def get_mobject_key(mobject: VMobject) -> int:
mobject.save_state()
mobject.center()
mobject.set_height(1)
result = hash(np.round(mobject.get_points(), 3).tobytes())
mobject.restore()
return result
class Polarization(Scene):
CONFIG = {
"period": 6,
"camera_config": {
"background_color": Color("white")
},
"axes_scale": 0.9,
"vector_length": 2,
"vector_args": {
"max_stroke_width_to_length_ratio": 10000,
"max_tip_length_to_length_ratio": 0.95,
},
"xy_line_stroke_width": DEFAULT_STROKE_WIDTH / 2,
"xy_line_color": Color("blue"),
"path_color": Color("red"),
"axes_color": BLACK,
"axes_vector_color": Color("green"),
"xy_vector_color": Color("blue"),
}
def construct(self):
self.phase = 0
point_x, point_y = self.comp_point(0)
self.make_axes()
self.ellipse = VMobject(color=self.path_color)
self.phi = TexMobject(r"\Delta \Phi = ").set_color(BLACK).shift(4 *
RIGHT +
2 * UP)
self.phi_0 = TexMobject("0").set_color(BLACK).next_to(self.phi, RIGHT)
self.phi_pi_2 = TexMobject(r"\frac{\pi}{2}").set_color(BLACK).next_to(
self.phi, RIGHT).shift(0.06 * DOWN)
self.phi_3_pi_4 = TexMobject(r"\frac{3 \pi}{4}").set_color(
BLACK).next_to(self.phi, RIGHT)
self.x_vector = Vector(point_x * RIGHT,
color=self.axes_vector_color,
**self.vector_args)
self.y_vector = Vector(point_y * UP,
color=self.axes_vector_color,
**self.vector_args)
self.xy_vector = Vector(point_x * RIGHT + point_y * UP,
color=self.xy_vector_color,
**self.vector_args)
update_group = VGroup(
self.ellipse,
self.xy_vector,
self.x_vector,
self.y_vector,
)
self.wait(1.6)
self.add(self.ellipse)
self.play(FadeIn(self.x_vector))
# self.wait(1)
self.play(FadeIn(self.y_vector))
self.wait(4)
self.play(FadeIn(self.xy_vector))
self.play(UpdateFromAlphaFunc(update_group,
self.do_vectors_and_ellipse_period),
run_time=self.period,
rate_func=linear)
self.play(
UpdateFromAlphaFunc(update_group,
self.do_vectors_only_period,
run_time=self.period,
rate_func=linear))
self.play(
AnimationGroup(UpdateFromAlphaFunc(update_group,
self.do_vectors_only_period,
run_time=self.period,
rate_func=linear),
AnimationGroup(FadeIn(self.phi),
FadeIn(self.phi_0)),
lag_ratio=0.7))
self.play(
UpdateFromAlphaFunc(update_group,
self.do_vectors_only_period,
run_time=self.period,
rate_func=linear))
self.x_vector.set_color(BLACK)
self.play(UpdateFromAlphaFunc(update_group,
self.do_90_phase_shift,
rate_func=linear),
FadeOut(self.ellipse),
FadeOut(self.phi_0),
FadeIn(self.phi_pi_2),
run_time=self.period / 4)
self.phase = np.pi / 2
self.ellipse.set_points([])
self.x_vector.set_color(self.axes_vector_color)
self.play(UpdateFromAlphaFunc(update_group,
self.do_vectors_and_ellipse_period),
run_time=self.period,
rate_func=linear)
for _ in range(3):
self.play(UpdateFromAlphaFunc(update_group,
self.do_vectors_only_period),
run_time=self.period,
rate_func=linear)
self.x_vector.set_color(BLACK)
self.play(UpdateFromAlphaFunc(update_group,
self.do_45_phase_shift,
rate_func=linear),
FadeOut(self.ellipse),
FadeOut(self.phi_pi_2),
FadeIn(self.phi_3_pi_4),
run_time=self.period / 8)
self.phase = 3 * np.pi / 4
self.ellipse.set_points([])
self.x_vector.set_color(self.axes_vector_color)
self.play(UpdateFromAlphaFunc(update_group,
self.do_vectors_and_ellipse_period),
run_time=self.period,
rate_func=linear)
self.play(
AnimationGroup(UpdateFromAlphaFunc(
update_group,
self.do_vectors_only_period_hide,
rate_func=linear,
run_time=self.period),
AnimationGroup(FadeOut(self.phi_3_pi_4),
FadeOut(self.phi)),
lag_ratio=0.7))
self.play(FadeOut(self.axes), FadeOut(self.axes_labels))
self.wait()
def make_axes(self):
self.axes = Axes(x_min=-self.axes_scale * FRAME_X_RADIUS,
x_max=self.axes_scale * FRAME_X_RADIUS,
y_min=-self.axes_scale * FRAME_Y_RADIUS,
y_max=self.axes_scale * FRAME_Y_RADIUS,
x_axis_config={"include_ticks": False},
y_axis_config={"include_ticks": False},
number_line_config={"color": self.axes_color})
self.axes_labels = self.axes.get_axis_labels(
x_label_tex="E_x", y_label_tex="E_y").set_color(self.axes_color)
self.play(
AnimationGroup(GrowFromCenter(self.axes),
FadeIn(self.axes_labels),
lag_ratio=0.4))
def do_vectors_and_ellipse_period(self, _, alpha):
point_x, point_y = self.comp_point(alpha)
self.add_point_to_ellipse(point_x, point_y)
self.set_vector_positions(point_x, point_y)
def do_vectors_only_period(self, _, alpha):
point_x, point_y = self.comp_point(alpha)
self.set_vector_positions(point_x, point_y)
def do_90_phase_shift(self, _, alpha):
alpha = interpolate(0, 1 / 4, alpha)
x_point, y_point = self.comp_point(alpha)
self.y_vector.put_start_and_end_on(ORIGIN, y_point * UP)
self.xy_vector.put_start_and_end_on(ORIGIN, y_point * UP + 2 * RIGHT)
def do_45_phase_shift(self, _, alpha):
alpha = interpolate(0, 1 / 8, alpha)
x_point, y_point = self.comp_point(alpha)
self.y_vector.put_start_and_end_on(ORIGIN, y_point * UP)
self.xy_vector.put_start_and_end_on(ORIGIN, y_point * UP + 2 * RIGHT)
def set_vector_positions(self, x, y):
self.x_vector.put_start_and_end_on(ORIGIN, x * RIGHT)
self.y_vector.put_start_and_end_on(ORIGIN, y * UP)
self.xy_vector.put_start_and_end_on(ORIGIN, x * RIGHT + y * UP)
def add_point_to_ellipse(self, x, y):
if not len(self.ellipse.get_points()):
self.ellipse.set_points([UP * y + RIGHT * x])
else:
self.ellipse.add_points_as_corners([UP * y + RIGHT * x])
def do_vectors_only_period_hide(self, _, alpha):
fade_ratio = 3
if alpha >= (fade_ratio - 1) / fade_ratio:
opacity = 1 - smooth(fade_ratio * alpha - (fade_ratio - 1))
self.x_vector.set_opacity(opacity)
self.y_vector.set_opacity(opacity)
self.xy_vector.set_opacity(opacity)
self.ellipse.set_stroke(opacity=opacity)
self.do_vectors_only_period(_, alpha)
def comp_point(self, alpha):
point_x = self.vector_length * np.cos(
2 * np.pi * alpha) * RIGHT + 0.01 * RIGHT
point_y = self.vector_length * np.cos(2 * np.pi * alpha +
self.phase) * UP + 0.01 * UP
return point_x, point_y
