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Final animations for diffyq chapter 3
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Grant Sanderson
parent
62c2772982
commit
dfeb11a2ab
4 changed files with 211 additions and 5 deletions
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@ -99,7 +99,7 @@ class ShowNewRuleAtDiscreteBoundary(DiscreteSetup):
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)
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self.wait()
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# Point to inward neighbord
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# Point to inward neighbor
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new_arrows = VGroup(*[
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Arrow(
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d1.get_center(),
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@ -1140,7 +1140,7 @@ class EndScreen(PatreonEndScreen):
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"Jonathan Eppele",
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"Kai-Siang Ang",
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"Kanan Gill",
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"Kartik Cating-Subramanian",
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"Kartik\\\\Cating-Subramanian",
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"L0j1k",
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"Lee Redden",
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"Linh Tran",
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@ -45,7 +45,7 @@ class TemperatureGraphScene(SpecialThreeDScene):
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if include_labels:
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self.add_axes_labels(axes)
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# Adjust axis orinetations
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# Adjust axis orientation
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axes.x_axis.rotate(
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90 * DEGREES, RIGHT,
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about_point=axes.c2p(0, 0, 0),
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@ -674,9 +674,9 @@ class OceanOfPossibilities(TemperatureGraphScene):
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def setup_axes(self):
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axes = self.get_three_d_axes(include_numbers=True)
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axes.add(axes.input_plane)
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axes.scale(0.9)
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axes.scale(0.8)
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axes.center()
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axes.shift(0.5 * OUT + RIGHT)
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axes.shift(OUT + RIGHT)
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self.add(axes)
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self.axes = axes
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@ -2073,6 +2073,7 @@ class ManipulateSinExpSurface(TemperatureGraphScene):
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"^2": WHITE,
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},
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},
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"graph_config": {},
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"initial_phi": -90 * DEGREES,
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"initial_omega": 1,
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}
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@ -2094,6 +2095,7 @@ class ManipulateSinExpSurface(TemperatureGraphScene):
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L = TexMobject("L")
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L.rotate(90 * DEGREES, RIGHT)
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L.next_to(axes.x_axis.get_end(), IN)
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axes.x_axis.label = L
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axes.x_axis.add(L)
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axes.shift(5 * LEFT + 0.5 * IN)
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@ -2424,6 +2426,7 @@ class ManipulateSinExpSurface(TemperatureGraphScene):
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lambda: self.get_time_slice_graph(
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self.axes, self.func,
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t=self.t_tracker.get_value(),
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**self.graph_config
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)
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)
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@ -2769,3 +2772,58 @@ class ShowHarmonicSurfaces(ManipulateSinExpSurface):
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)
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result.to_edge(UP)
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return result
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class Thumbnail(ShowHarmonicSurfaces):
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CONFIG = {
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"default_surface_config": {
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"resolution": (40, 30),
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# "resolution": (10, 10),
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},
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"graph_config": {
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"stroke_width": 8,
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},
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}
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def construct(self):
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self.setup_axes()
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self.initialize_parameter_trackers()
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self.add_surface()
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self.add_graph()
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#
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self.omega_tracker.set_value(3 * PI / 10)
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self.set_camera_orientation(
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theta=-70 * DEGREES,
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)
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axes = self.axes
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for axis in [axes.y_axis, axes.z_axis]:
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axis.numbers.set_opacity(0)
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axis.remove(*axis.numbers)
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axes.x_axis.label.set_opacity(0)
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axes.z_axis.label.set_opacity(0)
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for n in range(2, 16, 2):
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new_graph = self.get_time_slice_graph(
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axes, self.func, t=n,
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**self.graph_config
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)
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new_graph.set_shade_in_3d(True)
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new_graph.set_stroke(
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width=8 / np.sqrt(n),
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# opacity=1 / n**(1 / 4),
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)
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self.add(new_graph)
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words = TextMobject(
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"Sine waves + Linearity + Fourier = Solution"
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)
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words.set_width(FRAME_WIDTH - 1)
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words.to_edge(DOWN)
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words.shift(2 * DOWN)
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self.add_fixed_in_frame_mobjects(words)
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self.camera.frame_center.shift(DOWN)
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self.update_mobjects(0)
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self.surface.set_stroke(width=0.1)
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self.surface.set_fill(opacity=0.2)
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@ -176,6 +176,94 @@ class BorderRect(Scene):
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self.add(rect)
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class SeekIdealized(Scene):
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def construct(self):
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phrases = VGroup(*[
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TextMobject(
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"Seek", text, "problems",
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tex_to_color_map={
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"realistic": GREEN,
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"{idealized}": YELLOW,
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"over-idealized": YELLOW,
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"general": BLUE,
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}
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)
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for text in [
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"realistic",
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"{idealized}",
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"over-idealized",
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"general",
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]
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])
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phrases.scale(2)
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words = VGroup()
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for phrase in phrases:
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phrase.center()
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word = phrase[1]
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words.add(word)
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phrase.remove(word)
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arrow = Vector(DOWN)
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arrow.set_stroke(WHITE, 6)
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arrow.next_to(words[3], UP)
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low_arrow = arrow.copy()
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low_arrow.next_to(words[3], DOWN)
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solutions = TextMobject("solutions")
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solutions.scale(2)
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solutions.move_to(phrases[3][1], UL)
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models = TextMobject("models")
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models.scale(2)
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models.next_to(
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words[0], RIGHT, buff=0.35,
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aligned_edge=DOWN
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)
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phrases.center()
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phrase = phrases[0]
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self.add(phrase)
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self.add(words[0])
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self.wait()
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words[0].save_state()
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self.play(
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words[0].to_edge, DOWN,
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words[0].set_opacity, 0.5,
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Transform(phrase, phrases[1]),
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FadeInFrom(words[1], UP)
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)
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self.wait()
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# self.play(
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# words[1].move_to, words[2], RIGHT,
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# FadeIn(words[2]),
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# Transform(phrase, phrases[2])
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# )
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# self.wait()
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self.play(
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words[1].next_to, arrow, UP,
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ShowCreation(arrow),
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MaintainPositionRelativeTo(
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phrase, words[1]
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),
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FadeInFrom(solutions, LEFT),
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FadeIn(words[3]),
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)
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self.wait()
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words[0].generate_target()
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words[0].target.next_to(low_arrow, DOWN)
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words[0].target.set_opacity(1)
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models.shift(
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words[0].target.get_center() -
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words[0].saved_state.get_center()
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)
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self.play(
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MoveToTarget(words[0]),
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ShowCreation(low_arrow),
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FadeInFrom(models, LEFT)
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)
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self.wait()
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class SecondDerivativeOfSine(Scene):
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def construct(self):
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equation = TexMobject(
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@ -769,3 +857,63 @@ class CompareFreqDecays2to4(CompareFreqDecays1to2):
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CONFIG = {
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"freqs": [2, 4],
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}
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class WorryAboutGenerality(TeacherStudentsScene, WriteHeatEquationTemplate):
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def construct(self):
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eq = self.get_d1_equation()
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diffyq = self.get_diffyq_set()
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is_in = TexMobject("\\in")
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is_in.scale(2)
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group = VGroup(eq, is_in, diffyq)
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group.arrange(RIGHT, buff=MED_LARGE_BUFF)
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group.to_edge(UP)
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arrow = Vector(DOWN)
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arrow.set_stroke(WHITE, 5)
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arrow.next_to(eq, DOWN)
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themes = TextMobject("Frequent themes")
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themes.scale(1.5)
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themes.next_to(arrow, DOWN)
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self.play(
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self.get_student_changes(
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"sad", "tired", "pleading"
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),
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self.teacher.change, "raise_right_hand",
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FadeInFromDown(eq)
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)
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self.play(Write(group[1:]))
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self.wait(2)
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self.play(
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ShowCreation(arrow),
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self.get_student_changes(*3 * ["pondering"]),
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)
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self.play(
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FadeInFrom(themes, UP),
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self.get_student_changes(*3 * ["thinking"]),
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self.teacher.change, "happy"
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)
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self.wait(4)
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# def get_d1_equation(self):
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# result = super().get_d1_equation()
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# lp, rp = parens = TexMobject("(", ")")
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# parens.match_height(result)
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# lp.next_to(result, LEFT, SMALL_BUFF)
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# rp.next_to(result, RIGHT, SMALL_BUFF)
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# result.add_to_back(lp)
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# result.add(rp)
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# return result
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def get_diffyq_set(self):
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words = TextMobject(
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"Differential\\\\equations"
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)
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words.scale(1.5)
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words.set_color(BLUE)
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lb = Brace(words, LEFT)
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rb = Brace(words, RIGHT)
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return VGroup(lb, words, rb)
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