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https://github.com/3b1b/manim.git
synced 2025-08-02 19:46:21 +08:00
Up to AskAboutEllipses in lost_lecture project
This commit is contained in:
Grant Sanderson
@ -13,6 +13,8 @@ class Orbiting(ContinualAnimation):
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self.ellipse = ellipse
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# Proportion of the way around the ellipse
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self.proportion = 0
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planet.move_to(ellipse.point_from_proportion(0))
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ContinualAnimation.__init__(self, planet, **kwargs)
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def update_mobject(self, dt):
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@ -30,6 +32,32 @@ class Orbiting(ContinualAnimation):
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self.proportion = self.proportion % 1
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planet.move_to(ellipse.point_from_proportion(self.proportion))
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class SunAnimation(ContinualAnimation):
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CONFIG = {
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"rate": 0.2,
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"angle": 60 * DEGREES,
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}
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def __init__(self, sun, **kwargs):
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self.sun = sun
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self.rotated_sun = sun.deepcopy()
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self.rotated_sun.rotate(60 * DEGREES)
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ContinualAnimation.__init__(
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self, Group(sun, self.rotated_sun), **kwargs
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)
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def update_mobject(self, dt):
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time = self.internal_time
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a = (np.sin(self.rate * time * TAU) + 1) / 2.0
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self.rotated_sun.rotate(-self.angle)
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self.rotated_sun.move_to(self.sun)
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self.rotated_sun.rotate(self.angle)
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self.rotated_sun.pixel_array = np.array(
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a * self.sun.pixel_array,
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dtype=self.sun.pixel_array.dtype
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)
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# Animations
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@ -37,7 +65,7 @@ class ShowEmergingEllipse(Scene):
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CONFIG = {
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"circle_radius": 3,
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"circle_color": BLUE,
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"num_lines": 100,
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"num_lines": 150,
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"lines_stroke_width": 1,
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"eccentricity_vector": 2 * RIGHT,
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"ghost_lines_stroke_color": LIGHT_GREY,
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@ -128,7 +156,7 @@ class ShowEmergingEllipse(Scene):
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self.wait()
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self.play(
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ShowCreation(ellipse),
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Write(ellipse_words, run_time=1)
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FadeInFromDown(ellipse_words)
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)
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self.wait()
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@ -408,12 +436,361 @@ class FeynmanLecturesScreenCaptureFrame(Scene):
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class TheMotionOfPlanets(Scene):
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CONFIG = {
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"camera_config": {"background_opacity": 1},
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"random_seed": 2,
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}
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def construct(self):
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self.add_title()
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self.setup_orbits()
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def add_title(self):
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pass
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title = TextMobject("``The motion of planets around the sun''")
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title.set_color(YELLOW)
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title.to_edge(UP)
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title.add_to_back(title.copy().set_stroke(BLACK, 5))
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self.add(title)
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self.title = title
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def setup_orbits(self):
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pass
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sun = ImageMobject("sun")
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sun.scale_to_fit_height(0.7)
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planets, ellipses, orbits = self.get_planets_ellipses_and_orbits(sun)
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archivist_words = TextMobject(
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"Judith Goodstein (Caltech archivist)"
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)
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archivist_words.to_corner(UL)
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archivist_words.shift(1.5 * DOWN)
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archivist_words.add_background_rectangle()
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alt_name = TextMobject("David Goodstein (Caltech physicist)")
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alt_name.next_to(archivist_words, DOWN, aligned_edge=LEFT)
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alt_name.add_background_rectangle()
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book = ImageMobject("Lost_Lecture_cover")
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book.scale_to_fit_height(4)
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book.next_to(alt_name, DOWN)
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self.add(SunAnimation(sun))
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self.add(ellipses, planets)
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self.add(self.title)
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self.add(*orbits)
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self.add_foreground_mobjects(planets)
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self.wait(10)
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self.play(
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VGroup(ellipses, sun).shift, 3 * RIGHT,
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FadeInFromDown(archivist_words),
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Animation(self.title)
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)
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self.add_foreground_mobjects(archivist_words)
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self.wait(3)
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self.play(FadeInFromDown(alt_name))
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self.add_foreground_mobjects(alt_name)
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self.wait()
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self.play(FadeInFromDown(book))
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self.wait(15)
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def get_planets_ellipses_and_orbits(self, sun):
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planets = VGroup(
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ImageMobject("mercury"),
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ImageMobject("venus"),
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ImageMobject("earth"),
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ImageMobject("mars"),
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ImageMobject("comet")
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)
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sizes = [0.383, 0.95, 1.0, 0.532, 0.3]
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orbit_radii = [0.254, 0.475, 0.656, 1.0, 3.0]
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orbit_eccentricies = [0.206, 0.006, 0.0167, 0.0934, 0.967]
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for planet, size in zip(planets, sizes):
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planet.scale_to_fit_height(0.5)
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planet.scale(size)
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ellipses = VGroup(*[
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Circle(radius=r, color=WHITE, stroke_width=1)
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for r in orbit_radii
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])
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for circle, ec in zip(ellipses, orbit_eccentricies):
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a = circle.get_height() / 2
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c = ec * a
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b = np.sqrt(a**2 - c**2)
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circle.stretch(b / a, 1)
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c = np.sqrt(a**2 - b**2)
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circle.shift(c * RIGHT)
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for circle in ellipses:
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circle.rotate(
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TAU * np.random.random(),
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about_point=ORIGIN
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)
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ellipses.scale(3.5, about_point=ORIGIN)
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orbits = [
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Orbiting(
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planet, sun, circle,
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rate=0.25 * r**(2 / 3)
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)
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for planet, circle, r in zip(planets, ellipses, orbit_radii)
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]
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orbits[-1].proportion = 0.15
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orbits[-1].rate = 0.5
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return planets, ellipses, orbits
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class AskAboutEllipses(TheMotionOfPlanets):
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CONFIG = {
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"camera_config": {"background_opacity": 1},
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"animate_sun": True,
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}
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def construct(self):
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self.add_title()
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self.add_sun()
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self.add_orbit()
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self.add_focus_lines()
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self.add_force_labels()
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self.comment_on_imperfections()
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self.set_up_differential_equations()
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def add_title(self):
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title = Title("Why are orbits ellipses?")
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self.add(title)
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self.title = title
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def add_sun(self):
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sun = ImageMobject("sun", height=0.5)
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self.sun = sun
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self.add(sun)
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if self.animate_sun:
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self.add(SunAnimation(sun))
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def add_orbit(self):
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sun = self.sun
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comet = ImageMobject("comet")
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comet.scale_to_fit_height(0.2)
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ellipse = self.get_ellipse()
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orbit = Orbiting(comet, sun, ellipse)
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self.add(ellipse)
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self.add(orbit)
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self.ellipse = ellipse
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self.comet = comet
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self.orbit = orbit
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def add_focus_lines(self):
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f1, f2 = self.focus_points
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comet = self.comet
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lines = VGroup(Line(LEFT, RIGHT), Line(LEFT, RIGHT))
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lines.set_stroke(LIGHT_GREY, 1)
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def update_lines(lines):
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l1, l2 = lines
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P = comet.get_center()
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l1.put_start_and_end_on(f1, P)
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l2.put_start_and_end_on(f2, P)
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return lines
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animation = ContinualUpdateFromFunc(
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lines, update_lines
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)
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self.add(animation)
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self.wait(8)
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self.focus_lines = lines
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self.focus_lines_animation = animation
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def add_force_labels(self):
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radial_line = self.focus_lines[0]
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# Radial line measurement
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radius_measurement_kwargs = {
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"num_decimal_places": 3,
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"color": BLUE,
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}
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radius_measurement = DecimalNumber(1, **radius_measurement_kwargs)
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def update_radial_measurement(measurement):
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angle = -radial_line.get_angle() + np.pi
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radial_line.rotate(angle, about_point=ORIGIN)
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new_decimal = DecimalNumber(
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radial_line.get_length(),
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**radius_measurement_kwargs
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)
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max_width = 0.6 * radial_line.get_width()
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if new_decimal.get_width() > max_width:
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new_decimal.scale_to_fit_width(max_width)
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new_decimal.next_to(radial_line, UP, SMALL_BUFF)
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VGroup(new_decimal, radial_line).rotate(
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-angle, about_point=ORIGIN
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)
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Transform(measurement, new_decimal).update(1)
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radius_measurement_animation = ContinualUpdateFromFunc(
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radius_measurement, update_radial_measurement
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)
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# Force equation
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force_equation = TexMobject(
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"F = {GMm \\over (0.000)^2}",
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tex_to_color_map={
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"F": YELLOW,
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"0.000": BLACK,
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}
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)
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force_equation.next_to(self.title, DOWN)
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force_equation.to_edge(RIGHT)
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radius_in_denominator_ref = force_equation.get_part_by_tex("0.000")
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radius_in_denominator = DecimalNumber(
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0, **radius_measurement_kwargs
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)
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radius_in_denominator.scale(0.95)
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update_radius_in_denominator = ContinualChangingDecimal(
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radius_in_denominator,
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lambda a: radial_line.get_length(),
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position_update_func=lambda mob: mob.move_to(
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radius_in_denominator_ref,
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)
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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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)
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inverse_square_law_words = TextMobject(
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"``Inverse square law''"
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)
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inverse_square_law_words.next_to(force_equation, DOWN, MED_LARGE_BUFF)
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inverse_square_law_words.to_edge(RIGHT)
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force_equation.next_to(inverse_square_law_words, UP, MED_LARGE_BUFF)
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def v_fade_in(mobject):
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return UpdateFromAlphaFunc(
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mobject,
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lambda mob, alpha: mob.set_fill(opacity=alpha)
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)
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self.add(update_radius_in_denominator)
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self.add(radius_measurement_animation)
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self.play(
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FadeIn(force_equation),
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v_fade_in(radius_in_denominator),
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v_fade_in(radius_measurement)
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)
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self.add(force_arrow_animation)
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self.play(v_fade_in(force_arrow))
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self.wait(8)
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self.play(Write(inverse_square_law_words))
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self.wait(9)
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self.force_equation = force_equation
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self.inverse_square_law_words = inverse_square_law_words
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self.force_arrow = force_arrow
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self.radius_measurement = radius_measurement
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def comment_on_imperfections(self):
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planets, ellipses, orbits = self.get_planets_ellipses_and_orbits(self.sun)
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orbits.pop(-1)
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ellipses.submobjects.pop(-1)
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planets.submobjects.pop(-1)
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scale_factor = 20
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center = self.sun.get_center()
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ellipses.save_state()
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ellipses.scale(scale_factor, about_point=center)
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self.add(*orbits)
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self.play(ellipses.restore, Animation(planets))
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self.wait(7)
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self.play(
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ellipses.scale, scale_factor, {"about_point": center},
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Animation(planets)
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)
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self.remove(*orbits)
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self.remove(planets, ellipses)
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self.wait(2)
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def set_up_differential_equations(self):
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d_dt = TexMobject("{d \\over dt}")
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in_vect = Matrix(np.array([
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"x(t)",
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"y(t)",
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"\\dot{x}(t)",
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"\\dot{y}(t)",
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]))
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equals = TexMobject("=")
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out_vect = Matrix(np.array([
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"\\dot{x}(t)",
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"\\dot{y}(t)",
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"-x(t) / (x(t)^2 + y(t)^2)^{3/2}",
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"-y(t) / (x(t)^2 + y(t)^2)^{3/2}",
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]), element_alignment_corner=ORIGIN)
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equation = VGroup(d_dt, in_vect, equals, out_vect)
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equation.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
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equation.scale_to_fit_width(6)
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equation.to_corner(DR, buff=MED_LARGE_BUFF)
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cross = Cross(equation)
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self.play(Write(equation))
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self.wait(6)
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self.play(ShowCreation(cross))
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self.wait(6)
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# Helpers
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def get_ellipse(self):
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a = 7.0
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b = 4.0
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c = np.sqrt(a**2 - b**2)
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ellipse = Circle(radius=a / 2)
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ellipse.set_stroke(WHITE, 1)
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ellipse.stretch(b / a, dim=1)
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ellipse.move_to(
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self.sun.get_center() + c * LEFT / 2
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)
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self.focus_points = [
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self.sun.get_center(),
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self.sun.get_center() + c * LEFT,
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]
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return ellipse
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class FeynmanElementaryQuote(Scene):
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def construct(self):
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quote = TextMobject(
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"""
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I am going to give what I will call an
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\\emph{elementary} demonstration. But elementary
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does not mean easy to understand. Elementary
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means that [nothing] very little is requried
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to know ahead of time in order to understand it,
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except to have an infinite amount of intelligence.
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""",
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tex_to_color_map={
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"\\emph{elementary}": BLUE,
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"elementary": BLUE,
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"Elementary": BLUE,
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}
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)
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self.add(quote)
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Reference in New Issue
Block a user