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Preliminary end to fourier project
This commit is contained in:
Grant Sanderson
parent
4d7bb5c3f1
commit
dc3b43591d
1 changed files with 303 additions and 7 deletions
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@ -1,3 +1,4 @@
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# -*- coding: utf-8 -*-
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from helpers import *
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import scipy
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@ -1064,6 +1065,7 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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}
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def construct(self):
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self.show_initial_signal()
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self.show_finite_interval()
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self.wrap_around_circle()
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self.show_time_sweeps()
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self.compare_two_frequencies()
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@ -1101,6 +1103,38 @@ class WrapCosineGraphAroundCircle(FourierMachineScene):
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self.beats_per_second_label = words
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self.graph = graph
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def show_finite_interval(self):
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axes = self.time_axes
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v_line = DashedLine(
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axes.coords_to_point(0, 0),
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axes.coords_to_point(0, axes.y_max),
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color = RED,
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stroke_width = 6,
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)
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h_line = Line(
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axes.coords_to_point(0, 0),
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axes.coords_to_point(axes.x_max, 0),
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)
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rect = Rectangle(
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stroke_width = 0,
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fill_color = TEAL,
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fill_opacity = 0.5,
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)
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rect.match_height(v_line)
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rect.match_width(h_line, stretch = True)
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rect.move_to(v_line, DOWN+LEFT)
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right_v_line = v_line.copy()
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right_v_line.move_to(rect, RIGHT)
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rect.save_state()
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rect.stretch(0, 0, about_edge = ORIGIN)
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self.play(rect.restore, run_time = 2)
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self.play(FadeOut(rect))
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for line in v_line, right_v_line:
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self.play(ShowCreation(line))
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self.play(FadeOut(line))
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self.wait()
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def wrap_around_circle(self):
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graph = self.graph
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freq = self.initial_winding_frequency
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@ -1338,7 +1372,7 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
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com_label = self.center_of_mass_label
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com_label.add_background_rectangle()
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frequency_axes = self.get_frequency_axes()
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x_coord_label = TextMobject("$x$-coordiante for center of mass")
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x_coord_label = TextMobject("$x$-coordiate for center of mass")
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x_coord_label.highlight(self.center_of_mass_color)
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x_coord_label.scale(self.text_scale_val)
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x_coord_label.next_to(
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@ -1594,6 +1628,20 @@ class StudentsHorrifiedAtScene(TeacherStudentsScene):
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)
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self.wait(4)
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class AskAboutAlmostFouierName(TeacherStudentsScene):
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def construct(self):
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self.student_says(
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"``Almost'' Fourier transform?",
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target_mode = "sassy"
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)
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self.change_student_modes("confused", "sassy", "confused")
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self.wait()
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self.teacher_says(
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"We'll get to the real \\\\ one in a few minutes",
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added_anims = [self.get_student_changes(*["plain"]*3)]
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)
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self.wait(2)
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class ShowLowerFrequency(DrawFrequencyPlot):
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CONFIG = {
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"signal_frequency" : 2.0,
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@ -2126,6 +2174,15 @@ class ShowCommutativeDiagram(ShowLinearity):
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spike_rect.set_fill(YELLOW, 0.5)
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return spike_rect
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class PauseAndPonder(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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"Pause and \\\\ ponder!",
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target_mode = "hooray"
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)
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self.change_student_modes(*["thinking"]*3)
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self.wait(4)
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class BeforeGettingToTheFullMath(TeacherStudentsScene):
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def construct(self):
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formula = TexMobject(
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@ -2786,7 +2843,7 @@ class WriteComplexExponentialExpression(DrawFrequencyPlot):
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Write(time_label),
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GrowArrow(time_label.arrow),
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)
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self.wait(6.5) #Leave time to say let's slow down
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self.wait(12.5) #Leave time to say let's slow down
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self.remove(ambient_ghost_dot_movement)
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self.play(
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FadeOut(time_label),
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@ -3045,6 +3102,16 @@ class WriteComplexExponentialExpression(DrawFrequencyPlot):
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)
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return VGroup(time_graph.dots, pol_graph.dots)
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class EulersFormulaViaGroupTheoryWrapper(Scene):
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def construct(self):
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title = TextMobject("Euler's formula with introductory group theory")
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title.to_edge(UP)
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screen_rect = ScreenRectangle(height = 6)
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screen_rect.next_to(title, DOWN)
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self.add(title)
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self.play(ShowCreation(screen_rect))
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self.wait(2)
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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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@ -3636,8 +3703,7 @@ class SummarizeTheFullTransform(DrawFrequencyPlot):
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GrowArrow, arrow,
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FadeOut, arrow,
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Animation, Mobject(), {"run_time" : 5},
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Transform, g_hat_f.target.copy().fade(1), real_part[1].copy().fade(1),
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Write, real_part[0], {"run_time" : 1},
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Write, real_part, {"run_time" : 2},
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Animation, Mobject(), {"run_time" : 3},
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ShowCreation, imaginary_fourier_graph, {"run_time" : 3},
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rate_func = squish_rate_func(
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@ -3710,7 +3776,6 @@ class SummarizeFormula(Scene):
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expression.to_edge(UP)
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return expression
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class OneSmallNote(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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@ -3788,7 +3853,7 @@ class BoundsAtInfinity(SummarizeFormula):
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lambda m, a : m.set_fill(opacity = 1-a)
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),
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*decimal_updates,
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run_time = 8,
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run_time = 12,
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rate_func = bezier([0, 0, 1, 1])
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)
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self.wait()
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@ -3835,6 +3900,155 @@ class BoundsAtInfinity(SummarizeFormula):
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rect.move_to(line, DOWN)
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return rect
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class MoreToCover(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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"Much more to say...",
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target_mode = "hooray",
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run_time = 1,
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)
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self.wait()
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self.teacher_says(
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"SO MUCH!",
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target_mode = "surprised",
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added_anims = [self.get_student_changes(*3*["happy"])],
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run_time = 0.5
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)
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self.wait(2)
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class ShowUncertaintyPrinciple(Scene):
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def construct(self):
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title = TextMobject("Uncertainty principle")
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self.add(title)
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top_axes = Axes(
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x_min = -SPACE_WIDTH,
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x_max = SPACE_WIDTH,
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y_min = 0,
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y_max = 3,
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y_axis_config = {
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"unit_size" : 0.6,
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"include_tip" : False,
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}
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)
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bottom_axes = top_axes.deepcopy()
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arrow = Vector(DOWN, color = WHITE)
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group = VGroup(
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title, top_axes, arrow, bottom_axes
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)
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group.arrange_submobjects(DOWN)
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title.shift(MED_SMALL_BUFF*UP)
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group.to_edge(UP)
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fourier_word = TextMobject("Fourier transform")
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fourier_word.next_to(arrow, RIGHT)
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self.add(group, fourier_word)
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ghost_dot = Dot(RIGHT, fill_opacity = 0)
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def get_bell_func(factor = 1):
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return lambda x : 2*np.exp(-factor*x**2)
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top_graph = top_axes.get_graph(get_bell_func())
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top_graph.highlight(YELLOW)
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bottom_graph = bottom_axes.get_graph(get_bell_func())
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bottom_graph.highlight(RED)
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def get_update_func(axes):
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def update_graph(graph):
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f = ghost_dot.get_center()[0]
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if axes == bottom_axes:
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f = 1./f
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new_graph = axes.get_graph(get_bell_func(f))
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graph.points = new_graph.points
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return update_graph
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factors = [0.3, 0.1, 2, 10, 100, 0.01, 0.5]
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self.play(ShowCreation(top_graph))
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self.play(ReplacementTransform(
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top_graph.copy(),
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bottom_graph,
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))
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self.wait(2)
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self.add(*[
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ContinualUpdateFromFunc(graph, get_update_func(axes))
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for graph, axes in (top_graph, top_axes), (bottom_graph, bottom_axes)
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])
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for factor in factors:
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self.play(
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ghost_dot.move_to, factor*RIGHT,
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run_time = 2
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)
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self.wait()
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class XCoordinateLabelTypoFix(Scene):
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def construct(self):
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words = TextMobject("$x$-coordinate for center of mass")
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words.highlight(RED)
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self.add(words)
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class NextVideoWrapper(Scene):
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def construct(self):
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title = TextMobject("Next video")
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title.to_edge(UP)
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screen_rect = ScreenRectangle(height = 6)
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screen_rect.next_to(title, DOWN)
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self.add(title)
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self.play(ShowCreation(screen_rect))
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self.wait(2)
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class SubscribeOrBinge(PiCreatureScene):
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def construct(self):
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morty = self.pi_creature
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morty.center().to_edge(DOWN, LARGE_BUFF)
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subscribe = TextMobject("Subscribe")
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subscribe.highlight(RED)
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subscribe.next_to(morty, UP+RIGHT)
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binge = TextMobject("Binge")
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binge.highlight(BLUE)
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binge.next_to(morty, UP+LEFT)
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videos = VGroup(*[VideoIcon() for x in range(30)])
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colors = it.cycle([BLUE_D, BLUE_E, BLUE_C, GREY_BROWN])
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for video, color in zip(videos, colors):
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video.highlight(color)
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videos.move_to(binge.get_bottom(), UP)
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video_anim = LaggedStart(
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Succession, videos,
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lambda v : (
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FadeIn, v,
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ApplyMethod, v.shift, 5*DOWN, {"run_time" : 6},
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),
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run_time = 10
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)
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sub_arrow = Arrow(
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subscribe.get_bottom(),
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Dot().to_corner(DOWN+RIGHT, buff = LARGE_BUFF),
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color = RED
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)
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for word in subscribe, binge:
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word.save_state()
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word.shift(DOWN)
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word.set_fill(opacity = 0)
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self.play(
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subscribe.restore,
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morty.change, "raise_left_hand"
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)
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self.play(GrowArrow(sub_arrow))
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self.wait()
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self.play(
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video_anim,
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Succession(
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AnimationGroup(
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ApplyMethod(binge.restore),
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ApplyMethod(morty.change, "raise_right_hand", binge),
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),
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Blink, morty,
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ApplyMethod, morty.change, "shruggie", videos,
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Animation, Mobject(), {"run_time" : 2},
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Blink, morty,
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Animation, Mobject(), {"run_time" : 4}
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)
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)
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class CloseWithAPuzzle(TeacherStudentsScene):
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def construct(self):
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@ -3888,7 +4102,89 @@ class SponsorScreenGrab(PiCreatureScene):
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self.play(morty.change, mode, screen)
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self.wait(4)
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class FourierEndScreen(PatreonEndScreen):
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CONFIG = {
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"specific_patrons" : [
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"CrypticSwarm",
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"Ali Yahya",
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"Juan Benet",
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"Markus Persson",
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"Damion Kistler",
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"Burt Humburg",
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"Yu Jun",
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"Dave Nicponski",
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"Kaustuv DeBiswas",
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"Joseph John Cox",
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"Luc Ritchie",
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"Achille Brighton",
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"Rish Kundalia",
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"Yana Chernobilsky",
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"Shìmín Kuang",
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"Mathew Bramson",
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"Jerry Ling",
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"Mustafa Mahdi",
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"Meshal Alshammari",
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"Mayank M. Mehrotra",
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"Lukas Biewald",
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"Robert Teed",
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"One on Epsilon",
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"Samantha D. Suplee",
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"Mark Govea",
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"John Haley",
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"Julian Pulgarin",
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"Jeff Linse",
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"Cooper Jones",
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"Boris Veselinovich",
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"Ryan Dahl",
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"Ripta Pasay",
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"Eric Lavault",
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"Mads Elvheim",
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"Andrew Busey",
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"Randall Hunt",
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"Desmos",
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"Tianyu Ge",
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"Awoo",
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"Dr David G. Stork",
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"Linh Tran",
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"Jason Hise",
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"Bernd Sing",
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"Ankalagon",
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"Mathias Jansson",
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"David Clark",
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"Ted Suzman",
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"Eric Chow",
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"Michael Gardner",
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"Jonathan Eppele",
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"Clark Gaebel",
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"David Kedmey",
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"Jordan Scales",
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"Ryan Atallah",
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"supershabam",
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"1stViewMaths",
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"Jacob Magnuson",
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"Thomas Tarler",
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"Isak Hietala",
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"James Thornton",
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"Egor Gumenuk",
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"Waleed Hamied",
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"Oliver Steele",
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"Yaw Etse",
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"David B",
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"Julio Cesar Campo Neto",
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"Delton Ding",
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"George Chiesa",
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"Chloe Zhou",
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"Alexander Nye",
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"Ross Garber",
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"Wang HaoRan",
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"Felix Tripier",
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"Arthur Zey",
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"Norton",
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"Kevin Le",
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"Alexander Feldman",
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"David MacCumber",
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],
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}
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