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Scenes up to IntroduceShapeOfVelocities
This commit is contained in:
Grant Sanderson
parent
f4022d6c75
commit
a443ddc8f2
1 changed files with 314 additions and 18 deletions
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@ -706,23 +706,8 @@ class AskAboutEllipses(TheMotionOfPlanets):
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)
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# Force arrow
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force_arrow = Arrow(LEFT, RIGHT, color=YELLOW)
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def update_force_arrow(arrow):
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radius = radial_line.get_length()
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# target_length = 1 / radius**2
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target_length = 1 / radius # Lies!
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arrow.scale(
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target_length / arrow.get_length()
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)
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arrow.rotate(
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np.pi + radial_line.get_angle() - arrow.get_angle()
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)
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arrow.shift(
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radial_line.get_end() - arrow.get_start()
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)
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force_arrow_animation = ContinualUpdateFromFunc(
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force_arrow, update_force_arrow
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force_arrow, force_arrow_animation = self.get_force_arrow_and_update(
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self.comet
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)
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inverse_square_law_words = TextMobject(
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@ -831,6 +816,43 @@ class AskAboutEllipses(TheMotionOfPlanets):
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]
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return ellipse
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def get_force_arrow_and_update(self, comet, scale_factor=1):
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force_arrow = Arrow(LEFT, RIGHT, color=YELLOW)
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sun = self.sun
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def update_force_arrow(arrow):
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radial_line = Line(
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sun.get_center(), comet.get_center()
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)
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radius = radial_line.get_length()
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# target_length = 1 / radius**2
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target_length = scale_factor / radius # Lies!
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arrow.scale(
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target_length / arrow.get_length()
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)
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arrow.rotate(
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np.pi + radial_line.get_angle() - arrow.get_angle()
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)
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arrow.shift(
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radial_line.get_end() - arrow.get_start()
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)
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force_arrow_animation = ContinualUpdateFromFunc(
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force_arrow, update_force_arrow
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)
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return force_arrow, force_arrow_animation
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def get_radial_line_and_update(self, comet):
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line = Line(LEFT, RIGHT)
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line.set_stroke(LIGHT_GREY, 1)
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line_update = ContinualUpdateFromFunc(
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line, lambda l: l.put_start_and_end_on(
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self.sun.get_center(),
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comet.get_center(),
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)
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)
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return line, line_update
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class FeynmanElementaryQuote(Scene):
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def construct(self):
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@ -928,6 +950,47 @@ class AskAboutInfiniteIntelligence(TeacherStudentsScene):
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self.wait(5)
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class TableOfContents(Scene):
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def construct(self):
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items = VGroup(
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TextMobject("How the ellipse will arise"),
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TextMobject("Kepler's 2nd law"),
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TextMobject("The shape of velocities"),
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)
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items.arrange_submobjects(
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DOWN, buff=LARGE_BUFF, aligned_edge=LEFT
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)
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items.to_edge(LEFT, buff=1.5)
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for item in items:
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item.add(Dot().next_to(item, LEFT))
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item.generate_target()
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item.target.set_fill(GREY, opacity=0.5)
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title = Title("The plan")
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scale_factor = 1.2
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self.add(title)
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self.play(LaggedStart(
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FadeIn, items,
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run_time=1,
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lag_ratio=0.7,
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))
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self.wait()
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for item in items:
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other_items = VGroup(*filter(
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lambda m: m is not item,
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items
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))
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new_item = item.copy()
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new_item.scale(scale_factor, about_edge=LEFT)
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new_item.set_fill(WHITE, 1)
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self.play(
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Transform(item, new_item),
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*map(MoveToTarget, other_items)
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)
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self.wait()
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class ShowEllipseDefiningProperty(Scene):
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CONFIG = {
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"camera_config": {"background_opacity": 1},
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@ -2414,5 +2477,238 @@ class HistoryOfAngularMomentum(TeacherStudentsScene):
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class FeynmanRecountingNewton(Scene):
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CONFIG = {
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"camera_config": {"background_opacity": 1},
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}
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def construct(self):
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pass
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feynman_teaching = ImageMobject("Feynman_teaching")
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feynman_teaching.scale_to_fit_width(FRAME_WIDTH)
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newton = ImageMobject("Newton")
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principia = ImageMobject("Principia_equal_area")
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images = [newton, principia]
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for image in images:
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image.scale_to_fit_height(5)
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newton.to_corner(UL)
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principia.next_to(newton, RIGHT)
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for image in images:
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image.rect = SurroundingRectangle(
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image, color=WHITE, buff=0,
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)
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self.play(FadeInFromDown(feynman_teaching, run_time=2))
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self.wait()
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self.play(
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FadeInFromDown(newton),
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FadeInFromDown(newton.rect),
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)
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self.wait()
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self.play(*[
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FadeInAndShiftFromDirection(
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mob, direction=3 * LEFT
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)
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for mob in principia, principia.rect
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])
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self.wait()
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class IntroduceShapeOfVelocities(AskAboutEllipses, MovingCameraScene):
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CONFIG = {
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"animate_sun": False,
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"sun_center": 2 * RIGHT,
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"a": 4.0,
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"b": 3.5,
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"num_vectors": 25,
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}
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def construct(self):
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self.setup_orbit()
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self.warp_orbit()
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self.reference_inverse_square_law()
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self.show_velocity_vectors()
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self.collect_velocity_vectors()
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def setup_orbit(self):
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self.add_sun()
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self.add_orbit()
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self.add_foreground_mobjects(self.comet)
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def warp_orbit(self):
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def func(z, c=6):
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return 1 * (np.exp((1.0 / c) * (z) + 1) - np.exp(1))
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ellipse = self.ellipse
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ellipse.save_state()
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ellipse.generate_target()
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ellipse.target.apply_complex_function(func)
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ellipse.target.replace(ellipse, dim_to_match=0)
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self.wait(5)
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self.play(MoveToTarget(ellipse, run_time=2))
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self.wait(5)
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def reference_inverse_square_law(self):
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ellipse = self.ellipse
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force_equation = TexMobject(
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"F", "=", "{G", "M", "m", "\\over", "R^2}"
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)
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force_equation.move_to(ellipse)
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force_equation.set_color_by_tex("F", YELLOW)
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force_arrow, force_arrow_update = self.get_force_arrow_and_update(
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self.comet, scale_factor=3,
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)
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radial_line, radial_line_update = self.get_radial_line_and_update(
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self.comet
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)
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self.add(radial_line_update)
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self.add(force_arrow_update)
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self.play(
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Restore(ellipse),
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Write(force_equation),
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UpdateFromAlphaFunc(
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force_arrow,
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lambda m, a: m.set_fill(opacity=a)
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),
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UpdateFromAlphaFunc(
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radial_line,
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lambda m, a: m.set_stroke(width=a)
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),
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)
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self.wait(10)
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def show_velocity_vectors(self):
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alphas = np.linspace(0, 1, self.num_vectors, endpoint=False)
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vectors = VGroup(*[
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self.get_velocity_vector(alpha)
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for alpha in alphas
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])
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moving_vector = self.get_velocity_vector(0)
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def update_moving_vector(vector):
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new_vector = self.get_velocity_vector(
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self.orbit.proportion,
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# scalar=4.0,
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)
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Transform(vector, new_vector).update(1)
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moving_vector_animation = ContinualUpdateFromFunc(
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moving_vector, update_moving_vector
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)
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self.play(LaggedStart(
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ShowCreation, vectors,
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lag_ratio=0.2,
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run_time=3,
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))
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self.wait(5)
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self.add(moving_vector_animation)
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self.play(
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FadeOut(vectors),
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VFadeIn(moving_vector)
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)
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self.wait(10)
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vectors.set_fill(opacity=0.5)
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self.play(
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LaggedStart(ShowCreation, vectors),
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Animation(moving_vector)
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)
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self.wait(5)
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self.velocity_vectors = vectors
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self.moving_vector = moving_vector
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def collect_velocity_vectors(self):
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vectors = self.velocity_vectors.copy()
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frame = self.camera_frame
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ellipse = self.ellipse
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frame_shift = 2.5 * LEFT
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root_point = ellipse.get_left() + 3 * LEFT + 1 * UP
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vector_targets = VGroup()
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for vector in vectors:
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vector.target = Arrow(
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root_point,
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root_point + vector.get_vector(),
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buff=0,
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rectangular_stem_width=0.025,
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tip_length=0.2,
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color=vector.get_color(),
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)
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vector.target.add_to_back(
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vector.target.copy().set_stroke(BLACK, 5)
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)
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vector_targets.add(vector.target)
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circle = Circle(color=YELLOW)
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circle.replace(vector_targets)
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velocity_space = TextMobject("Velocity space")
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velocity_space.next_to(circle, UP)
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rect = SurroundingRectangle(
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VGroup(circle, velocity_space),
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buff=MED_LARGE_BUFF,
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color=WHITE,
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)
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self.play(
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ApplyMethod(
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frame.shift, frame_shift,
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run_time=2,
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),
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LaggedStart(
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MoveToTarget, vectors,
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run_time=4,
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),
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FadeInFromDown(velocity_space),
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FadeInFromDown(rect),
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)
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self.wait(2)
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self.play(
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ShowCreation(circle),
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Animation(vectors)
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)
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self.wait(24)
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# Helpers
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def get_velocity_vector(self, alpha, d_alpha=0.01, scalar=3.0):
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norm = np.linalg.norm
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ellipse = self.ellipse
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sun_center = self.sun.get_center()
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min_length = 0.1 * scalar
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max_length = 0.5 * scalar
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p1, p2 = [
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ellipse.point_from_proportion(a)
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for a in alpha, alpha + d_alpha
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]
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vector = Arrow(
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p1, p2, buff=0
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)
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radius_vector = p1 - sun_center
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curr_v_perp = norm(np.cross(
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vector.get_vector(),
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radius_vector / norm(radius_vector)
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))
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vector.scale(
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scalar / (norm(curr_v_perp) * norm(radius_vector)),
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about_point=vector.get_start()
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)
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vector.set_color(
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interpolate_color(
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BLUE, RED, inverse_interpolate(
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min_length, max_length,
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vector.get_length()
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)
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)
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)
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vector.add_to_back(
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vector.copy().set_stroke(BLACK, 5)
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)
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return vector
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