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Finished ScaleUpCenterOfMass of fourier
This commit is contained in:
Grant Sanderson
parent
ad4ceb3f1a
commit
27c6658eb1
1 changed files with 300 additions and 18 deletions
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@ -1474,6 +1474,9 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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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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kwargs["rate_func"] = kwargs.get(
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"rate_func", bezier([0, 0, 1, 1])
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)
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added_anims = kwargs.get("added_anims", [])
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freq_label = filter(
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lambda sm : isinstance(sm, DecimalNumber),
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@ -2425,11 +2428,12 @@ class WriteComplexExponentialExpression(DrawFrequencyPlot):
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circle_plane.add(circle)
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time_axes = self.get_time_axes()
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time_axes.add_to_back(BackgroundRectangle(
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time_axes.background_rectangle = BackgroundRectangle(
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time_axes,
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fill_opacity = 0.9,
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buff = MED_SMALL_BUFF,
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))
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)
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time_axes.add_to_back(time_axes.background_rectangle)
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time_axes.scale(self.time_axes_scale_val)
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time_axes.to_corner(UP+LEFT, buff = 0)
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time_axes.set_stroke(color = WHITE, width = 1)
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@ -2956,7 +2960,6 @@ class WriteComplexExponentialExpression(DrawFrequencyPlot):
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)
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return VGroup(time_graph.dots, pol_graph.dots)
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class WhyAreYouTellingUsThis(TeacherStudentsScene):
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def construct(self):
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self.student_says("Why are you \\\\ telling us this?")
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@ -3010,19 +3013,23 @@ class BuildUpExpressionStepByStep(TeacherStudentsScene):
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class ScaleUpCenterOfMass(WriteComplexExponentialExpression):
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CONFIG = {
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"time_axes_scale_val" : 0.6,
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"initial_winding_frequency" : 1.95
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"initial_winding_frequency" : 2.05
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}
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def construct(self):
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self.remove(self.pi_creature)
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self.setup_plane()
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self.setup_graph()
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self.add_expression()
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self.add_center_of_mass_dot()
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self.add_expression()
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self.cross_out_denominator()
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self.scale_up_center_of_mass()
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self.what_this_means_for_various_winding_frequencies()
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self.comment_on_current_signal()
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def add_center_of_mass_dot(self):
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self.center_of_mass_dot = self.get_center_of_mass_dot()
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self.generate_center_of_mass_dot_update_anim()
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self.add(self.center_of_mass_dot)
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def add_expression(self):
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expression = TexMobject(
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@ -3035,30 +3042,305 @@ class ScaleUpCenterOfMass(WriteComplexExponentialExpression):
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g[2].highlight(YELLOW)
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dt[1].highlight(YELLOW)
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f.highlight(GREEN)
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expression.add_background_rectangle()
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self.expression = expression
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self.add(expression)
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self.winding_freq_label.to_edge(RIGHT)
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self.winding_freq_label[1].match_color(f)
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def add_center_of_mass_dot(self):
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self.center_of_mass_dot = self.get_center_of_mass_dot()
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self.generate_center_of_mass_dot_update_anim()
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self.add(self.center_of_mass_dot)
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self.winding_freq_label.align_to(
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self.circle_plane.coords_to_point(0, 0.1), DOWN
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)
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def cross_out_denominator(self):
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frac = self.expression[0]
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integral = VGroup(*self.expression[1:])
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integral = self.expression[1:]
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for mob in frac, integral:
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mob.add_to_back(BackgroundRectangle(mob))
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self.add(mob)
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cross = Cross(frac)
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brace = Brace(integral, DOWN)
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label = brace.get_text("The actual \\\\ Fourier transform")
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label.add_background_rectangle()
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label.shift_onto_screen()
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rect = SurroundingRectangle(integral)
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self.play(ShowCreation(cross))
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self.wait()
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self.play(ShowCreation(rect))
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self.play(
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GrowFromCenter(brace),
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FadeIn(label)
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)
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self.wait(2)
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self.integral = integral
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self.frac = frac
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self.frac_cross = cross
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self.integral_rect = rect
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self.integral_brace = brace
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self.integral_label = label
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def scale_up_center_of_mass(self):
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pass
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plane = self.circle_plane
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origin = plane.coords_to_point(0, 0)
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com_dot = self.center_of_mass_dot
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com_vector = Arrow(
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origin, com_dot.get_center(),
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buff = 0
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)
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com_vector.match_style(com_dot)
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vector_to_scale = com_vector.copy()
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def get_com_vector_copies(n):
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com_vector_copies = VGroup(*[
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com_vector.copy().shift(x*com_vector.get_vector())
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for x in range(1, n+1)
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])
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com_vector_copies.highlight(TEAL)
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return com_vector_copies
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com_vector_update = UpdateFromFunc(
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com_vector,
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lambda v : v.put_start_and_end_on(origin, com_dot.get_center())
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)
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circle = Circle(color = TEAL)
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circle.surround(com_dot, buffer_factor = 1.2)
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time_span = Rectangle(
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stroke_width = 0,
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fill_color = TEAL,
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fill_opacity = 0.4
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)
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axes = self.time_axes
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time_span.replace(
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Line(axes.coords_to_point(0, 0), axes.coords_to_point(3, 1.5)),
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stretch = True
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)
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time_span.save_state()
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time_span.stretch(0, 0, about_edge = LEFT)
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graph = self.graph
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short_graph, long_graph = [
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axes.get_graph(
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graph.underlying_function, x_min = 0, x_max = t_max,
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).match_style(graph)
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for t_max in 3, 6
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]
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for g in short_graph, long_graph:
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self.get_polarized_mobject(g, freq = self.initial_winding_frequency)
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self.play(
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FocusOn(circle, run_time = 2),
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Succession(
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ShowCreation, circle,
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FadeOut, circle,
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),
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)
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self.play(
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com_dot.fade, 0.5,
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FadeIn(vector_to_scale)
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)
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self.wait()
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self.play(vector_to_scale.scale, 4, {"about_point" : origin})
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self.wait()
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self.play(
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FadeOut(vector_to_scale),
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FadeIn(com_vector),
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)
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self.remove(graph.polarized_mobject)
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self.play(
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com_dot.move_to,
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center_of_mass(short_graph.polarized_mobject.points),
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com_vector_update,
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time_span.restore,
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ShowCreation(short_graph.polarized_mobject),
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)
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self.wait()
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# dot = Dot(fill_opacity = 0.5).move_to(time_span)
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# self.play(
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# dot.move_to, com_vector,
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# dot.set_fill, {"opacity" : 0},
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# remover = True
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# )
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com_vector_copies = get_com_vector_copies(2)
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self.play(*[
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ReplacementTransform(
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com_vector.copy(), cvc,
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path_arc = -TAU/10
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)
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for cvc in com_vector_copies
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])
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self.wait()
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#Squish_graph
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to_squish = VGroup(
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axes, graph,
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time_span,
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)
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to_squish.generate_target()
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squish_factor = 0.75
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to_squish.target.stretch(squish_factor, 0, about_edge = LEFT)
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pairs = zip(
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to_squish.family_members_with_points(),
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to_squish.target.family_members_with_points()
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)
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to_unsquish = list(axes.x_axis.numbers) + list(axes.labels)
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for sm, tsm in pairs:
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if sm in to_unsquish:
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tsm.stretch(1/squish_factor, 0)
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if sm is axes.background_rectangle:
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tsm.stretch(1/squish_factor, 0, about_edge = LEFT)
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long_graph.stretch(squish_factor, 0)
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self.play(
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MoveToTarget(to_squish),
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FadeOut(com_vector_copies)
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)
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long_graph.move_to(graph, LEFT)
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self.play(
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com_dot.move_to,
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center_of_mass(long_graph.polarized_mobject.points),
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com_vector_update,
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time_span.stretch, 2, 0, {"about_edge" : LEFT},
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*[
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ShowCreation(
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mob,
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rate_func = lambda a : interpolate(
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0.5, 1, smooth(a)
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)
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)
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for mob in long_graph, long_graph.polarized_mobject
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],
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run_time = 2
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)
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self.remove(graph, short_graph.polarized_mobject)
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self.graph = long_graph
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self.wait()
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self.play(FocusOn(com_dot))
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com_vector_copies = get_com_vector_copies(5)
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self.play(*[
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ReplacementTransform(
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com_vector.copy(), cvc,
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path_arc = -TAU/10
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)
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for cvc in com_vector_copies
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])
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self.wait()
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# Scale graph out even longer
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to_shift = VGroup(self.integral, self.integral_rect)
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to_fade = VGroup(
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self.integral_brace, self.integral_label,
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self.frac, self.frac_cross
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)
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self.play(
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to_shift.shift, 2*DOWN,
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FadeOut(to_fade),
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axes.background_rectangle.stretch, 2, 0, {"about_edge" : LEFT},
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Animation(axes),
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Animation(self.graph),
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FadeOut(com_vector_copies),
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)
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self.change_frequency(2.0, added_anims = [com_vector_update])
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very_long_graph = axes.get_graph(
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graph.underlying_function,
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x_min = 0, x_max = 12,
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)
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very_long_graph.match_style(graph)
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self.get_polarized_mobject(very_long_graph, freq = 2.0)
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self.play(
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com_dot.move_to,
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center_of_mass(very_long_graph.polarized_mobject.points),
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com_vector_update,
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ShowCreation(
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very_long_graph,
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rate_func = lambda a : interpolate(0.5, 1, a)
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),
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ShowCreation(very_long_graph.polarized_mobject)
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)
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self.remove(graph, graph.polarized_mobject)
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self.graph = very_long_graph
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self.wait()
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self.play(
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com_vector.scale, 12, {"about_point" : origin},
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run_time = 2
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)
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# com_vector_copies = get_com_vector_copies(11)
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# self.play(ReplacementTransform(
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# VGroup(com_vector.copy()),
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# com_vector_copies,
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# path_arc = TAU/10,
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# run_time = 1.5,
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# submobject_mode = "lagged_start"
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# ))
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self.wait()
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self.com_vector = com_vector
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self.com_vector_update = com_vector_update
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self.com_vector_copies = com_vector_copies
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def comment_on_current_signal(self):
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graph = self.graph
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com_dot = self.center_of_mass_dot
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com_vector = self.com_vector
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com_vector_update = self.com_vector_update
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axes = self.time_axes
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origin = self.circle_plane.coords_to_point(0, 0)
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wps_label = self.winding_freq_label
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new_com_vector_update = UpdateFromFunc(
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com_vector, lambda v : v.put_start_and_end_on(
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origin, com_dot.get_center()
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).scale(12, about_point = origin)
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)
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v_lines = self.get_v_lines_indicating_periods(
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freq = 1.0, n_lines = 3
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)[:2]
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graph_portion = axes.get_graph(
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graph.underlying_function, x_min = 1, x_max = 2
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)
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graph_portion.highlight(TEAL)
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bps_label = TextMobject("2 beats per second")
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bps_label.scale(0.75)
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bps_label.next_to(graph_portion, UP, aligned_edge = LEFT)
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bps_label.shift(SMALL_BUFF*RIGHT)
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bps_label.add_background_rectangle()
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self.play(
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ShowCreation(v_lines, submobject_mode = "all_at_once"),
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ShowCreation(graph_portion),
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FadeIn(bps_label),
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)
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self.wait()
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self.play(ReplacementTransform(
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bps_label[1][0].copy(), wps_label[1]
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))
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self.wait()
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self.play(
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com_vector.scale, 0.5, {"about_point" : origin},
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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(2)
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self.change_frequency(2.5,
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added_anims = [new_com_vector_update],
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run_time = 20,
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rate_func = None,
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)
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self.wait()
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class TakeAStepBack(TeacherStudentsScene):
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def construct(self):
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self.student_says(
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"Hang on, go over \\\\ that again?",
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target_mode = "confused"
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),
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self.change_student_modes(*["confused"]*3)
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self.play(self.teacher.change, "happy")
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self.wait(3)
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def what_this_means_for_various_winding_frequencies(self):
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pass
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class CloseWithAPuzzle(TeacherStudentsScene):
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