mirror of
https://github.com/3b1b/manim.git
synced 2025-08-01 06:22:54 +08:00
More ode part1 scenes
This commit is contained in:
Grant Sanderson
@ -1,15 +1,21 @@
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from active_projects.ode.part1.pendulum import *
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from active_projects.ode.part1.staging import *
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from active_projects.ode.part1.pi_scenes import *
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OUTPUT_DIRECTORY = "ode/part1"
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ALL_SCENE_CLASSES = [
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IntroducePendulum,
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MultiplePendulumsOverlayed,
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# FormulasAreLies,
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FormulasAreLies,
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MediumAnglePendulum,
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MediumHighAnglePendulum,
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HighAnglePendulum,
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LowAnglePendulum,
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SomeOfYouWatching,
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SmallAngleApproximationTex,
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VeryLowAnglePendulum,
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FollowThisThread,
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StrogatzQuote,
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# Tests
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PendulumTest,
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VectorFieldTest,
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@ -1,13 +1,5 @@
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from big_ol_pile_of_manim_imports import *
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Lg_formula_config = {
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"tex_to_color_map": {
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"\\theta_0": WHITE,
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"{L}": BLUE,
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"{g}": YELLOW,
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},
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}
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from active_projects.ode.part1.shared_constructs import *
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class Pendulum(VGroup):
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@ -828,36 +820,30 @@ class HighAnglePendulum(LowAnglePendulum):
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}
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class PendulumTest(Scene):
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def construct(self):
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pendulum = Pendulum(
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initial_theta=170 * DEGREES,
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top_point=ORIGIN,
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damping=0
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)
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pendulum.add_velocity_vector()
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pendulum.add_theta_label()
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gravity_vector = GravityVector(pendulum)
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gravity_vector.add_component_lines()
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axes = ThetaVsTAxes(
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y_max=PI,
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y_min=-PI,
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y_axis_config={
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"unit_size": 0.7,
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"tick_frequency": PI / 4,
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class VeryLowAnglePendulum(LowAnglePendulum):
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CONFIG = {
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"pendulum_config": {
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"initial_theta": 10 * DEGREES,
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"n_steps_per_frame": 1000,
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"top_point": ORIGIN,
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"length": 3,
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},
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x_max=14
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)
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axes.to_corner(UL)
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axes.add_live_drawn_graph(pendulum)
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"axes_config": {
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"y_axis_config": {"unit_size": 2},
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"y_max": PI / 4,
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"y_min": -PI / 4,
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"number_line_config": {
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"tip_length": 0.3,
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"stroke_width": 2,
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}
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},
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"pendulum_shift_vect": 1 * RIGHT,
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}
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self.add(pendulum, gravity_vector)
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self.add(axes)
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pendulum.start_swinging()
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self.wait(14)
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class BuildUpEquation(Scene):
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def construct(self):
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pass
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class NewSceneName(Scene):
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108
active_projects/ode/part1/pi_scenes.py
Normal file
108
active_projects/ode/part1/pi_scenes.py
Normal file
@ -0,0 +1,108 @@
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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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class SomeOfYouWatching(TeacherStudentsScene):
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CONFIG = {
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"camera_config": {
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"background_color": DARKER_GREY,
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}
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}
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def construct(self):
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screen = self.screen
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screen.scale(1.25, about_edge=UL)
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screen.set_fill(BLACK, 1)
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self.add(screen)
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self.teacher.change("raise_right_hand")
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for student in self.students:
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student.change("pondering", screen)
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self.student_says(
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"Well...yeah",
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target_mode="tease"
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)
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self.wait(3)
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class FormulasAreLies(PiCreatureScene):
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def construct(self):
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you = self.pi_creature
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t2c = {
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"{L}": BLUE,
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"{g}": YELLOW,
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"\\theta_0": WHITE,
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"\\sqrt{\\,": WHITE,
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}
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kwargs = {"tex_to_color_map": t2c}
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period_eq = TexMobject(
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"\\text{Period} = 2\\pi \\sqrt{\\,{L} / {g}}",
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**kwargs
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)
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theta_eq = TexMobject(
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"\\theta(t) = \\theta_0 \\cos\\left("
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"\\sqrt{\\,{L} / {g}} \\cdot t"
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"\\right)",
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**kwargs
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)
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equations = VGroup(theta_eq, period_eq)
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equations.arrange(DOWN, buff=LARGE_BUFF)
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for eq in period_eq, theta_eq:
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i = eq.index_of_part_by_tex("\\sqrt")
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eq.sqrt_part = eq[i:i + 4]
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theta0 = theta_eq.get_part_by_tex("\\theta_0")
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theta0_words = TextMobject("Starting angle")
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theta0_words.next_to(theta0, UL)
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theta0_words.shift(UP + 0.5 * RIGHT)
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arrow = Arrow(
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theta0_words.get_bottom(),
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theta0,
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color=WHITE,
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tip_length=0.25,
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)
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bubble = SpeechBubble()
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bubble.pin_to(you)
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bubble.write("Lies!")
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bubble.content.scale(2)
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bubble.resize_to_content()
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self.add(period_eq)
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you.change("pondering", period_eq)
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self.wait()
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theta_eq.remove(*theta_eq.sqrt_part)
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self.play(
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TransformFromCopy(
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period_eq.sqrt_part,
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theta_eq.sqrt_part,
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),
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FadeIn(theta_eq)
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)
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theta_eq.add(*theta_eq.sqrt_part)
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self.play(
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FadeInFrom(theta0_words, LEFT),
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GrowArrow(arrow),
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)
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self.wait()
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self.play(you.change, "confused")
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self.wait(0)
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self.play(
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you.change, "angry",
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ShowCreation(bubble),
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FadeInFromPoint(bubble.content, you.mouth),
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equations.to_edge, LEFT,
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FadeOut(arrow),
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FadeOut(theta0_words),
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)
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self.wait()
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def create_pi_creature(self):
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return You().flip().to_corner(DR)
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class NewSceneName(Scene):
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def construct(self):
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pass
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16
active_projects/ode/part1/shared_constructs.py
Normal file
16
active_projects/ode/part1/shared_constructs.py
Normal file
@ -0,0 +1,16 @@
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from big_ol_pile_of_manim_imports import *
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Lg_formula_config = {
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"tex_to_color_map": {
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"\\theta_0": WHITE,
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"{L}": BLUE,
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"{g}": YELLOW,
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},
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}
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class You(PiCreature):
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CONFIG = {
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"color": BLUE_C,
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}
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@ -1,4 +1,5 @@
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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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def pendulum_vector_field(point, mu=0.1, g=9.8, L=3):
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@ -44,83 +45,177 @@ class VectorFieldTest(Scene):
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self.wait(10)
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class FormulasAreLies(PiCreatureScene):
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class SmallAngleApproximationTex(Scene):
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def construct(self):
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morty = self.pi_creature
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t2c = {
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"{L}": BLUE,
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"{g}": YELLOW,
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"\\theta_0": WHITE,
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"\\sqrt{\\,": WHITE,
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approx = TexMobject(
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"\\sin", "(", "\\theta", ") \\approx \\theta",
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tex_to_color_map={"\\theta": RED},
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arg_separator="",
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)
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implies = TexMobject("\\Downarrow")
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period = TexMobject(
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"\\text{Period}", "\\approx",
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"2\\pi \\sqrt{\\,{L} / {g}}",
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**Lg_formula_config,
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)
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group = VGroup(approx, implies, period)
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group.arrange(DOWN)
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approx_brace = Brace(approx, UP, buff=SMALL_BUFF)
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approx_words = TextMobject(
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"For small $\\theta$",
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tex_to_color_map={"$\\theta$": RED},
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)
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approx_words.scale(0.75)
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approx_words.next_to(approx_brace, UP, SMALL_BUFF)
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self.add(approx, approx_brace, approx_words)
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self.play(
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Write(implies),
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FadeInFrom(period, LEFT)
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)
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self.wait()
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class FollowThisThread(Scene):
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CONFIG = {
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"screen_rect_style": {
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"stroke_width": 2,
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"stroke_color": WHITE,
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"fill_opacity": 1,
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"fill_color": DARKER_GREY,
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}
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}
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kwargs = {"tex_to_color_map": t2c}
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period_eq = TexMobject(
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"\\text{Period} = 2\\pi \\sqrt{\\,{L} / {g}}",
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**kwargs
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)
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theta_eq = TexMobject(
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"\\theta(t) = \\theta_0 \\cos\\left("
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"\\sqrt{\\,{L} / {g}} \\cdot t"
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"\\right)",
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**kwargs
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)
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equations = VGroup(theta_eq, period_eq)
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equations.arrange(DOWN, buff=LARGE_BUFF)
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for eq in period_eq, theta_eq:
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i = eq.index_of_part_by_tex("\\sqrt")
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eq.sqrt_part = eq[i:i + 4]
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theta0 = theta_eq.get_part_by_tex("\\theta_0")
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theta0_words = TextMobject("Starting angle")
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theta0_words.next_to(theta0, UL)
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theta0_words.shift(UP + 0.5 * RIGHT)
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arrow = Arrow(
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theta0_words.get_bottom(),
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theta0,
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color=WHITE,
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tip_length=0.25,
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)
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bubble = SpeechBubble()
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bubble.pin_to(morty)
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bubble.write("Lies!")
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bubble.content.scale(2)
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bubble.resize_to_content()
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self.add(period_eq)
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morty.change("pondering", period_eq)
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self.wait()
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theta_eq.remove(*theta_eq.sqrt_part)
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self.play(
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TransformFromCopy(
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period_eq.sqrt_part,
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theta_eq.sqrt_part,
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),
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FadeIn(theta_eq)
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)
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theta_eq.add(*theta_eq.sqrt_part)
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self.play(
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FadeInFrom(theta0_words, LEFT),
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GrowArrow(arrow),
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)
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self.wait()
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self.play(morty.change, "confused")
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self.wait(0)
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self.play(
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morty.change, "angry",
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ShowCreation(bubble),
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FadeInFromPoint(bubble.content, morty.mouth),
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equations.to_edge, LEFT,
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FadeOut(arrow),
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FadeOut(theta0_words),
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)
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self.wait()
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def create_pi_creature(self):
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return Mortimer().to_corner(DR)
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class NewSceneName(Scene):
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def construct(self):
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pass
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self.show_thumbnails()
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self.show_words()
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def show_thumbnails(self):
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# TODO, replace each of these with a picture?
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thumbnails = self.thumbnails = VGroup(
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ScreenRectangle(**self.screen_rect_style),
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ScreenRectangle(**self.screen_rect_style),
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ScreenRectangle(**self.screen_rect_style),
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ScreenRectangle(**self.screen_rect_style),
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ScreenRectangle(**self.screen_rect_style),
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)
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n = len(thumbnails)
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thumbnails.set_height(1.5)
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line = self.line = CubicBezier([
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[-5, 3, 0],
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[3, 3, 0],
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[-3, -3, 0],
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[5, -3, 0],
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])
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for thumbnail, a in zip(thumbnails, np.linspace(0, 1, n)):
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thumbnail.move_to(line.point_from_proportion(a))
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self.play(
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ShowCreation(
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line,
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rate_func=lambda t: np.clip(t * (n + 1) / n, 0, 1)
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),
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LaggedStart(*[
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GrowFromCenter(
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thumbnail,
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rate_func=squish_rate_func(
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smooth,
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0, 0.7,
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)
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)
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for thumbnail in thumbnails
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], lag_ratio=1),
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run_time=5
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)
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def show_words(self):
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words = VGroup(
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TextMobject("Generalize"),
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TextMobject("Put in context"),
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TextMobject("Modify"),
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)
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# words.arrange(DOWN, aligned_edge=LEFT, buff=LARGE_BUFF)
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words.scale(1.5)
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words.to_corner(UR)
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words.add_to_back(VectorizedPoint(words.get_center()))
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words.add(VectorizedPoint(words.get_center()))
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diffEq = TextMobject("Differential\\\\equations")
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diffEq.scale(1.5)
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diffEq.to_corner(DL, buff=LARGE_BUFF)
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for word1, word2 in zip(words, words[1:]):
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self.play(
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FadeInFromDown(word2),
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FadeOutAndShift(word1, UP),
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)
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self.wait()
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self.play(
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ReplacementTransform(
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VGroup(self.thumbnails).copy().fade(1),
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diffEq,
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lag_ratio=0.01,
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)
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)
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self.wait()
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class StrogatzQuote(Scene):
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def construct(self):
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law_words = "laws of physics"
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language_words = "language of differential equations"
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author = "-Steven Strogatz"
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quote = TextMobject(
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"""
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\\Large
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``Since Newton, mankind has come to realize
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that the laws of physics are always expressed
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in the language of differential equations.''\\\\
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""" + author,
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alignment="",
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arg_separator=" ",
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substrings_to_isolate=[law_words, language_words, author]
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)
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law_part = quote.get_part_by_tex(law_words)
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language_part = quote.get_part_by_tex(language_words)
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author_part = quote.get_part_by_tex(author)
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quote.set_width(12)
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quote.to_edge(UP)
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quote[-2].shift(SMALL_BUFF * LEFT)
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author_part.shift(RIGHT + 0.5 * DOWN)
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author_part.scale(1.2, about_edge=UL)
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movers = VGroup(*quote[:-1].family_members_with_points())
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for mover in movers:
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mover.save_state()
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disc = Circle(radius=0.05)
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disc.set_stroke(width=0)
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disc.set_fill(BLACK, 0)
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disc.move_to(mover)
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mover.become(disc)
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self.play(
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FadeInFrom(author_part, LEFT),
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LaggedStartMap(
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# FadeInFromLarge,
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# quote[:-1].family_members_with_points(),
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Restore, movers,
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lag_ratio=0.005,
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run_time=2,
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)
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# FadeInFromDown(quote[:-1]),
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# lag_ratio=0.01,
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)
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self.wait()
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self.play(
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Write(law_part.copy().set_color(YELLOW)),
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run_time=1,
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)
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self.wait()
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self.play(
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Write(language_part.copy().set_color(BLUE)),
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run_time=1.5,
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)
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self.wait(2)
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