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Finished DrawFrequencyPlot of Fourier
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Grant Sanderson
parent
d8b49f471a
commit
a28d13fc3e
1 changed files with 157 additions and 35 deletions
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@ -707,10 +707,7 @@ class FourierMachineScene(Scene):
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for label in labels:
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label.scale(self.text_scale_val)
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time_label.next_to(time_axes.coords_to_point(3.5,0), DOWN)
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intensity_label.next_to(
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time_axes.y_axis.get_top(), RIGHT,
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aligned_edge = UP,
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)
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intensity_label.next_to(time_axes.y_axis.get_top(), RIGHT)
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time_axes.labels = labels
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time_axes.add(labels)
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time_axes.to_corner(UP+LEFT)
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@ -764,8 +761,10 @@ class FourierMachineScene(Scene):
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graph = self.time_axes.get_graph(func, **config)
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return graph
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def get_cosine_wave(self, freq = 1):
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return self.get_time_graph(lambda t : 1 + 0.5*np.cos(TAU*freq*t))
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def get_cosine_wave(self, freq = 1, shift_val = 1, scale_val = 0.9):
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return self.get_time_graph(
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lambda t : shift_val + scale_val*np.cos(TAU*freq*t)
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)
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def get_fourier_transform_graph(self, time_graph, **kwargs):
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if not hasattr(self, "frequency_axes"):
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@ -795,7 +794,6 @@ class FourierMachineScene(Scene):
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)[0]
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return fourier_transform
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def get_polarized_mobject(self, mobject, freq = 1.0):
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if not hasattr(self, "circle_plane"):
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self.get_circle_plane()
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@ -958,6 +956,8 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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for x in 1, 2
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])
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words = self.get_bps_label()
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words.save_state()
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words.next_to(axes.coords_to_point(1.5, 0), DOWN, MED_LARGE_BUFF)
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self.add(axes)
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self.play(ShowCreation(graph, run_time = 2, rate_func = None))
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@ -967,7 +967,10 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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*map(ShowCreation, v_lines)
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)
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self.wait()
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self.play(FadeOut(VGroup(braces, v_lines)))
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self.play(
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FadeOut(VGroup(braces, v_lines)),
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words.restore,
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)
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self.wait()
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self.beats_per_second_label = words
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@ -1101,7 +1104,7 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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braces = VGroup(*self.get_peak_braces()[3:6])
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words = TextMobject("3 beats/second")
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words.scale_to_fit_width(0.9*braces.get_width())
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words.next_to(braces, UP, SMALL_BUFF)
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words.move_to(braces, DOWN)
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return words
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class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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@ -1112,9 +1115,9 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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def construct(self):
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self.remove(self.pi_creature)
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self.setup_graph()
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# self.indicate_weight_of_wire()
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self.indicate_weight_of_wire()
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self.show_center_of_mass_dot()
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# self.change_to_various_frequencies()
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self.change_to_various_frequencies()
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self.introduce_frequency_plot()
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self.draw_full_frequency_plot()
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self.recap_objects_on_screen()
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@ -1229,6 +1232,7 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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),
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t_min = 0, t_max = TAU,
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)
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flower_path.move_to(self.center_of_mass_dot)
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self.play(
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wps_label.move_to, self.circle_plane.get_top(),
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@ -1245,6 +1249,8 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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))
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self.wait()
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self.x_coord_label = x_coord_label
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def draw_full_frequency_plot(self):
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graph = self.graph
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fourier_graph = self.get_fourier_transform_graph(graph)
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@ -1255,51 +1261,129 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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stroke_width = 6,
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color = fourier_graph.get_color()
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)
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dot = Dot(color = fourier_graph.get_color())
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def update_dot(dot):
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f = self.graph.polarized_mobject.frequency
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dot.move_to(self.frequency_axes.input_to_graph_point(
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f, fourier_graph
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))
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dot_update_anim = UpdateFromFunc(dot, update_dot)
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self.change_frequency(0.0)
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dot_update_anim.update(0)
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self.generate_fourier_dot_transform(fourier_graph)
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self.wait()
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self.play(ShowCreation(v_line))
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self.play(GrowFromCenter(dot), FadeOut(v_line))
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self.play(
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GrowFromCenter(self.fourier_graph_dot),
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FadeOut(v_line)
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)
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f_max = int(self.frequency_axes.x_max)
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for freq in range(1, f_max+1):
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for freq in [0.2, 1.5, 3.0, 4.0, 5.0]:
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fourier_graph.restore()
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self.change_frequency(
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freq,
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added_anims = [
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ShowCreation(
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fourier_graph,
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rate_func = lambda t : interpolate(
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(freq-1.)/f_max,
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float(freq)/f_max,
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smooth(t)
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),
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added_anims = [ShowCreation(
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fourier_graph,
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rate_func = lambda t : interpolate(
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(freq-1.)/f_max,
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float(freq)/f_max,
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smooth(t)
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),
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dot_update_anim
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],
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)],
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run_time = 5,
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)
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self.wait()
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self.play(FadeOut(dot))
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self.fourier_graph = fourier_graph
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def recap_objects_on_screen(self):
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rect = FullScreenFadeRectangle()
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time_group = VGroup(
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self.graph,
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self.time_axes,
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self.beats_per_second_label,
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).copy()
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circle_group = VGroup(
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self.graph.polarized_mobject,
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self.circle_plane,
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self.winding_freq_label,
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self.center_of_mass_label,
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self.center_of_mass_dot,
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).copy()
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frequency_group = VGroup(
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self.fourier_graph,
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self.frequency_axes,
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self.x_coord_label,
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).copy()
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groups = [time_group, circle_group, frequency_group]
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self.play(FadeIn(rect))
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self.wait()
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for group in groups:
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self.play(FadeIn(group))
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self.play(ShowCreation(group[0]))
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self.wait()
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self.play(FadeOut(group))
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self.wait()
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self.play(FadeOut(rect))
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def lower_graph(self):
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pass
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graph = self.graph
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time_axes = self.time_axes
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shift_vect = time_axes.coords_to_point(0, 1)
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shift_vect -= time_axes.coords_to_point(0, 0)
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fourier_graph = self.fourier_graph
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new_graph = self.get_cosine_wave(
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self.signal_frequency, shift_val = 0
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)
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new_fourier_graph = self.get_fourier_transform_graph(new_graph)
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for mob in graph, time_axes, fourier_graph:
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mob.save_state()
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new_freq = 0.03
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self.change_frequency(new_freq)
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self.wait()
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self.play(
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time_axes.shift, shift_vect/2,
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graph.shift, -shift_vect/2,
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self.get_frequency_change_animation(
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self.graph, new_freq
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),
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self.center_of_mass_dot_anim,
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self.get_period_v_lines_update_anim(),
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Transform(fourier_graph, new_fourier_graph),
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self.fourier_graph_dot.move_to,
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self.frequency_axes.coords_to_point(new_freq, 0),
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run_time = 2
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)
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self.wait()
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self.remove(self.fourier_graph_dot)
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self.generate_fourier_dot_transform(new_fourier_graph)
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self.change_frequency(3.0, run_time = 15, rate_func = None)
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self.wait()
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self.play(
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graph.restore,
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time_axes.restore,
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self.get_frequency_change_animation(
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self.graph, 3.0
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),
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self.center_of_mass_dot_anim,
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self.get_period_v_lines_update_anim(),
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fourier_graph.restore,
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Animation(self.fourier_graph_dot),
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run_time = 2
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)
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self.generate_fourier_dot_transform(self.fourier_graph)
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self.wait()
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self.play(FocusOn(self.fourier_graph_dot))
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self.wait()
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def label_as_almost_fourier(self):
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pass
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x_coord_label = self.x_coord_label
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almost_fourier_label = TextMobject(
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"``Almost Fourier Transform''",
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)
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almost_fourier_label.move_to(x_coord_label, UP+LEFT)
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x_coord_label.generate_target()
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x_coord_label.target.next_to(almost_fourier_label, DOWN)
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self.play(
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MoveToTarget(x_coord_label),
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Write(almost_fourier_label)
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)
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self.wait(2)
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##
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@ -1314,6 +1398,18 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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# result += self.circle_plane.get_center()
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return result
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def generate_fourier_dot_transform(self, fourier_graph):
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self.fourier_graph_dot = Dot(color = WHITE, radius = 0.05)
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def update_dot(dot):
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f = self.graph.polarized_mobject.frequency
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dot.move_to(self.frequency_axes.input_to_graph_point(
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f, fourier_graph
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))
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self.fourier_graph_dot_anim = UpdateFromFunc(
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self.fourier_graph_dot, update_dot
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)
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self.fourier_graph_dot_anim.update(0)
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def change_frequency(self, new_freq, **kwargs):
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kwargs["run_time"] = kwargs.get("run_time", 3)
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added_anims = kwargs.get("added_anims", [])
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@ -1329,14 +1425,40 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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self.get_period_v_lines_update_anim(),
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]
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anims += added_anims
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#TODO, conditionals for center of mass
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if hasattr(self, "center_of_mass_dot"):
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anims.append(self.center_of_mass_dot_anim)
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if hasattr(self, "fourier_graph_dot"):
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anims.append(self.fourier_graph_dot_anim)
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self.play(*anims, **kwargs)
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def create_pi_creature(self):
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return Mortimer().to_corner(DOWN+RIGHT)
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class StudentsHorrifiedAtScene(TeacherStudentsScene):
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def construct(self):
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self.change_student_modes(
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*3*["horrified"],
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look_at_arg = 2*UP + 3*LEFT
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)
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self.wait(4)
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class ShowLinearity(DrawFrequencyPlot):
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def construct(self):
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self.show_lower_frequency_signal()
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self.play_with_lower_frequency_signal()
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self.point_out_fourier_spike()
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