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https://github.com/3b1b/videos.git
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Finalize Fourier monster animations
This commit is contained in:
Grant Sanderson
parent
2aec2f2c7b
commit
3dd96ca2f7
3 changed files with 108 additions and 80 deletions
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@ -157,27 +157,31 @@ class FourierCirclesScene(Scene):
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def get_drawn_path_alpha(self):
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return self.get_vector_time()
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def get_drawn_path(self, vectors, stroke_width=None, **kwargs):
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def get_drawn_path(self, vectors, stroke_width=None, fade_rate=0.2, **kwargs):
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if stroke_width is None:
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stroke_width = self.drawn_path_stroke_width
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path = self.get_vector_sum_path(vectors, **kwargs)
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broken_path = CurvesAsSubmobjects(path)
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path.set_stroke(self.drawn_path_color, stroke_width)
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self.add_path_fader(path, fade_rate)
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return path
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def update_path(path, dt):
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def add_path_fader(self, path, fade_rate=0.2):
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stroke_width = np.max(path.get_stroke_width())
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stroke_opacity = np.max(path.get_stroke_opacity())
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def update_path(path_, dt):
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alpha = self.get_vector_time()
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n_curves = len(path)
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for a, sp in zip(np.linspace(0, 1, n_curves), path):
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b = alpha - a
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if b < 0:
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width = 0
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else:
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width = stroke_width * (1 - (b % 1))
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sp.set_stroke(width=width)
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return path
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n = path_.get_num_points()
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fade_factors = (np.linspace(0, 1, n) - alpha) % 1
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fade_factors = fade_factors**fade_rate
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path_.set_stroke(
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width=stroke_width * fade_factors,
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opacity=stroke_opacity * fade_factors,
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)
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return path_
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broken_path.set_color(self.drawn_path_color)
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broken_path.add_updater(update_path)
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return broken_path
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path.add_updater(update_path)
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return path
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def get_y_component_wave(self,
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vectors,
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@ -3,16 +3,17 @@ from _2022.piano.fourier_animations import DecomposeAudioSegment
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from _2019.diffyq.part2.fourier_series import FourierCirclesScene
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class DecomposeRoar(DecomposeAudioSegment):
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class DecomposeRoar_SlowFPS(DecomposeAudioSegment):
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audio_file = "/Users/grant/Dropbox/3Blue1Brown/videos/2022/infinity/Roar.wav"
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graph_point = 0.428
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zoom_rect_dims = (0.2, 6.0)
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def construct(self):
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self.add_full_waveform()
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self.add_full_waveform(run_time=2.5)
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self.zoom_in_on_segment(
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self.axes, self.graph,
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self.graph_point, self.zoom_rect_dims
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self.graph_point, self.zoom_rect_dims,
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run_time=3,
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)
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self.prepare_for_3d()
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self.show_all_waves()
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@ -55,7 +56,8 @@ class DecomposeRoar(DecomposeAudioSegment):
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x_range=(0, t_max),
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)
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wave.match_y(f_axes.c2p(freq, 0))
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wave.set_stroke(opacity=0.75)
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# wave.set_stroke(opacity=0.75)
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wave.set_stroke(opacity=1.0)
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wave.amp = amp
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wave.freq = freq
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wave.phase = phase
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@ -85,14 +87,14 @@ class DecomposeRoar(DecomposeAudioSegment):
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),
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lag_ratio=1 / len(sine_waves),
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),
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run_time=8
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run_time=4
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)
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self.wait(3)
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class CombineWavesToImage(FourierCirclesScene):
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class CombineWavesToImage_SlowFPS(FourierCirclesScene):
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CONFIG = {
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"peace_sign_height": 6.0,
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"drawing_height": 6.0,
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"n_shown_waves": 5,
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"n_vectors": 500,
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# "n_vectors": 50,
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@ -102,6 +104,7 @@ class CombineWavesToImage(FourierCirclesScene):
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# "parametric_function_step_size": 0.01,
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"drawn_path_color": YELLOW,
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"remove_background_waves": False,
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"drawing_file": "/Users/grant/Dropbox/3Blue1Brown/videos/2022/infinity/monster-holding-piece-sign-3.svg",
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}
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def construct(self):
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@ -157,10 +160,10 @@ class CombineWavesToImage(FourierCirclesScene):
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))
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all_axes.arrange(DOWN, buff=1.0)
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dots = VGroup(Tex("\\vdots", font_size=100), Tex(""))
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dots.arrange(RIGHT)
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dots = Tex("\\vdots", font_size=100)
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dots.next_to(all_axes, DOWN, buff=0.5)
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dots.match_x(all_axes[0].get_origin())
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dots.set_fill(WHITE)
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frame = self.camera.frame
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group = Group(all_axes, dots)
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@ -216,10 +219,9 @@ class CombineWavesToImage(FourierCirclesScene):
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true_path = self.path
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fade_region = self.get_fade_region(true_path)
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sf = self.get_slow_factor()
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rt = 5
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future_vt = self.get_vector_time() + sf * rt
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self.wait((1.0 - (future_vt % 1.0)) / sf)
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# sf = self.get_slow_factor()
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# future_vt = self.get_vector_time() + sf * rt
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label = VGroup(Integer(100, edge_to_fix=DR), Text("terms"))
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label.arrange(RIGHT, buff=0.15)
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@ -227,7 +229,6 @@ class CombineWavesToImage(FourierCirclesScene):
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label[0].set_value(self.n_shown_waves)
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# Animate entry
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drawn_path = self.get_drawn_path(self.vectors[:self.n_shown_waves + 1])
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terms = self.get_terms(self.n_shown_waves)
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self.play(
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FadeIn(fade_region, lag_ratio=0.1),
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@ -241,16 +242,21 @@ class CombineWavesToImage(FourierCirclesScene):
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), lag_ratio=0.1),
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FadeIn(label),
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Write(terms),
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# self.slow_factor_tracker.animate.set_value(0.1),
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run_time=rt,
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)
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self.vector_clock.set_value(0)
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# Set up drawn paths
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self.add(drawn_path, terms)
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drawn_path = self.get_drawn_path(self.vectors[:self.n_shown_waves + 1])
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dot = self.add_draw_dot(self.vectors[:self.n_shown_waves + 1])
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self.add(drawn_path, terms, dot)
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anims = [
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UpdateFromAlphaFunc(drawn_path, lambda m, a: m.set_stroke(interpolate_color(BLACK, YELLOW, a))),
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UpdateFromAlphaFunc(dot, lambda m, a: m.set_opacity(a)),
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]
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if self.remove_background_waves:
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self.play(
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fade_region.animate.set_height(2 * FRAME_WIDTH).set_opacity(0.05),
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*anims,
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run_time=2
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)
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self.remove(
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@ -260,7 +266,7 @@ class CombineWavesToImage(FourierCirclesScene):
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fade_region,
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)
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else:
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self.wait(2)
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self.play(*anims, run_time=2)
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# Now add on new vectors one at a time
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drawn_paths = dict()
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@ -280,8 +286,8 @@ class CombineWavesToImage(FourierCirclesScene):
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drawn_paths[n] = self.get_drawn_path(self.vectors[:n])
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if n not in all_terms:
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all_terms[n] = self.get_terms(n)
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group[0].become(drawn_paths[n])
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group[1].become(all_terms[n])
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group.replace_submobject(0, drawn_paths[n])
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group.replace_submobject(1, all_terms[n])
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group[2][0].set_value(n)
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group[3].set_submobjects(self.vectors[:n])
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group[4].set_submobjects(self.circles[:n])
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@ -289,11 +295,14 @@ class CombineWavesToImage(FourierCirclesScene):
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self.style_vectors(group[3])
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self.style_circles(group[4])
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if n > 25:
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group[4].set_stroke(opacity=(1.0 / (n - 25))**0.2)
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group.update()
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return group
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self.remove(self.vectors, self.circles, drawn_path, terms)
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self.remove(self.vectors, self.circles, drawn_path, terms, dot)
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self.add_draw_dot(drawing_group[3])
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self.play(UpdateFromAlphaFunc(
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drawing_group, update_drawing_group,
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run_time=15,
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@ -303,24 +312,30 @@ class CombineWavesToImage(FourierCirclesScene):
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inf = Tex("\\infty")
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inf.match_height(label[0])
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inf.move_to(label[0], RIGHT)
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inf.set_fill(WHITE)
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drawn_path = drawing_group[0]
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# self.add_path_fader(true_path, fade_rate=1)
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true_path.set_stroke(width=1.0)
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self.add(drawn_path, true_path, self.circles, self.vectors)
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self.play(
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FadeIn(true_path),
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VFadeOut(drawn_path),
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UpdateFromAlphaFunc(drawn_path, lambda m, a: m.set_stroke(interpolate_color(YELLOW, BLACK, a))),
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VFadeIn(true_path),
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ChangeDecimalToValue(label[0], 1000),
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VFadeOut(label[0]),
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FadeIn(inf),
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run_time=3,
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)
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self.remove(drawn_path)
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self.wait(12)
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##
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def get_drawing(self):
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# drawing = self.get_peace_sign()
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svg = SVGMobject("/Users/grant/Dropbox/3Blue1Brown/videos/2022/infinity/monster-holding-heart.svg")
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svg = SVGMobject(self.drawing_file)
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drawing = svg[1]
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drawing.set_height(self.peace_sign_height)
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drawing.set_height(self.drawing_height)
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drawing.set_stroke(self.drawn_path_color, 2)
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return drawing
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@ -355,47 +370,55 @@ class CombineWavesToImage(FourierCirclesScene):
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for k, circle in zip(it.count(0), circles):
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circle.set_stroke(width=mcsw / (1 + k / 4), opacity=1)
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if len(circles) > 25:
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circles.set_stroke(opacity=(1.0 / (len(circles) - 25))**0.2)
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return circles
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def get_fade_region(self, path, n_disks=100):
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disk = Circle(radius=path.get_width() / 2)
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disks = VGroup(*(
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disk.copy().scale(sf)
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for sf in np.linspace(1.0, 2.25, n_disks)
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))
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disks.set_stroke(width=0)
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disks.set_fill(BLACK, opacity=3.0 / n_disks)
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return disks
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def get_fade_region(self, path):
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dot = GlowDot()
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dot.set_radius(1.0 * path.get_width())
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dot.set_glow_factor(0.2)
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dot.set_color(BLACK, 0.95)
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return dot
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def get_drawn_path(self, vectors):
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if len(vectors) == 0:
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nv = len(vectors)
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if nv == 0:
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return VGroup()
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return super().get_drawn_path(vectors, stroke_width=4).set_stroke(self.drawn_path_color)
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fade_rate = 10 * np.exp(0.01 * (5 - nv)) + 1.0
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path = super().get_drawn_path(vectors, stroke_width=4, fade_rate=fade_rate)
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path.set_stroke(self.drawn_path_color)
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return path
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def get_terms(self, n_terms, max_terms=40, max_width=12):
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tex_str = ""
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def get_terms(self, n_terms, max_terms=100, max_width=12):
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ks = list(range(-int(np.floor(n_terms / 2)), int(np.ceil(n_terms / 2))))
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ks.sort(key=abs)
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ks = ks[:max_terms]
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ks.sort()
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font_size = max(180 / n_terms, 5)
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terms = VGroup()
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for k in ks:
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tex_str += "c_{k} e^{k \\cdot 2 \\pi i \\cdot t} +".replace("k", str(k))
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terms.add(MTex("c_{k} e^{k \\cdot 2 \\pi i \\cdot t} +".replace("k", str(k))))
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if n_terms <= max_terms:
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tex_str = tex_str[:-1] # Remove trailing plus
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terms[-1][-1].set_opacity(0)
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else:
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tex_str = "\\cdots + " + tex_str + "\\cdots"
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terms.add_to_back(MTex("\\cdots + "))
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terms.add(MTex("\\cdots"))
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font_size = 180 / n_terms
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result = Tex(tex_str, font_size=font_size)
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result.set_max_width(max_width)
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result.next_to(self.path, UP, MED_SMALL_BUFF)
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terms.arrange(RIGHT, SMALL_BUFF)
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terms.scale(font_size / 48)
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terms.set_max_width(max_width)
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terms.next_to(self.path, UP, SMALL_BUFF)
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max_light_terms = 15
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if n_terms > max_light_terms:
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result.set_fill(opacity=max_light_terms / (n_terms - max_light_terms))
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result.set_stroke(width=0)
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terms.set_fill(opacity=max_light_terms / (n_terms - max_light_terms))
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terms.set_stroke(width=0)
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return result
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return terms
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def add_draw_dot(self, vectors):
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dot = GlowDot()
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dot.add_updater(lambda d: d.move_to(
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vectors[-1].get_end() if len(vectors) > 0 else ORIGIN
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))
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self.add(dot)
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return dot
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@ -210,7 +210,7 @@ class DecomposeAudioSegment(Scene):
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self.break_down_into_fourier_components()
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self.back_to_full_signal()
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def add_full_waveform(self):
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def add_full_waveform(self, run_time=5):
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axes, graph = self.get_signal_graph()
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self.add(axes)
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@ -224,7 +224,7 @@ class DecomposeAudioSegment(Scene):
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time_width=0.1,
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rate_func=linear,
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),
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run_time=5,
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run_time=run_time,
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)
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self.axes = axes
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@ -261,20 +261,21 @@ class DecomposeAudioSegment(Scene):
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zoom_rect.target.set_stroke(width=0)
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axes.target.set_stroke(opacity=0)
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self.play(Write(zoom_rect))
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self.play(
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*map(MoveToTarget, movers),
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run_time=run_time
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)
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self.remove(graph, axes)
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self.wait()
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# Swap axes
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new_axes = Axes((-2, 12), (-1, 1, 0.25), width=FRAME_WIDTH + 1)
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new_axes.shift(LEFT_SIDE + RIGHT - new_axes.get_origin())
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if fade_in_new_axes:
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self.play(FadeIn(new_axes))
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self.play(Write(zoom_rect))
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self.play(
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*map(MoveToTarget, movers),
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FadeIn(new_axes),
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run_time=run_time,
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)
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self.remove(graph, axes)
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# Swap axes
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# if fade_in_new_axes:
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# self.play(FadeIn(new_axes))
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self.original_graph = graph
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self.original_axes = axes
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