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Finished LongAndShortSignalsInWindingMachine in uncertainty project

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This commit is contained in:
Grant Sanderson 2018-02-15 18:36:29 -08:00
parent 5a8af8e0b6
commit 2b43f03952
2 changed files with 175 additions and 17 deletions
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1
active_projects/fourier.py
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@ -65,6 +65,7 @@ def get_fourier_transform(
func, t_min, t_max,
complex_to_real_func = DEFAULT_COMPLEX_TO_REAL_FUNC,
use_almost_fourier = USE_ALMOST_FOURIER_BY_DEFAULT,
**kwargs ##Just eats these
):
scalar = 1./(t_max - t_min) if use_almost_fourier else 1.0
def fourier_transform(f):

191
active_projects/uncertainty.py
View file

@ -404,6 +404,10 @@ class MentionUncertaintyPrinciple(TeacherStudentsScene):
self.wait()
class FourierTradeoff(Scene):
CONFIG = {
"show_text" : True,
"complex_to_real_func" : abs,
}
def construct(self):
#Setup axes
time_mean = 4
@ -476,8 +480,7 @@ class FourierTradeoff(Scene):
t_min = time_mean - time_radius,
t_max = time_mean + time_radius,
n_samples = 2*time_radius*17,
# complex_to_real_func = abs,
complex_to_real_func = abs,
complex_to_real_func = self.complex_to_real_func,
color = FREQUENCY_COLOR,
)
@ -508,24 +511,25 @@ class FourierTradeoff(Scene):
#Draw items
self.add(time_axes, frequency_axes)
self.play(ShowCreation(wave_packet, rate_func = double_smooth))
self.play(
ReplacementTransform(
wave_packet.copy(),
fourier_graph,
),
GrowArrow(arrow),
Write(fourier_words, run_time = 1)
)
anims = [ReplacementTransform(
wave_packet.copy(), fourier_graph
)]
if self.show_text:
anims += [
GrowArrow(arrow),
Write(fourier_words, run_time = 1)
]
self.play(*anims)
# self.play(FadeOut(arrow))
self.wait()
for width in 6, 0.1, 1:
for width in 6, 0.02, 1:
self.play(
width_tracker.move_to, width*RIGHT,
wave_packet_update,
fourier_graph_update,
run_time = 3
)
if sub_words not in self.mobjects:
if sub_words not in self.mobjects and self.show_text:
self.play(FadeIn(sub_words))
else:
self.wait()
@ -1479,6 +1483,9 @@ class AskAboutLongVsShort(TeacherStudentsScene):
self.wait(5)
class LongAndShortSignalsInWindingMachine(FourierRecapScene):
CONFIG = {
"num_fourier_graph_points" : 1000,
}
def construct(self):
self.setup_axes()
self.extend_for_long_time()
@ -1489,19 +1496,169 @@ class LongAndShortSignalsInWindingMachine(FourierRecapScene):
def setup_axes(self):
FourierRecapScene.setup_axes(self)
self.add(self.circle_plane)
self.add(self.frequency_graph)
self.add(self.frequency_axes)
self.time_graph = self.graph = self.get_time_graph(width = 2)
self.add(self.time_graph)
self.force_skipping()
self.wrap_signal_around_circle()
fourier_graph = self.get_fourier_transform_graph(self.time_graph)
self.fourier_graph = fourier_graph
self.add(fourier_graph)
self.change_frequency(5)
self.revert_to_original_skipping_status()
def extend_for_long_time(self):
pass
short_time_graph = self.time_graph
long_time_graph = self.get_time_graph(
width = 10,
num_graph_points = 500,
)
long_time_graph.set_stroke(width = 2)
new_freq = 5.1
long_pol_graph = self.get_polarized_mobject(
long_time_graph,
freq = new_freq
)
fourier_graph = self.fourier_graph
self.change_frequency(new_freq)
self.play(
FadeOut(self.graph),
FadeOut(self.graph.polarized_mobject),
FadeOut(fourier_graph)
)
self.play(
ShowCreation(long_time_graph, rate_func = None),
ShowCreation(long_pol_graph, rate_func = None),
run_time = 5
)
self.wait()
self.time_graph = self.graph = long_time_graph
def note_sharp_fourier_peak(self):
pass
fourier_graph = self.get_fourier_transform_graph(
self.time_graph,
num_graph_points = self.num_fourier_graph_points
)
self.fourier_graph = fourier_graph
self.note_fourier_peak(fourier_graph, 5, 5.1)
def very_short_signal(self):
pass
time_graph = self.time_graph
fourier_graph = self.fourier_graph
short_time_graph = self.get_time_graph(width = 0.6)
new_freq = 5.1
short_pol_graph = self.get_polarized_mobject(
short_time_graph,
freq = new_freq
)
self.play(
FadeOut(fourier_graph),
FadeOut(time_graph),
FadeOut(time_graph.polarized_mobject),
)
self.play(
ShowCreation(short_time_graph),
ShowCreation(short_time_graph.polarized_mobject),
)
self.graph = self.time_graph = short_time_graph
self.change_frequency(6.66, run_time = 5)
def note_wide_fourier_peak(self):
pass
fourier_graph = self.get_fourier_transform_graph(
self.graph,
num_graph_points = self.num_fourier_graph_points
)
self.fourier_graph = fourier_graph
self.note_fourier_peak(fourier_graph, 5, 6.66)
###
def note_fourier_peak(self, fourier_graph, freq1, freq2):
fourier_graph = self.fourier_graph
dots = self.get_fourier_graph_dots(fourier_graph, freq1, freq2)
self.get_center_of_mass_dot()
self.generate_center_of_mass_dot_update_anim()
self.generate_fourier_dot_transform(fourier_graph)
dot = self.fourier_graph_dot
arrow = Arrow(UP, ORIGIN, buff = SMALL_BUFF)
arrow.next_to(dot, UP, buff = SMALL_BUFF)
self.play(ShowCreation(fourier_graph))
self.change_frequency(freq1,
added_anims = [
MaintainPositionRelativeTo(arrow, dot),
UpdateFromAlphaFunc(
arrow,
lambda m, a : m.set_fill(opacity = a)
),
],
run_time = 3,
)
self.wait()
self.change_frequency(freq2,
added_anims = [
MaintainPositionRelativeTo(arrow, dot)
],
run_time = 3
)
self.wait()
self.play(*map(FadeOut, [
dot, arrow, self.center_of_mass_dot
]))
#This is not great...
for attr in "center_of_mass_dot", "fourier_graph_dot":
self.__dict__.pop(attr)
def get_fourier_graph_dots(self, fourier_graph, *freqs):
axis_point = self.frequency_axes.coords_to_point(4.5, -0.25)
dots = VGroup()
for freq in freqs:
point = self.frequency_axes.input_to_graph_point(freq, fourier_graph)
dot = Dot(point)
dot.scale(0.5)
dots.add(dot)
vect = point - axis_point
vect *= 1.3/np.linalg.norm(vect)
arrow = Arrow(vect, ORIGIN, buff = SMALL_BUFF)
arrow.highlight(YELLOW)
arrow.shift(point)
dot.arrow = arrow
return dots
class CleanerFourierTradeoff(FourierTradeoff):
CONFIG = {
"show_text" : False,
"complex_to_real_func" : lambda z : z.real,
}