def __init__(self, complex_homotopy, mobject = ComplexPlane, **kwargs):
"""
Complex Hootopy a function Cx[0, 1] to C
"""
def homotopy((x, y, z, t)):
c = complex_homotopy((complex(x, y), t))
return (c.real, c.imag, z)
Homotopy.__init__(self, homotopy, mobject, *args, **kwargs)
def __init__(self, complex_homotopy, mobject = ComplexPlane, **kwargs):
"""
Complex Hootopy a function Cx[0, 1] to C
"""
def homotopy((x, y, z, t)):
c = complex_homotopy((complex(x, y), t))
return (c.real, c.imag, z)
Homotopy.__init__(self, homotopy, mobject, *args, **kwargs)
def discontinuous_point(self):
point_description = TextMobject("Point where the function jumps")
point_description.shift(3 * RIGHT)
discontinuous_at_A = TextMobject("``Discontinuous at A''",
size="\\Large")
discontinuous_at_A.shift(2 * UP).to_edge(LEFT)
text = TextMobject("""
Circle around ouput \\\\
points can never \\\\
be smaller than \\\\
the jump
""")
text.scale(0.75)
text.shift(3.5 * RIGHT)
input_value = 0.5
input_radius = 0.04
vary_circles = VaryCircles(
self,
input_value,
input_radius,
run_time=5,
)
for dot in self.input_dot, self.output_dot:
dot.center()
kwargs = {
"rate_func": lambda t: interpolate(0.45, input_value, smooth(t))
}
self.play(Homotopy(self.input_homotopy, self.input_dot, **kwargs),
Homotopy(self.output_homotopy, self.output_dot, **kwargs))
discontinuous_arrow = Arrow(discontinuous_at_A, self.input_dot)
arrow = Arrow(point_description,
self.output_dot,
buff=0.05,
color=self.output_color)
self.play(ShimmerIn(point_description), ShowCreation(arrow))
self.dither()
self.remove(point_description, arrow)
tup = self.get_circles_and_points(input_value - input_radius,
input_value + input_radius)
input_circle, input_points, output_circle, output_points = tup
input_points_copy = input_points.copy()
self.play(ShowCreation(input_circle))
self.play(ShowCreation(input_points))
self.play(Transform(input_points_copy, output_points), run_time=2)
self.play(ShowCreation(output_circle))
self.dither()
self.play(ShimmerIn(text))
self.remove(input_circle, input_points, output_circle,
input_points_copy)
self.play(vary_circles)
self.dither()
self.play(ShimmerIn(discontinuous_at_A),
ShowCreation(discontinuous_arrow))
self.dither(3)
self.remove(vary_circles.mobject, discontinuous_at_A,
discontinuous_arrow)
def draw_circles(self):
input_value = 0.45
input_radius = 0.04
for dot in self.input_dot, self.output_dot:
dot.center()
kwargs = {
"rate_func" : lambda t : interpolate(1, input_value, smooth(t))
}
self.play(
Homotopy(self.input_homotopy, self.input_dot, **kwargs),
Homotopy(self.output_homotopy, self.output_dot, **kwargs)
)
A, B = map(Mobject.get_center, [self.input_dot, self.output_dot])
A_text = TextMobject("A")
A_text.shift(A+2*(LEFT+UP))
A_arrow = Arrow(
A_text, self.input_dot,
color = self.input_color
)
B_text = TextMobject("B")
B_text.shift(B+2*RIGHT+DOWN)
B_arrow = Arrow(
B_text, self.output_dot,
color = self.output_color
)
tup = self.get_circles_and_points(
input_value-input_radius,
input_value+input_radius
)
input_circle, input_points, output_circle, output_points = tup
for text, arrow in [(A_text, A_arrow), (B_text, B_arrow)]:
self.play(
ShimmerIn(text),
ShowCreation(arrow)
)
self.wait()
self.remove(A_text, A_arrow, B_text, B_arrow)
self.play(ShowCreation(input_circle))
self.wait()
self.play(ShowCreation(input_points))
self.wait()
input_points_copy = input_points.copy()
self.play(
Transform(input_points_copy, output_points),
run_time = 2
)
self.wait()
self.play(ShowCreation(output_circle))
self.wait()
self.wait()
self.remove(*[
input_circle, input_points,
output_circle, input_points_copy
])
def move_dot(self):
kwargs = {
"rate_func" : None,
"run_time" : 3
}
self.play(
Homotopy(self.input_homotopy, self.input_dot, **kwargs),
Homotopy(self.output_homotopy, self.output_dot, **kwargs),
ShowCreation(self.output, **kwargs)
)
self.wait()
