Finished DrawFrequencyPlot of Fourier

This commit is contained in:
Grant Sanderson 2018-01-19 18:35:58 -08:00
parent d8b49f471a
commit a28d13fc3e

View file

@ -707,10 +707,7 @@ class FourierMachineScene(Scene):
for label in labels:
label.scale(self.text_scale_val)
time_label.next_to(time_axes.coords_to_point(3.5,0), DOWN)
intensity_label.next_to(
time_axes.y_axis.get_top(), RIGHT,
aligned_edge = UP,
)
intensity_label.next_to(time_axes.y_axis.get_top(), RIGHT)
time_axes.labels = labels
time_axes.add(labels)
time_axes.to_corner(UP+LEFT)
@ -764,8 +761,10 @@ class FourierMachineScene(Scene):
graph = self.time_axes.get_graph(func, **config)
return graph
def get_cosine_wave(self, freq = 1):
return self.get_time_graph(lambda t : 1 + 0.5*np.cos(TAU*freq*t))
def get_cosine_wave(self, freq = 1, shift_val = 1, scale_val = 0.9):
return self.get_time_graph(
lambda t : shift_val + scale_val*np.cos(TAU*freq*t)
)
def get_fourier_transform_graph(self, time_graph, **kwargs):
if not hasattr(self, "frequency_axes"):
@ -795,7 +794,6 @@ class FourierMachineScene(Scene):
)[0]
return fourier_transform
def get_polarized_mobject(self, mobject, freq = 1.0):
if not hasattr(self, "circle_plane"):
self.get_circle_plane()
@ -958,6 +956,8 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
for x in 1, 2
])
words = self.get_bps_label()
words.save_state()
words.next_to(axes.coords_to_point(1.5, 0), DOWN, MED_LARGE_BUFF)
self.add(axes)
self.play(ShowCreation(graph, run_time = 2, rate_func = None))
@ -967,7 +967,10 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
*map(ShowCreation, v_lines)
)
self.wait()
self.play(FadeOut(VGroup(braces, v_lines)))
self.play(
FadeOut(VGroup(braces, v_lines)),
words.restore,
)
self.wait()
self.beats_per_second_label = words
@ -1101,7 +1104,7 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
braces = VGroup(*self.get_peak_braces()[3:6])
words = TextMobject("3 beats/second")
words.scale_to_fit_width(0.9*braces.get_width())
words.next_to(braces, UP, SMALL_BUFF)
words.move_to(braces, DOWN)
return words
class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
@ -1112,9 +1115,9 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
def construct(self):
self.remove(self.pi_creature)
self.setup_graph()
# self.indicate_weight_of_wire()
self.indicate_weight_of_wire()
self.show_center_of_mass_dot()
# self.change_to_various_frequencies()
self.change_to_various_frequencies()
self.introduce_frequency_plot()
self.draw_full_frequency_plot()
self.recap_objects_on_screen()
@ -1229,6 +1232,7 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
),
t_min = 0, t_max = TAU,
)
flower_path.move_to(self.center_of_mass_dot)
self.play(
wps_label.move_to, self.circle_plane.get_top(),
@ -1245,6 +1249,8 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
))
self.wait()
self.x_coord_label = x_coord_label
def draw_full_frequency_plot(self):
graph = self.graph
fourier_graph = self.get_fourier_transform_graph(graph)
@ -1255,51 +1261,129 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
stroke_width = 6,
color = fourier_graph.get_color()
)
dot = Dot(color = fourier_graph.get_color())
def update_dot(dot):
f = self.graph.polarized_mobject.frequency
dot.move_to(self.frequency_axes.input_to_graph_point(
f, fourier_graph
))
dot_update_anim = UpdateFromFunc(dot, update_dot)
self.change_frequency(0.0)
dot_update_anim.update(0)
self.generate_fourier_dot_transform(fourier_graph)
self.wait()
self.play(ShowCreation(v_line))
self.play(GrowFromCenter(dot), FadeOut(v_line))
self.play(
GrowFromCenter(self.fourier_graph_dot),
FadeOut(v_line)
)
f_max = int(self.frequency_axes.x_max)
for freq in range(1, f_max+1):
for freq in [0.2, 1.5, 3.0, 4.0, 5.0]:
fourier_graph.restore()
self.change_frequency(
freq,
added_anims = [
ShowCreation(
fourier_graph,
rate_func = lambda t : interpolate(
(freq-1.)/f_max,
float(freq)/f_max,
smooth(t)
),
added_anims = [ShowCreation(
fourier_graph,
rate_func = lambda t : interpolate(
(freq-1.)/f_max,
float(freq)/f_max,
smooth(t)
),
dot_update_anim
],
)],
run_time = 5,
)
self.wait()
self.play(FadeOut(dot))
self.fourier_graph = fourier_graph
def recap_objects_on_screen(self):
rect = FullScreenFadeRectangle()
time_group = VGroup(
self.graph,
self.time_axes,
self.beats_per_second_label,
).copy()
circle_group = VGroup(
self.graph.polarized_mobject,
self.circle_plane,
self.winding_freq_label,
self.center_of_mass_label,
self.center_of_mass_dot,
).copy()
frequency_group = VGroup(
self.fourier_graph,
self.frequency_axes,
self.x_coord_label,
).copy()
groups = [time_group, circle_group, frequency_group]
self.play(FadeIn(rect))
self.wait()
for group in groups:
self.play(FadeIn(group))
self.play(ShowCreation(group[0]))
self.wait()
self.play(FadeOut(group))
self.wait()
self.play(FadeOut(rect))
def lower_graph(self):
pass
graph = self.graph
time_axes = self.time_axes
shift_vect = time_axes.coords_to_point(0, 1)
shift_vect -= time_axes.coords_to_point(0, 0)
fourier_graph = self.fourier_graph
new_graph = self.get_cosine_wave(
self.signal_frequency, shift_val = 0
)
new_fourier_graph = self.get_fourier_transform_graph(new_graph)
for mob in graph, time_axes, fourier_graph:
mob.save_state()
new_freq = 0.03
self.change_frequency(new_freq)
self.wait()
self.play(
time_axes.shift, shift_vect/2,
graph.shift, -shift_vect/2,
self.get_frequency_change_animation(
self.graph, new_freq
),
self.center_of_mass_dot_anim,
self.get_period_v_lines_update_anim(),
Transform(fourier_graph, new_fourier_graph),
self.fourier_graph_dot.move_to,
self.frequency_axes.coords_to_point(new_freq, 0),
run_time = 2
)
self.wait()
self.remove(self.fourier_graph_dot)
self.generate_fourier_dot_transform(new_fourier_graph)
self.change_frequency(3.0, run_time = 15, rate_func = None)
self.wait()
self.play(
graph.restore,
time_axes.restore,
self.get_frequency_change_animation(
self.graph, 3.0
),
self.center_of_mass_dot_anim,
self.get_period_v_lines_update_anim(),
fourier_graph.restore,
Animation(self.fourier_graph_dot),
run_time = 2
)
self.generate_fourier_dot_transform(self.fourier_graph)
self.wait()
self.play(FocusOn(self.fourier_graph_dot))
self.wait()
def label_as_almost_fourier(self):
pass
x_coord_label = self.x_coord_label
almost_fourier_label = TextMobject(
"``Almost Fourier Transform''",
)
almost_fourier_label.move_to(x_coord_label, UP+LEFT)
x_coord_label.generate_target()
x_coord_label.target.next_to(almost_fourier_label, DOWN)
self.play(
MoveToTarget(x_coord_label),
Write(almost_fourier_label)
)
self.wait(2)
##
@ -1314,6 +1398,18 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
# result += self.circle_plane.get_center()
return result
def generate_fourier_dot_transform(self, fourier_graph):
self.fourier_graph_dot = Dot(color = WHITE, radius = 0.05)
def update_dot(dot):
f = self.graph.polarized_mobject.frequency
dot.move_to(self.frequency_axes.input_to_graph_point(
f, fourier_graph
))
self.fourier_graph_dot_anim = UpdateFromFunc(
self.fourier_graph_dot, update_dot
)
self.fourier_graph_dot_anim.update(0)
def change_frequency(self, new_freq, **kwargs):
kwargs["run_time"] = kwargs.get("run_time", 3)
added_anims = kwargs.get("added_anims", [])
@ -1329,14 +1425,40 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
self.get_period_v_lines_update_anim(),
]
anims += added_anims
#TODO, conditionals for center of mass
if hasattr(self, "center_of_mass_dot"):
anims.append(self.center_of_mass_dot_anim)
if hasattr(self, "fourier_graph_dot"):
anims.append(self.fourier_graph_dot_anim)
self.play(*anims, **kwargs)
def create_pi_creature(self):
return Mortimer().to_corner(DOWN+RIGHT)
class StudentsHorrifiedAtScene(TeacherStudentsScene):
def construct(self):
self.change_student_modes(
*3*["horrified"],
look_at_arg = 2*UP + 3*LEFT
)
self.wait(4)
class ShowLinearity(DrawFrequencyPlot):
def construct(self):
self.show_lower_frequency_signal()
self.play_with_lower_frequency_signal()
self.point_out_fourier_spike()