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3/4 of AmbiguityInLongEchos in uncertainty
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Grant Sanderson
parent
2c5c651e99
commit
542958199a
1 changed files with 185 additions and 20 deletions
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@ -2302,11 +2302,12 @@ class AmbiguityInLongEchos(IntroduceDopplerRadar, PiCreatureScene):
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}
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def construct(self):
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self.setup_axes()
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self.setup_objects()
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self.send_long_pulse_single_echo()
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self.introduce_multiple_objects()
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self.use_short_pulse()
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self.transition_to_frequency_view()
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self.fourier_transform_of_one_pulse()
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self.show_echos_of_moving_objects()
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self.overlapping_frequenies_of_various_objects()
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self.echos_of_long_pure_signal_in_frequency_space()
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self.concentrated_fourier_requires_long_time()
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@ -2328,6 +2329,7 @@ class AmbiguityInLongEchos(IntroduceDopplerRadar, PiCreatureScene):
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dish.to_edge(UP, buff = LARGE_BUFF)
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self.add(dish)
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def setup_objects(self):
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objects = self.objects = VGroup(
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Plane().flip(),
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SVGMobject(
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@ -2337,7 +2339,8 @@ class AmbiguityInLongEchos(IntroduceDopplerRadar, PiCreatureScene):
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),
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SVGMobject(
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file_name = "biplane",
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color = average_color(DARK_GREY, RED),
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# color = average_color(DARK_GREY, RED),
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color = RED_D,
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height = 0.5,
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),
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SVGMobject(
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@ -2353,6 +2356,14 @@ class AmbiguityInLongEchos(IntroduceDopplerRadar, PiCreatureScene):
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obj.align_to(self.dish)
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obj.shift(y*UP)
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self.object_velocities = [
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0.7*LEFT,
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0.1*RIGHT,
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0.4*LEFT,
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0.4*RIGHT,
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0.5*UP,
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]
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def send_long_pulse_single_echo(self):
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x = self.object_x_coords[0]
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plane = self.objects[0]
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@ -2505,15 +2516,28 @@ class AmbiguityInLongEchos(IntroduceDopplerRadar, PiCreatureScene):
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self.first_echo_graph = graphs[0]
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self.first_echo_graph.highlight(YELLOW)
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def transition_to_frequency_view(self):
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frequency_axes = self.axes.copy()
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def fourier_transform_of_one_pulse(self):
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frequency_axes = Axes(
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x_min = 0, x_max = 20,
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x_axis_config = {
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"unit_size" : 0.5,
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"tick_frequency" : 2,
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},
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y_min = -.01, y_max = .01,
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y_axis_config = {
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"unit_size" : 110,
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"tick_frequency" : 0.006
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}
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)
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frequency_label = TextMobject("Frequency")
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frequency_label.replace(frequency_axes[-1], dim_to_match = 1)
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frequency_axes.submobjects[-1] = frequency_label
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frequency_label.next_to(frequency_axes.x_axis.get_right(), UP)
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frequency_axes.add(frequency_label)
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first_echo_graph = self.first_echo_graph
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self.play(
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ApplyMethod(
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VGroup(self.axes, self.first_echo_graph).to_edge, UP,
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VGroup(self.axes, first_echo_graph).to_edge, UP,
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{"buff" : SMALL_BUFF},
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rate_func = squish_rate_func(smooth, 0.5, 1)
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),
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LaggedStart(FadeOut, self.objects),
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@ -2524,22 +2548,136 @@ class AmbiguityInLongEchos(IntroduceDopplerRadar, PiCreatureScene):
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)
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#
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frequency_axes.next_to(self.axes, DOWN, aligned_edge = LEFT)
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frequency_axes.next_to(self.axes, DOWN, LARGE_BUFF, LEFT)
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fourier_graph = get_fourier_graph(
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frequency_axes, first_echo_graph.underlying_function,
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t_min = 0, t_max = 25,
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complex_to_real_func = np.abs,
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)
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fourier_graph.save_state()
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fourier_graph.move_to(first_echo_graph)
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h_vect = 4*RIGHT
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fourier_graph.shift(h_vect)
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fourier_graph.fade(1)
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f = 8
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v_line = DashedLine(
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frequency_axes.coords_to_point(f, 0),
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frequency_axes.coords_to_point(f, frequency_axes.y_max),
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)
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v_lines = VGroup(
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v_line.copy().shift(2*LEFT),
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v_line.copy().shift(2*RIGHT),
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)
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rect = Rectangle(stroke_width = 0, fill_color = YELLOW, fill_opacity = 0.25)
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rect.replace(v_lines, stretch = True)
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rect.save_state()
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rect.stretch(0, 0)
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self.play(Write(frequency_axes, run_time = 1))
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self.play(
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ApplyFunction(
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lambda m : m.move_to(fourier_graph.saved_state).shift(-h_vect).fade(1),
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first_echo_graph.copy(),
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remover = True,
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),
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fourier_graph.restore
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)
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self.wait()
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self.play(ShowCreation(v_line))
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self.play(
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ReplacementTransform(VGroup(v_line), v_lines),
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rect.restore
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)
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self.wait()
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self.play(FadeOut(v_lines), FadeOut(rect))
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self.frequency_axes = frequency_axes
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self.fourier_graph = fourier_graph
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def show_echos_of_moving_objects(self):
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objects = self.objects
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objects.save_state()
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object_velocities = self.object_velocities
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movements = [
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AmbientMovement(
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obj,
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direction = v/np.linalg.norm(v),
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rate = np.linalg.norm(v)
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)
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for v, obj in zip(object_velocities, objects)
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]
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pulses = self.get_pulses()
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continual_anims = pulses+movements
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self.play(Write(frequency_axes))
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def fourier_transform_of_one_pulse(self):
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pass
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self.play(
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FadeOut(self.axes),
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FadeOut(self.first_echo_graph),
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LaggedStart(FadeIn, objects),
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FadeIn(self.dish)
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)
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self.add(*continual_anims)
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self.wait(4)
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self.play(*[
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UpdateFromAlphaFunc(
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obj,
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lambda m, a : m.set_fill(opacity = 1-a),
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)
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for obj in objects
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])
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self.remove(*continual_anims)
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self.wait()
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def overlapping_frequenies_of_various_objects(self):
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pass
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frequency_axes = self.frequency_axes
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fourier_graph = self.fourier_graph
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shifted_graphs = self.get_shifted_frequency_graphs(fourier_graph)
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color = fourier_graph.get_color()
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shifted_graphs.gradient_highlight(
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average_color(color, WHITE),
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color,
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average_color(color, BLACK),
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)
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sum_graph = self.get_sum_graph(frequency_axes, shifted_graphs)
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sum_graph.match_style(fourier_graph)
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shifted_graphs.save_state()
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self.play(ReplacementTransform(
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VGroup(fourier_graph), shifted_graphs,
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submobject_mode = "lagged_start",
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run_time = 2
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))
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self.wait()
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self.play(
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shifted_graphs.arrange_submobjects, DOWN,
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shifted_graphs.move_to, fourier_graph, DOWN,
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)
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self.wait()
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self.play(shifted_graphs.restore),
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self.play(ReplacementTransform(
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shifted_graphs, VGroup(sum_graph),
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))
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self.wait()
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self.curr_fourier_graph = sum_graph
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def echos_of_long_pure_signal_in_frequency_space(self):
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pass
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curr_fourier_graph = self.curr_fourier_graph
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f_max = self.frequency_axes.y_max
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new_fourier_graph = self.frequency_axes.get_graph(
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lambda x : f_max * np.exp(-100*(x-8)**2),
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num_graph_points = 1000,
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)
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new_fourier_graph.highlight(PINK)
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self.play(
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FadeOut(curr_fourier_graph),
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FadeIn(new_fourier_graph),
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)
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self.fourier_graph = new_fourier_graph
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self.overlapping_frequenies_of_various_objects()
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def concentrated_fourier_requires_long_time(self):
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pass
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@ -2564,7 +2702,7 @@ class AmbiguityInLongEchos(IntroduceDopplerRadar, PiCreatureScene):
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def get_pulses(self):
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return [
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self.get_pulse(
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self.dish.copy(),#.align_to(obj),
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self.dish.copy().shift(0.01*obj.get_center()[0]),
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obj
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)
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for obj in self.objects
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@ -2576,7 +2714,34 @@ class AmbiguityInLongEchos(IntroduceDopplerRadar, PiCreatureScene):
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randy.to_edge(RIGHT, buff = 1.7).shift(0.5*UP)
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return randy
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def get_shifted_frequency_graphs(self, fourier_graph):
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frequency_axes = self.frequency_axes
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def get_func(v):
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return lambda f : fourier_graph.underlying_function(np.clip(
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f-5*v[0],
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frequency_axes.x_min,
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frequency_axes.x_max,
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))
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def get_graph(func):
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return frequency_axes.get_graph(func)
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shifted_graphs = VGroup(*map(
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get_graph, map(get_func, self.object_velocities)
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))
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shifted_graphs.match_style(fourier_graph)
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return shifted_graphs
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def get_sum_graph(self, axes, graphs):
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def get_func(graph):
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return graph.underlying_function
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# t_min = axes.x_axis.point_to_number(graph.points[0])
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# t_max = axes.x_axis.point_to_number(graph.points[-1])
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# return lambda t : axes.y_axis.point_to_number(
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# graph.point_from_proportion((t-t_min)/(t_max - t_min))
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# )
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funcs = map(get_func, graphs)
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return axes.get_graph(
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lambda t : sum([func(t) for func in funcs]),
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)
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