
zc = known_agc.get_complex_center()
k4 = 2 * sum_k - kc
z4 = (2 * sum_kz - kc * zc) / k4
return k4, complex_to_R3(z4)
else:
# Calculate the curvatures of new circles
sum_k2 = k1**2 + k2**2 + k3**2
sum_k_cycle_prod = k1 * k2 + k2 * k3 + k3 * k1
b = (-2) * sum_k
c = sum_k2 - 2 * sum_k_cycle_prod
delta = b**2 - 4 * c
k4_1 = (-b + np.sqrt(delta)) / 2
k4_2 = (-b - np.sqrt(delta)) / 2
# Calculate the centers of new circles
# arxiv.org/abs/math/0101066v1 - Eqn 2.3
sum_k2z = k1**2 * z1 + k2**2 * z2 + k3**2 * z3
coeff_1 = (sum_k - k4_1) * k4_1
const_1 = 2 * sum_k2z - (sum_k + k4_1) * sum_kz
z4_1 = const_1 / coeff_1
coeff_2 = (sum_k - k4_2) * k4_2
const_2 = 2 * sum_k2z - (sum_k + k4_2) * sum_kz
z4_2 = const_2 / coeff_2
return [(k4_1, complex_to_R3(z4_1)), (k4_2, complex_to_R3(z4_2))]
def __init__(self, function, mobject, **kwargs):
if "path_func" not in kwargs:
self.path_func = path_along_arc(np.log(function(complex(1))).imag)
ApplyPointwiseFunction.__init__(
self,
lambda x_y_z: complex_to_R3(function(complex(x_y_z[0], x_y_z[1]))),
instantiate(mobject), **kwargs)
def __init__(self, **kwargs):
circle = Circle(color=WHITE)
ticks = []
for x in range(12):
alpha = x / 12.
point = complex_to_R3(np.exp(2 * np.pi * alpha * complex(0, 1)))
length = 0.2 if x % 3 == 0 else 0.1
ticks.append(Line(point, (1 - length) * point))
self.hour_hand = Line(ORIGIN, 0.3 * UP)
self.minute_hand = Line(ORIGIN, 0.6 * UP)
# for hand in self.hour_hand, self.minute_hand:
# #Balance out where the center is
# hand.add(VectorizedPoint(-hand.get_end()))
VGroup.__init__(self, circle, self.hour_hand, self.minute_hand, *ticks)
def __init__(self, **kwargs):
circle = Circle(color=WHITE)
ticks = []
for x in range(12):
alpha = x / 12.
point = complex_to_R3(
np.exp(2 * np.pi * alpha * complex(0, 1))
)
length = 0.2 if x % 3 == 0 else 0.1
ticks.append(
Line(point, (1 - length) * point)
)
self.hour_hand = Line(ORIGIN, 0.3 * UP)
self.minute_hand = Line(ORIGIN, 0.6 * UP)
# for hand in self.hour_hand, self.minute_hand:
# #Balance out where the center is
# hand.add(VectorizedPoint(-hand.get_end()))
VGroup.__init__(
self, circle,
self.hour_hand, self.minute_hand,
*ticks
)
