mirror of
https://github.com/3b1b/manim.git
synced 2025-07-31 05:52:34 +08:00
More ode animations
This commit is contained in:
Grant Sanderson
@ -23,4 +23,6 @@ ALL_SCENE_CLASSES = [
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BuildUpEquation,
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ShowDerivativeVideo,
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SubtleAirCurrents,
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DefineODE,
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ODEvsPDEinFrames,
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]
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@ -1187,6 +1187,8 @@ class AnalyzePendulumForce(MovingCameraScene):
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thought_term.next_to, self.pendulum, DOWN, LARGE_BUFF
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)
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self.accleration_equation = thought_term
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def emphasize_theta(self):
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pendulum = self.pendulum
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@ -1297,7 +1299,11 @@ class AnalyzePendulumForce(MovingCameraScene):
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pass
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def circle_g_sin_formula(self):
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pass
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self.play(
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ShowCreationThenFadeAround(
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self.accleration_equation
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)
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)
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#
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def set_theta(self, value, *added_anims, **kwargs):
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@ -1323,7 +1329,7 @@ class BuildUpEquation(Scene):
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}
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def construct(self):
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self.add_center_line()
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# self.add_center_line()
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self.show_derivatives()
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self.show_theta_double_dot_equation()
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self.talk_about_sine_component()
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@ -1,5 +1,7 @@
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from big_ol_pile_of_manim_imports import *
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from active_projects.ode.part1.shared_constructs import *
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from active_projects.ode.part1.pendulum import Pendulum
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from active_projects.ode.part1.pendulum import ThetaVsTAxes
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def pendulum_vector_field(point, mu=0.1, g=9.8, L=3):
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@ -415,10 +417,356 @@ class ShowGravityAcceleration(Scene):
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class ShowDerivativeVideo(Scene):
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CONFIG = {
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"camera_config": {"background_color": DARKER_GREY}
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}
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def construct(self):
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pass
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title = TextMobject("Essence of Calculus")
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title.scale(1.25)
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title.to_edge(UP)
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rect = ScreenRectangle(height=6)
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rect = rect.copy()
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rect.set_style(
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fill_opacity=1,
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fill_color=BLACK,
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stroke_width=0,
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)
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rect.next_to(title, DOWN)
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animated_rect = AnimatedBoundary(rect)
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self.add(title, rect)
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self.add(animated_rect)
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self.wait(10)
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class SubtleAirCurrents(Scene):
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def construct(self):
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pass
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class DefineODE(Scene):
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CONFIG = {
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"pendulum_config": {
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"length": 2,
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"top_point": 5 * RIGHT + 2 * UP,
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"initial_theta": 150 * DEGREES,
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"mu": 0.3,
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},
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"axes_config": {
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"y_axis_config": {"unit_size": 0.75},
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"y_max": PI,
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"y_min": -PI,
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"x_max": 10,
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"x_axis_config": {
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"numbers_to_show": range(2, 10, 2),
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"unit_size": 1,
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}
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},
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}
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def construct(self):
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self.add_graph()
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self.write_differential_equation()
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self.dont_know_the_value()
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self.show_value_slope_curvature()
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self.write_ode()
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self.show_second_order()
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self.show_changing_curvature_group()
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def add_graph(self):
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pendulum = Pendulum(**self.pendulum_config)
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axes = ThetaVsTAxes(**self.axes_config)
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axes.center()
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axes.to_corner(DL)
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graph = axes.get_live_drawn_graph(pendulum)
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pendulum.start_swinging()
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self.add(axes, pendulum, graph)
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self.pendulum = pendulum
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self.axes = axes
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self.graph = graph
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def write_differential_equation(self):
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de_word = TextMobject("Differential", "Equation")
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de_word.to_edge(UP)
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equation = TexMobject(
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"\\ddot \\theta({t}) = "
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"-\\mu \\dot \\theta({t})"
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"-{g \\over L} \\sin\\big(\\theta({t})\\big)",
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tex_to_color_map={
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"\\theta": BLUE,
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"{t}": WHITE
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}
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)
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equation.next_to(de_word, DOWN)
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thetas = equation.get_parts_by_tex("\\theta")
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lines = VGroup(*[
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Line(v, 1.2 * v)
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for v in compass_directions(25)
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])
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lines.replace(equation, stretch=True)
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lines.scale(1.5)
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lines.set_stroke(YELLOW)
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lines.shuffle()
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self.add(equation)
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self.wait(5)
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self.play(
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ShowPassingFlashWithThinningStrokeWidth(
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lines,
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lag_ratio=0.002,
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run_time=1.5,
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time_width=0.9,
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n_segments=5,
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)
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)
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self.play(FadeInFromDown(de_word))
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self.wait(2)
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self.play(
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LaggedStartMap(
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ApplyMethod, thetas,
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lambda m: (m.shift, 0.25 * DOWN),
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rate_func=there_and_back,
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)
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)
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self.wait()
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self.de_word = de_word
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self.equation = equation
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def dont_know_the_value(self):
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graph = self.graph
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pendulum = self.pendulum
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q_marks = VGroup(*[
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TexMobject("?").move_to(graph.point_from_proportion(a))
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for a in np.linspace(0, 1, 20)
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])
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q_marks.set_stroke(width=0, background=True)
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self.play(
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VFadeOut(graph),
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FadeOut(pendulum),
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LaggedStart(*[
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UpdateFromAlphaFunc(
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q_mark,
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lambda m, a: m.set_height(0.5 * (1 + a)).set_fill(
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opacity=there_and_back(a)
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),
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)
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for q_mark in q_marks
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], lag_ratio=0.01, run_time=2)
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)
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self.remove(q_marks)
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def show_value_slope_curvature(self):
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axes = self.axes
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p = self.pendulum
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graph = axes.get_graph(
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lambda t: p.initial_theta * np.cos(
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np.sqrt(p.gravity / p.length) * t
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) * np.exp(-p.mu * t / 2)
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)
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tex_config = {
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"tex_to_color_map": {"\\theta": BLUE},
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"height": 0.5,
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}
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theta, d_theta, dd_theta = [
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TexMobject(s + "\\theta(t)", **tex_config)
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for s in ("", "\\dot", "\\ddot")
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]
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t_tracker = ValueTracker(2.5)
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get_t = t_tracker.get_value
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def get_point(t):
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return graph.point_from_proportion(t / axes.x_max)
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def get_dot():
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return Dot(get_point(get_t())).scale(0.5)
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def get_v_line():
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point = get_point(get_t())
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x_point = axes.x_axis.number_to_point(
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axes.x_axis.point_to_number(point)
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)
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return DashedLine(
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x_point, point,
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dash_length=0.025,
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stroke_color=WHITE,
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stroke_width=2,
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)
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def get_tangent_line(curve, alpha):
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line = Line(
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ORIGIN, 1.5 * RIGHT,
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color=YELLOW,
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stroke_width=1.5,
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)
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da = 0.0001
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p0 = curve.point_from_proportion(alpha)
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p1 = curve.point_from_proportion(alpha - da)
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p2 = curve.point_from_proportion(alpha + da)
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angle = angle_of_vector(p2 - p1)
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line.rotate(angle)
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line.move_to(p0)
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return line
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def get_slope_line():
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return get_tangent_line(
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graph, get_t() / axes.x_max
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)
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def get_curve():
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curve = VMobject()
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t = get_t()
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curve.set_points_smoothly([
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get_point(t + a)
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for a in np.linspace(-0.5, 0.5, 11)
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])
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curve.set_stroke(RED, 1)
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return curve
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v_line = always_redraw(get_v_line)
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dot = always_redraw(get_dot)
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slope_line = always_redraw(get_slope_line)
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curve = always_redraw(get_curve)
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theta.next_to(v_line, RIGHT, SMALL_BUFF)
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d_theta.next_to(slope_line.get_end(), UP, SMALL_BUFF)
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dd_theta.next_to(curve.get_end(), RIGHT, SMALL_BUFF)
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thetas = VGroup(theta, d_theta, dd_theta)
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words = VGroup(
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TextMobject("= Height"),
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TextMobject("= Slope").set_color(YELLOW),
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TextMobject("= ``Curvature''").set_color(RED),
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)
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words.scale(0.75)
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for word, sym in zip(words, thetas):
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word.next_to(sym, RIGHT, buff=2 * SMALL_BUFF)
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sym.word = word
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self.play(
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ShowCreation(v_line),
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FadeInFromPoint(dot, v_line.get_start()),
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FadeInFrom(theta, DOWN),
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FadeInFrom(theta.word, DOWN),
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)
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self.add(slope_line, dot)
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self.play(
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ShowCreation(slope_line),
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FadeInFrom(d_theta, LEFT),
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FadeInFrom(d_theta.word, LEFT),
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)
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a_tracker = ValueTracker(0)
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curve_copy = curve.copy()
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changing_slope = always_redraw(
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lambda: get_tangent_line(
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curve_copy,
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a_tracker.get_value(),
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).set_stroke(
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opacity=there_and_back(a_tracker.get_value())
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)
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)
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self.add(curve, dot)
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self.play(
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ShowCreation(curve),
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FadeInFrom(dd_theta, LEFT),
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FadeInFrom(dd_theta.word, LEFT),
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)
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self.add(changing_slope)
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self.play(
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a_tracker.set_value, 1,
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run_time=3,
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)
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self.remove(changing_slope, a_tracker)
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self.t_tracker = t_tracker
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self.curvature_group = VGroup(
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v_line, slope_line, curve, dot
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)
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self.curvature_group_labels = VGroup(thetas, words)
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def write_ode(self):
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equation = self.equation
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axes = self.axes
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de_word = self.de_word
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ts = equation.get_parts_by_tex("{t}")
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t_rects = VGroup(*map(SurroundingRectangle, ts)) # Rawr
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x_axis = axes.x_axis
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x_axis_line = Line(
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x_axis.get_start(), x_axis.get_end(),
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stroke_color=YELLOW,
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stroke_width=5,
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)
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ordinary = TextMobject("Ordinary")
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de_word.generate_target()
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group = VGroup(ordinary, de_word.target)
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group.arrange(RIGHT)
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group.to_edge(UP)
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ordinary_underline = Line(LEFT, RIGHT)
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ordinary_underline.replace(ordinary, dim_to_match=0)
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ordinary_underline.next_to(ordinary, DOWN, SMALL_BUFF)
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ordinary_underline.set_color(YELLOW)
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self.play(
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ShowCreationThenFadeOut(
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t_rects,
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lag_ratio=0.8
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),
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ShowCreationThenFadeOut(x_axis_line)
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)
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self.play(
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MoveToTarget(de_word),
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FadeInFrom(ordinary, RIGHT),
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GrowFromCenter(ordinary_underline)
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)
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self.play(FadeOut(ordinary_underline))
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self.wait()
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self.remove(ordinary, de_word)
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ode_word = self.ode_word = VGroup(*ordinary, *de_word)
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ode_initials = VGroup(*[word[0] for word in ode_word])
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ode_initials.generate_target()
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ode_initials.target.scale(1.2)
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ode_initials.target.set_color(PINK)
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ode_initials.target.arrange(
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RIGHT, buff=0.5 * SMALL_BUFF, aligned_edge=DOWN
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)
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ode_initials.target.to_edge(UP, buff=MED_SMALL_BUFF)
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ode_remaining_letters = VGroup(*it.chain(*[
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word[1:] for word in ode_word
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]))
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ode_remaining_letters.generate_target()
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for mob in ode_remaining_letters.target:
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mob.shift(0.2 * UP)
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mob.fade(1)
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self.play(
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MoveToTarget(ode_initials),
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MoveToTarget(ode_remaining_letters, lag_ratio=0.05),
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)
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self.wait()
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self.ode_initials = ode_initials
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def show_second_order(self):
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pass
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def show_changing_curvature_group(self):
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pass
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class ODEvsPDEinFrames(Scene):
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def construct(self):
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pass
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Reference in New Issue
Block a user