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Further progress in IntroduceDopplerRadar
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Grant Sanderson
parent
7415b0aa6b
commit
321a5ccc1e
1 changed files with 147 additions and 30 deletions
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@ -1685,8 +1685,10 @@ class MentionDopplerRadar(TeacherStudentsScene):
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class IntroduceDopplerRadar(Scene):
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def construct(self):
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self.setup_axes()
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self.measure_distance_with_time()
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self.measure_velocity_with_frequency()
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# self.measure_distance_with_time()
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self.show_frequency_shift()
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self.shift_time_graph()
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self.show_frequency_shift_in_fourier()
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def setup_axes(self):
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self.dish = RadarDish()
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@ -1694,8 +1696,8 @@ class IntroduceDopplerRadar(Scene):
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axes = Axes(
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x_min = 0,
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x_max = 10,
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y_min = -2,
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y_max = 2
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y_min = -1.5,
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y_max = 1.5
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)
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axes.move_to(DOWN)
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time_label = TextMobject("Time")
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@ -1718,20 +1720,15 @@ class IntroduceDopplerRadar(Scene):
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randy.move_to(dish.get_right(), LEFT)
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randy.shift(distance*RIGHT)
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pulse_graph = self.get_single_pulse_graph(1, color = BLUE)
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echo_graph = self.get_single_pulse_graph(1+time_diff, color = YELLOW)
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sum_graph = axes.get_graph(
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lambda x : sum([
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pulse_graph.underlying_function(x),
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echo_graph.underlying_function(x),
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]),
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color = WHITE
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)
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sum_graph.background_image_file = "blue_yellow_gradient"
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pulse_graph, echo_graph, sum_graph = \
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self.get_pulse_and_echo_graphs(
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self.get_single_pulse_graph,
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(1,), (1+time_diff,)
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)
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words = ["Original signal", "Echo"]
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for graph, word in zip([pulse_graph, echo_graph], words):
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arrow = Vector(DOWN+LEFT)
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arrow.next_to(graph.peak_point, UP+RIGHT, SMALL_BUFF)
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arrow = Vector(DOWN)
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arrow.next_to(graph.peak_point, UP, SMALL_BUFF)
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arrow.match_color(graph)
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graph.arrow = arrow
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label = TextMobject(word)
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@ -1739,14 +1736,26 @@ class IntroduceDopplerRadar(Scene):
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label.match_color(graph)
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graph.label = label
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double_arrow = DoubleArrow(
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pulse_graph.peak_point,
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echo_graph.peak_point,
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color = WHITE
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)
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distance_text = TextMobject("$2 \\times$ distance/(signal speed)")
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distance_text.scale_to_fit_width(0.9*double_arrow.get_width())
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distance_text.next_to(double_arrow, UP, SMALL_BUFF)
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#v_line anim?
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pulse = RadarPulseSingleton(dish, randy, speed = speed)
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pulse = RadarPulseSingleton(
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dish, randy,
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speed = 0.97*speed, #Just needs slightly better alignment
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)
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graph_draw = NormalAnimationAsContinualAnimation(
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ShowCreation(
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sum_graph,
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rate_func = None,
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run_time = axes.x_max
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run_time = 0.97*axes.x_max
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)
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)
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randy_look_at = ContinualUpdateFromFunc(
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@ -1754,7 +1763,7 @@ class IntroduceDopplerRadar(Scene):
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)
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self.add(randy_look_at, ContinualAnimation(axes), graph_draw)
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self.wait()
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self.wait(0.5)
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self.add(pulse)
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self.play(
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Write(pulse_graph.label),
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@ -1768,35 +1777,143 @@ class IntroduceDopplerRadar(Scene):
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GrowArrow(echo_graph.arrow),
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run_time = 1
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)
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self.wait(3)
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graph_draw.update(10)
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self.add(sum_graph)
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self.wait()
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self.play(
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GrowFromCenter(double_arrow),
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FadeIn(distance_text)
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)
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self.wait()
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self.remove(graph_draw, pulse, randy_look_at)
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self.play(LaggedStart(FadeOut, VGroup(
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sum_graph, randy,
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pulse_graph.arrow, pulse_graph.label,
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echo_graph.arrow, echo_graph.label,
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double_arrow, distance_text
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)))
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def show_frequency_shift(self):
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axes = self.axes
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dish = self.dish
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plane = Plane()
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plane.flip()
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plane.move_to(dish)
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plane.to_edge(RIGHT)
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def measure_velocity_with_frequency(self):
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time_diff = 6
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pulse_graph, echo_graph, sum_graph = graphs = \
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self.get_pulse_and_echo_graphs(
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self.get_frequency_pulse_graph,
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(1,25), (1+time_diff,50)
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)
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for graph in graphs:
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graph.set_stroke(width = 3)
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signal_graph = self.get_frequency_pulse_graph(1)
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pulse_brace = Brace(Line(ORIGIN, RIGHT), UP)
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pulse_brace.move_to(axes.coords_to_point(1, 1.2))
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echo_brace = pulse_brace.copy()
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echo_brace.stretch(0.6, 0)
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echo_brace.move_to(axes.coords_to_point(7, 1.2))
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pulse_text = pulse_brace.get_text("Original signal")
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pulse_text.add_background_rectangle()
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echo_text = echo_brace.get_text("Echo")
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echo_subtext = TextMobject("(Higher frequency)")
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echo_subtext.next_to(echo_text, RIGHT)
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echo_subtext.match_color(echo_graph)
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graph_draw = NormalAnimationAsContinualAnimation(
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ShowCreation(sum_graph, run_time = 8, rate_func = None)
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)
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pulse = RadarPulse(dish, plane, n_pulse_singletons = 12)
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plane_flight = AmbientMovement(
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plane, direction = LEFT, rate = 1.5
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)
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self.add(graph_draw, pulse, plane_flight)
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self.play(UpdateFromAlphaFunc(
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plane, lambda m, a : m.set_fill(opacity = a)
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))
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self.play(
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GrowFromCenter(pulse_brace),
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FadeIn(pulse_text),
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)
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self.wait(3)
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self.play(
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GrowFromCenter(echo_brace),
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GrowFromCenter(echo_text),
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)
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self.play(UpdateFromAlphaFunc(
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plane, lambda m, a : m.set_fill(opacity = 1-a)
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))
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#Only for when -s is run
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graph_draw.update(10)
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self.wait(0.1)
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self.play(Write(echo_subtext, run_time = 1))
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self.wait()
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self.remove(graph_draw, pulse, plane_flight)
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self.time_graph_group = VGroup(
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axes, pulse_brace, pulse_text,
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echo_brace, echo_text, echo_subtext,
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sum_graph
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)
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self.pulse_echo_graph = sum_graph
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def shift_time_graph(self):
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self.play(
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self.time_graph_group.to_edge, UP,
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ApplyMethod(
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self.dish.shift, 2*UP,
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remover = True
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)
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)
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self.wait()
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def show_frequency_shift_in_fourier(self):
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pass
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###
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def get_single_pulse_graph(self, x, **kwargs):
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graph = self.axes.get_graph(
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self.get_single_pulse_function(x),
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**kwargs
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)
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def get_graph(self, func, **kwargs):
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graph = self.axes.get_graph(func, **kwargs)
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graph.peak_point = self.get_peak_point(graph)
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return graph
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def get_single_pulse_graph(self, x, **kwargs):
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return self.get_graph(self.get_single_pulse_function(x), **kwargs)
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def get_single_pulse_function(self, x):
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return lambda t : -2*np.sin(10*(t-x))*np.exp(-100*(t-x)**2)
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def get_frequency_pulse_graph(self, x, freq = 50, **kwargs):
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return self.get_graph(
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self.get_frequency_pulse_function(x, freq),
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num_graph_points = 700,
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**kwargs
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)
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def get_frequency_pulse_function(self, x, freq):
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return lambda t : 2*np.cos(2*freq*(t-x))*min(np.exp(-(freq**2/100)*(t-x)**2), 0.5)
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def get_peak_point(self, graph):
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anchors = graph.get_anchors()
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return anchors[np.argmax([p[1] for p in anchors])]
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def get_pulse_and_echo_graphs(self, func, args1, args2):
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pulse_graph = func(*args1, color = BLUE)
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echo_graph = func(*args2, color = YELLOW)
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sum_graph = self.axes.get_graph(
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lambda x : sum([
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pulse_graph.underlying_function(x),
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echo_graph.underlying_function(x),
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]),
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num_graph_points = echo_graph.get_num_anchor_points(),
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color = WHITE
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)
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sum_graph.background_image_file = "blue_yellow_gradient"
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return pulse_graph, echo_graph, sum_graph
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