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Initial progress of DrawFrequencyPlot in fourier.py
This commit is contained in:
Grant Sanderson
parent
c1f7f17151
commit
46f5e62cd0
1 changed files with 172 additions and 42 deletions
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@ -648,7 +648,7 @@ class FourierMachineScene(Scene):
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CONFIG = {
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"time_axes_config" : {
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"x_min" : 0,
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"x_max" : 3.4,
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"x_max" : 4.4,
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"x_axis_config" : {
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"unit_size" : 3,
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"tick_frequency" : 0.25,
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@ -687,7 +687,7 @@ class FourierMachineScene(Scene):
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labels = VGroup(time_label, intensity_label)
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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.x_axis.get_right(), DOWN)
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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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@ -791,7 +791,7 @@ class FourierMachineScene(Scene):
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graph_copy = polarized_graph.copy()
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def update_vector(vector, alpha):
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point = graph_copy.point_from_proportion(alpha)
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vector.put_start_and_end_on(origin, point)
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vector.put_start_and_end_on_with_projection(origin, point)
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return vector
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return UpdateFromAlphaFunc(vector, update_vector, **config)
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@ -858,36 +858,27 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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self.show_time_sweeps()
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self.compare_two_frequencies()
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self.change_wrapping_frequency()
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self.match_up_frequencies()
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def show_initial_signal(self):
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axes = self.get_time_axes()
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graph = self.get_cosine_wave(freq = self.signal_frequency)
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peak_points = [
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axes.input_to_graph_point(x, graph)
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for x in np.linspace(1, 2, 4)
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]
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braces = VGroup(*[
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Brace(Line(p1, p2), UP)
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for p1, p2 in zip(peak_points, peak_points[1:])
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])
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self.graph = graph
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braces = VGroup(*self.get_peak_braces()[3:6])
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v_lines = VGroup(*[
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DashedLine(
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ORIGIN, 2*UP, color = RED
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).move_to(axes.coords_to_point(x, 0), DOWN)
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for x in 1, 2
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])
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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 = self.get_bps_label()
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self.add(axes)
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self.play(ShowCreation(graph, run_time = 2))
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self.play(ShowCreation(graph, run_time = 2, rate_func = None))
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self.play(
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FadeIn(words),
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LaggedStart(FadeIn, braces),
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*map(ShowCreation, v_lines)
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)
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self.play(LaggedStart(FadeIn, braces))
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self.wait()
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self.play(FadeOut(VGroup(braces, v_lines)))
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self.wait()
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@ -903,7 +894,7 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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circle_plane = self.get_circle_plane()
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moving_graph = graph.copy()
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self.play(ShowCreation(circle_plane))
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self.play(ShowCreation(circle_plane, submobject_mode = "all_at_once"))
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self.play(ReplacementTransform(
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moving_graph,
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polarized_graph,
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@ -912,7 +903,11 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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))
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self.animate_frequency_change([graph], freq)
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self.wait()
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pg_copy = polarized_graph.copy()
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self.remove(polarized_graph)
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self.play(pg_copy.fade, 0.75)
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self.play(*self.get_vector_animations(graph), run_time = 15)
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self.remove(pg_copy)
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self.wait()
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def show_time_sweeps(self):
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@ -920,14 +915,7 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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graph = self.graph
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v_lines = self.get_v_lines_indicating_periods(freq)
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winding_freq_label = VGroup(
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DecimalNumber(freq, num_decimal_points = 2),
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TextMobject("cycles/second")
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)
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winding_freq_label.arrange_submobjects(RIGHT)
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winding_freq_label.next_to(
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self.circle_plane, RIGHT, aligned_edge = UP
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)
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winding_freq_label = self.get_winding_frequency_label()
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self.animate_time_sweep(
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freq = freq,
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@ -941,7 +929,6 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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)
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self.wait()
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self.winding_freq_label = winding_freq_label
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self.v_lines_indicating_periods = v_lines
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def compare_two_frequencies(self):
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@ -953,15 +940,7 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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)
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graph = self.graph
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freq = self.initial_winding_frequency
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peak_points = [
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self.time_axes.input_to_graph_point(x, graph)
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for x in np.arange(0, 3.5, 1./self.signal_frequency)
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]
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braces = VGroup(*[
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Brace(Line(p1, p2), UP, buff = 0)
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for p1, p2 in zip(peak_points, peak_points[1:])
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])
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braces = self.get_peak_braces(buff = 0)
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self.play(ShowCreation(bps_label.rect))
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self.play(FadeOut(bps_label.rect))
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@ -978,7 +957,7 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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freq_label = self.winding_freq_label[0]
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count = 0
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for target_freq in [2, 0.2, 1.55, self.signal_frequency]:
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for target_freq in [1.23, 0.2, 1.55, self.signal_frequency]:
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self.play(
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Transform(
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v_lines,
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@ -1006,13 +985,164 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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run_time = 15
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)
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def match_up_frequencies(self):
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##
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def get_winding_frequency_label(self):
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freq = self.initial_winding_frequency
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winding_freq_label = VGroup(
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DecimalNumber(freq, num_decimal_points = 2),
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TextMobject("cycles/second")
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)
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winding_freq_label.arrange_submobjects(RIGHT)
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winding_freq_label.next_to(
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self.circle_plane, RIGHT, aligned_edge = UP
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)
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self.winding_freq_label = winding_freq_label
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return winding_freq_label
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def get_peak_braces(self, **kwargs):
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peak_points = [
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self.time_axes.input_to_graph_point(x, self.graph)
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for x in np.arange(0, 3.5, 1./self.signal_frequency)
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]
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return VGroup(*[
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Brace(Line(p1, p2), UP, **kwargs)
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for p1, p2 in zip(peak_points, peak_points[1:])
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])
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def get_bps_label(self):
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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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return words
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class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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CONFIG = {
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"initial_winding_frequency" : 3.0,
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"center_of_mass_color" : RED,
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}
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def construct(self):
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self.force_skipping()
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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.show_center_of_mass_dot()
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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.label_as_almost_fourier()
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def setup_graph(self):
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self.add(self.get_time_axes())
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self.add(self.get_circle_plane())
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self.graph = self.get_cosine_wave(self.signal_frequency)
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self.add(self.graph)
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self.add(self.get_polarized_mobject(
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self.graph, self.initial_winding_frequency
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))
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self.add(self.get_winding_frequency_label())
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self.beats_per_second_label = self.get_bps_label()
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self.add(self.beats_per_second_label)
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self.v_lines_indicating_periods = self.get_v_lines_indicating_periods(
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self.initial_winding_frequency
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)
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self.add(self.v_lines_indicating_periods)
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self.change_frequency(1.03)
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self.wait()
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def indicate_weight_of_wire(self):
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graph = self.graph
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pol_graph = graph.polarized_mobject.copy()
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pol_graph.save_state()
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morty = self.pi_creature
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morty.change("raise_right_hand")
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morty.save_state()
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morty.change("plain")
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morty.fade(1)
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self.play(
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morty.restore,
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pol_graph.scale, 0.5,
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pol_graph.next_to, morty.get_corner(UP+LEFT), UP, -SMALL_BUFF,
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)
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self.play(
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morty.change, "lower_right_hand", pol_graph.get_bottom(),
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pol_graph.shift, 0.45*DOWN,
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rate_func = there_and_back,
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run_time = 2,
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)
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self.wait()
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metal_wire = pol_graph.copy().set_stroke(LIGHT_GREY)
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self.play(
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ShowCreationThenDestruction(metal_wire),
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run_time = 2,
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)
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self.play(
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pol_graph.restore,
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morty.change, "pondering"
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)
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self.remove(pol_graph)
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def show_center_of_mass_dot(self):
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color = self.center_of_mass_color
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dot = Dot(self.get_pol_graph_center_of_mass())
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dot.highlight(color)
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dot.save_state()
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arrow = Vector(DOWN+2*LEFT, color = color)
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arrow.next_to(dot, UP+RIGHT, buff = 0)
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dot.move_to(arrow.get_start())
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words = TextMobject("Center of mass")
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words.next_to(arrow.get_start(), RIGHT)
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words.highlight(color)
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self.revert_to_original_skipping_status()
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self.play(
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GrowArrow(arrow),
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dot.restore,
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)
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self.play(Write(words))
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self.wait()
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def change_to_various_frequencies(self):
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pass
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def introduce_frequency_plot(self):
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pass
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def draw_full_frequency_plot(self):
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pass
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def label_as_almost_fourier(self):
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pass
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##
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def get_pol_graph_center_of_mass(self):
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return center_of_mass(
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self.graph.polarized_mobject.get_anchors()
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)
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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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freq_label = self.winding_freq_label[0]
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anims = [
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Transform(
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self.v_lines_indicating_periods,
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self.get_v_lines_indicating_periods(new_freq)
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),
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ChangeDecimalToValue(freq_label, new_freq),
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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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]
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#TODO, conditionals for center of mass
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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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