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More Fourier + Heat animations
This commit is contained in:
Grant Sanderson
@ -10,6 +10,11 @@ ALL_SCENE_CLASSES = [
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FourierOfTrebleClef,
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FourierOfEighthNote,
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FourierOfN,
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FourierNailAndGear,
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FourierNDQ,
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FourierBatman,
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FourierGoogleG,
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FourierHeart,
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# CirclesDrawingWave,
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# Scenes for video
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ExplainCircleAnimations,
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@ -19,4 +24,7 @@ ALL_SCENE_CLASSES = [
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FourierSeriesIntroBackground20,
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FourierSeriesIntro,
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PartTwoOfTour,
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TwoDBodyWithManyTemperatures,
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TwoDBodyWithManyTemperaturesGraph,
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TwoDBodyWithManyTemperaturesContour,
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]
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@ -15,6 +15,13 @@ class FourierCirclesScene(Scene):
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"circle_style": {
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"stroke_width": 2,
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},
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"arrow_config": {
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"buff": 0,
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"max_tip_length_to_length_ratio": 0.35,
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"tip_length": 0.15,
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"max_stroke_width_to_length_ratio": 10,
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"stroke_width": 2,
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},
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"use_vectors": True,
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"base_frequency": 1,
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"slow_factor": 0.25,
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@ -77,18 +84,21 @@ class FourierCirclesScene(Scene):
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color=color,
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**self.circle_style,
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)
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if self.use_vectors:
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LineClass = Arrow
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else:
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LineClass = Line
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circle.radial_line = LineClass(
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line_points = (
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circle.get_center(),
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circle.get_start(),
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color=WHITE,
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buff=0,
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max_tip_length_to_length_ratio=0.1,
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**self.circle_style,
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)
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if self.use_vectors:
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circle.radial_line = Arrow(
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*line_points,
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**self.arrow_config,
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)
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else:
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circle.radial_line = Line(
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*line_points,
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color=WHITE,
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**self.circle_style,
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)
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circle.add(circle.radial_line)
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circle.freq = freq
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circle.phase = phase
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@ -154,10 +164,11 @@ class FourierCirclesScene(Scene):
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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(YELLOW, width=width)
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sp.set_stroke(width=width)
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path.curr_time += dt
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return path
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broken_path.set_color(YELLOW)
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broken_path.add_updater(update_path)
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return broken_path
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@ -365,13 +376,121 @@ class FourierOfEighthNote(FourierOfTrebleClef):
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class FourierOfN(FourierOfTrebleClef):
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CONFIG = {
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"height": 6,
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"n_circles": 200,
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"n_circles": 1000,
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}
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def get_shape(self):
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return TexMobject("N")
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class FourierNailAndGear(FourierOfTrebleClef):
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CONFIG = {
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"height": 6,
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"n_circles": 200,
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"run_time": 10,
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"arrow_config": {
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"tip_length": 0.1,
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"stroke_width": 2,
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}
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}
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def get_shape(self):
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shape = SVGMobject("Nail_And_Gear")[1]
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return shape
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class FourierBatman(FourierOfTrebleClef):
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CONFIG = {
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"height": 4,
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"n_circles": 100,
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"run_time": 10,
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"arrow_config": {
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"tip_length": 0.1,
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"stroke_width": 2,
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}
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}
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def get_shape(self):
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shape = SVGMobject("BatmanLogo")[1]
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return shape
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class FourierHeart(FourierOfTrebleClef):
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CONFIG = {
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"height": 4,
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"n_circles": 100,
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"run_time": 10,
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"arrow_config": {
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"tip_length": 0.1,
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"stroke_width": 2,
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}
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}
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def get_shape(self):
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shape = SuitSymbol("hearts")
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return shape
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def get_drawn_path(self, *args, **kwargs):
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kwargs["stroke_width"] = 5
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path = super().get_drawn_path(*args, **kwargs)
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path.set_color(PINK)
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return path
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class FourierNDQ(FourierOfTrebleClef):
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CONFIG = {
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"height": 4,
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"n_circles": 1000,
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"run_time": 10,
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"arrow_config": {
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"tip_length": 0.1,
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"stroke_width": 2,
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}
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}
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def get_shape(self):
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path = VMobject()
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shape = TexMobject("Hayley")
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for sp in shape.family_members_with_points():
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path.append_points(sp.points)
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return path
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class FourierGoogleG(FourierOfTrebleClef):
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CONFIG = {
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"n_circles": 10,
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"height": 5,
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"g_colors": [
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"#4285F4",
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"#DB4437",
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"#F4B400",
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"#0F9D58",
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]
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}
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def get_shape(self):
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g = SVGMobject("google_logo")[5]
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g.center()
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self.add(g)
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return g
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def get_drawn_path(self, *args, **kwargs):
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kwargs["stroke_width"] = 7
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path = super().get_drawn_path(*args, **kwargs)
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blue, red, yellow, green = self.g_colors
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path[:250].set_color(blue)
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path[250:333].set_color(green)
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path[333:370].set_color(yellow)
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path[370:755].set_color(red)
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path[755:780].set_color(yellow)
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path[780:860].set_color(green)
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path[860:].set_color(blue)
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return path
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class ExplainCircleAnimations(FourierCirclesScene):
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CONFIG = {
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"n_circles": 100,
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@ -521,26 +640,25 @@ class ExplainCircleAnimations(FourierCirclesScene):
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def show_as_vectors(self):
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top_circles = self.top_circles
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top_vectors = self.get_rotating_vectors(top_circles)
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top_vectors.set_color(RED)
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lines = VGroup(*filter(
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lambda sm: isinstance(sm, Line),
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top_circles.family_members_with_points()
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))
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top_vectors.set_color(WHITE)
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self.add(lines, top_circles)
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original_circles = top_circles.copy()
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self.play(
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FadeIn(top_vectors),
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lines.fade, 1,
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top_circles.set_opacity, 0,
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)
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self.wait(3)
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self.play(
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top_circles.match_style, original_circles
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)
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self.remove(top_vectors)
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self.top_vectors = top_vectors
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def show_vector_sum(self):
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# trackers = self.center_trackers.deepcopy()
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trackers = self.center_trackers.copy()
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trackers.sort(
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submob_func=lambda t: abs(t.circle.freq)
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submob_func=lambda t: abs(t.circle.freq - 0.1)
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)
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plane = self.plane = NumberPlane(
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x_min=-3,
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@ -556,7 +674,6 @@ class ExplainCircleAnimations(FourierCirclesScene):
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plane.move_to(self.center_point)
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self.play(
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# FadeOut(self.path),
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FadeOut(self.drawn_path),
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FadeOut(self.circles),
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self.slow_factor_tracker.set_value, 0.05,
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@ -565,7 +682,6 @@ class ExplainCircleAnimations(FourierCirclesScene):
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self.play(FadeIn(plane))
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new_circles = VGroup()
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new_vectors = VGroup()
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last_tracker = None
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for tracker in trackers:
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if last_tracker:
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@ -574,20 +690,11 @@ class ExplainCircleAnimations(FourierCirclesScene):
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tracker.new_location_func = lambda: self.center_point
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original_circle = tracker.circle
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original_vector = tracker.circle.vector
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tracker.circle = original_circle.copy()
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tracker.circle.center_func = tracker.get_location
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tracker.vector = original_vector.copy()
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tracker.vector.clear_updaters()
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tracker.vector.circle = tracker.circle
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tracker.vector.add_updater(lambda v: v.put_start_and_end_on(
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v.circle.get_center(),
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v.circle.get_start(),
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))
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new_circles.add(tracker.circle)
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new_vectors.add(tracker.vector)
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self.add(tracker, tracker.circle, tracker.vector)
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self.add(tracker, tracker.circle)
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start_point = tracker.get_location()
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self.play(
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UpdateFromAlphaFunc(
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@ -613,7 +720,6 @@ class ExplainCircleAnimations(FourierCirclesScene):
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self.slow_factor_tracker.set_value(0.1)
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self.add(
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self.top_circles,
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self.top_vectors,
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self.freq_numbers,
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self.path,
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)
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@ -629,7 +735,6 @@ class ExplainCircleAnimations(FourierCirclesScene):
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def tweak_starting_vectors(self):
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top_circles = self.top_circles
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top_vectors = self.top_vectors
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circles = self.circles
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path = self.path
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drawn_path = self.drawn_path
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@ -658,9 +763,7 @@ class ExplainCircleAnimations(FourierCirclesScene):
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self.wait()
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self.play(
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ReplacementTransform(top_circles, new_top_circles),
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ReplacementTransform(top_vectors, new_top_vectors),
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ReplacementTransform(circles, new_circles),
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# ReplacementTransform(path, new_path),
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FadeOut(path),
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run_time=3,
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)
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@ -1,6 +1,156 @@
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from big_ol_pile_of_manim_imports import *
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from active_projects.ode.part2.shared_constructs import *
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class NewSceneName(Scene):
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class TwoDBodyWithManyTemperatures(ThreeDScene):
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CONFIG = {
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"cells_per_side": 20,
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"body_height": 6,
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}
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def construct(self):
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self.introduce_body()
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self.show_temperature_at_all_points()
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def introduce_body(self):
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height = self.body_height
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buff = 0.025
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rows = VGroup(*[
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VGroup(*[
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Dot(
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# stroke_width=0.5,
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stroke_width=0,
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fill_opacity=1,
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)
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for x in range(self.cells_per_side)
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]).arrange(RIGHT, buff=buff)
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for y in range(self.cells_per_side)
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]).arrange(DOWN, buff=buff)
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for row in rows[1::2]:
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row.submobjects.reverse()
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body = self.body = VGroup(*it.chain(*rows))
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body.set_height(height)
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body.center()
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body.to_edge(LEFT)
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axes = self.axes = Axes(
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x_min=-5, x_max=5,
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y_min=-5, y_max=5,
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)
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axes.match_height(body)
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axes.move_to(body)
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for cell in body:
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self.color_cell(cell)
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# body.set_stroke(WHITE, 0.5) # Do this?
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plate = Square(
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stroke_width=0,
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fill_color=DARK_GREY,
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sheen_direction=UL,
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sheen_factor=1,
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fill_opacity=1,
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)
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plate.replace(body)
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plate_words = TextMobject("Piece of \\\\ metal")
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plate_words.scale(2)
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plate_words.set_stroke(BLACK, 2, background=True)
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plate_words.set_color(BLACK)
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plate_words.move_to(plate)
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self.play(
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DrawBorderThenFill(plate),
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Write(
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plate_words,
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run_time=2,
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rate_func=squish_rate_func(smooth, 0.5, 1)
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)
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)
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self.wait()
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self.remove(plate_words)
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def show_temperature_at_all_points(self):
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body = self.body
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start_corner = body[0].get_center()
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dot = Dot(radius=0.01, color=WHITE)
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dot.move_to(start_corner)
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get_point = dot.get_center
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lhs = TexMobject("T = ")
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lhs.next_to(body, RIGHT, LARGE_BUFF)
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decimal = DecimalNumber(
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num_decimal_places=1,
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unit="^\\circ"
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)
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decimal.next_to(lhs, RIGHT, MED_SMALL_BUFF, DOWN)
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decimal.add_updater(
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lambda d: d.set_value(
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40 + 50 * self.point_to_temp(get_point())
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)
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)
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arrow = Arrow(color=YELLOW)
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arrow.set_stroke(BLACK, 8, background=True)
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arrow.tip.set_stroke(BLACK, 2, background=True)
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# arrow.add_to_back(arrow.copy().set_stroke(BLACK, 5))
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arrow.add_updater(lambda a: a.put_start_and_end_on(
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lhs.get_left() + MED_SMALL_BUFF * LEFT,
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get_point(),
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))
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dot.add_updater(lambda p: p.move_to(
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body[-1] if (1 < len(body)) else start_corner
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))
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self.add(body, dot, lhs, decimal, arrow)
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self.play(
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ShowIncreasingSubsets(
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body,
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run_time=10,
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rate_func=linear,
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)
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)
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self.wait()
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self.remove(dot)
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self.play(
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FadeOut(arrow),
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FadeOut(lhs),
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FadeOut(decimal),
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)
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#
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def point_to_temp(self, point, time=0):
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x, y = self.axes.point_to_coords(point)
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return two_d_temp_func(
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0.3 * x, 0.3 * y, t=time
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)
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def color_cell(self, cell, vect=RIGHT):
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p0 = cell.get_corner(-vect)
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p1 = cell.get_corner(vect)
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colors = []
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for point in p0, p1:
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temp = self.point_to_temp(point)
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color = temperature_to_color(temp)
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colors.append(color)
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cell.set_color(color=colors)
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cell.set_sheen_direction(vect)
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return cell
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|
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class TwoDBodyWithManyTemperaturesGraph(ExternallyAnimatedScene):
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pass
|
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|
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|
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class TwoDBodyWithManyTemperaturesContour(ExternallyAnimatedScene):
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pass
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|
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|
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class BringTwoRodsTogether(Scene):
|
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def construct(self):
|
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pass
|
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|
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35
active_projects/ode/part2/shared_constructs.py
Normal file
35
active_projects/ode/part2/shared_constructs.py
Normal file
@ -0,0 +1,35 @@
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from big_ol_pile_of_manim_imports import *
|
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|
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TIME_COLOR = YELLOW
|
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X_COLOR = GREEN
|
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|
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|
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def get_heat_equation():
|
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pass
|
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|
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|
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def temperature_to_color(temp, min_temp=-1, max_temp=1):
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colors = [BLUE, TEAL, GREEN, YELLOW, "#ff0000"]
|
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|
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alpha = inverse_interpolate(min_temp, max_temp, temp)
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index, sub_alpha = integer_interpolate(
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0, len(colors) - 1, alpha
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)
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return interpolate_color(
|
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colors[index], colors[index + 1], sub_alpha
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)
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|
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|
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def two_d_temp_func(x, y, t):
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return np.sum([
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c * np.sin(f * var) * np.exp(-(f**2) * t)
|
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for c, f, var in [
|
||||
(0.2, 1, x),
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(0.3, 3, x),
|
||||
(0.02, 5, x),
|
||||
(0.01, 7, x),
|
||||
(0.5, 2, y),
|
||||
(0.1, 10, y),
|
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(0.01, 20, y),
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||||
]
|
||||
])
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@ -56,7 +56,7 @@ class FourierSeriesIntro(Scene):
|
||||
TransformFromCopy(
|
||||
title.get_part_by_tex("Fourier"),
|
||||
name.get_part_by_tex("Fourier"),
|
||||
path_arc=-45 * DEGREES,
|
||||
path_arc=90 * DEGREES,
|
||||
),
|
||||
FadeIn(name.get_part_by_tex("Joseph")),
|
||||
)
|
||||
@ -81,3 +81,8 @@ class PartTwoOfTour(TourOfDifferentialEquations):
|
||||
CONFIG = {
|
||||
"zoomed_thumbnail_index": 1,
|
||||
}
|
||||
|
||||
|
||||
class CompareODEToPDE(Scene):
|
||||
def construct(self):
|
||||
pass
|
||||
|
||||
Reference in New Issue
Block a user