manim/active_projects/lost_lecture.py

from __future__ import absolute_import
from big_ol_pile_of_manim_imports import *


class Orbiting(ContinualAnimation):
    CONFIG = {
        "rate": 0.3,
    }

    def __init__(self, planet, star, ellipse, **kwargs):
        self.planet = planet
        self.star = star
        self.ellipse = ellipse
        # Proportion of the way around the ellipse
        self.proportion = 0
        planet.move_to(ellipse.point_from_proportion(0))

        ContinualAnimation.__init__(self, planet, **kwargs)

    def update_mobject(self, dt):
        # time = self.internal_time
        rate = self.rate

        planet = self.planet
        star = self.star
        ellipse = self.ellipse

        rate *= 1 / np.linalg.norm(
            planet.get_center() - star.get_center()
        )
        self.proportion += rate * dt
        self.proportion = self.proportion % 1
        planet.move_to(ellipse.point_from_proportion(self.proportion))


class SunAnimation(ContinualAnimation):
    CONFIG = {
        "rate": 0.2,
        "angle": 60 * DEGREES,
    }

    def __init__(self, sun, **kwargs):
        self.sun = sun
        self.rotated_sun = sun.deepcopy()
        self.rotated_sun.rotate(60 * DEGREES)
        ContinualAnimation.__init__(
            self, Group(sun, self.rotated_sun), **kwargs
        )

    def update_mobject(self, dt):
        time = self.internal_time
        a = (np.sin(self.rate * time * TAU) + 1) / 2.0
        self.rotated_sun.rotate(-self.angle)
        self.rotated_sun.move_to(self.sun)
        self.rotated_sun.rotate(self.angle)
        self.rotated_sun.pixel_array = np.array(
            a * self.sun.pixel_array,
            dtype=self.sun.pixel_array.dtype
        )


class ShowWord(Animation):
    CONFIG = {
        "time_per_char": 0.06,
        "rate_func": None,
    }

    def __init__(self, word, **kwargs):
        assert(isinstance(word, SingleStringTexMobject))
        digest_config(self, kwargs)
        run_time = kwargs.pop(
            "run_time",
            self.time_per_char * len(word)
        )
        self.stroke_width = word.get_stroke_width()
        Animation.__init__(self, word, run_time=run_time, **kwargs)

    def update_mobject(self, alpha):
        word = self.mobject
        stroke_width = self.stroke_width
        count = int(alpha * len(word))
        remainder = (alpha * len(word)) % 1
        word[:count].set_fill(opacity=1)
        word[:count].set_stroke(width=stroke_width)
        if count < len(word):
            word[count].set_fill(opacity=remainder)
            word[count].set_stroke(width=remainder * stroke_width)
            word[count + 1:].set_fill(opacity=0)
            word[count + 1:].set_stroke(width=0)

# Animations


class ShowEmergingEllipse(Scene):
    CONFIG = {
        "circle_radius": 3,
        "circle_color": BLUE,
        "num_lines": 150,
        "lines_stroke_width": 1,
        "eccentricity_vector": 2 * RIGHT,
        "ghost_lines_stroke_color": LIGHT_GREY,
        "ghost_lines_stroke_width": 0.5,
        "ellipse_color": PINK,
    }

    def construct(self):
        circle = self.get_circle()
        e_point = self.get_eccentricity_point()
        e_dot = Dot(e_point, color=YELLOW)
        lines = self.get_lines()
        ellipse = self.get_ellipse()

        fade_rect = FullScreenFadeRectangle()

        line = lines[len(lines) / 5]
        line_dot = Dot(line.get_center(), color=YELLOW)
        line_dot.scale(0.5)

        ghost_line = self.get_ghost_lines(line)
        ghost_lines = self.get_ghost_lines(lines)

        rot_words = TextMobject("Rotate $90^\\circ$ \\\\ about center")
        rot_words.next_to(line_dot, RIGHT)

        elbow = VGroup(Line(UP, UL), Line(UL, LEFT))
        elbow.set_stroke(width=1)
        elbow.scale(0.2, about_point=ORIGIN)
        elbow.rotate(
            line.get_angle() - 90 * DEGREES,
            about_point=ORIGIN
        )
        elbow.shift(line.get_center())

        eccentric_words = TextMobject("``Eccentric'' point")
        eccentric_words.next_to(circle.get_center(), DOWN)

        ellipse_words = TextMobject("Perfect ellipse")
        ellipse_words.next_to(ellipse, UP, SMALL_BUFF)

        for text in rot_words, ellipse_words:
            text.add_to_back(text.copy().set_stroke(BLACK, 5))

        shuffled_lines = VGroup(*lines)
        random.shuffle(shuffled_lines.submobjects)

        self.play(ShowCreation(circle))
        self.play(
            FadeInAndShiftFromDirection(e_dot, LEFT),
            Write(eccentric_words, run_time=1)
        )
        self.wait()
        self.play(
            LaggedStart(ShowCreation, shuffled_lines),
            Animation(VGroup(e_dot, circle)),
            FadeOut(eccentric_words)
        )
        self.add(ghost_lines)
        self.add(e_dot, circle)
        self.wait()
        self.play(
            FadeIn(fade_rect),
            Animation(line),
            GrowFromCenter(line_dot),
            FadeInFromDown(rot_words),
        )
        self.wait()
        self.add(ghost_line)
        self.play(
            MoveToTarget(line, path_arc=90 * DEGREES),
            Animation(rot_words),
            ShowCreation(elbow)
        )
        self.wait()
        self.play(
            FadeOut(fade_rect),
            FadeOut(line_dot),
            FadeOut(rot_words),
            FadeOut(elbow),
            Animation(line),
            Animation(ghost_line)
        )
        self.play(
            LaggedStart(MoveToTarget, lines, run_time=4),
            Animation(VGroup(e_dot, circle))
        )
        self.wait()
        self.play(
            ShowCreation(ellipse),
            FadeInFromDown(ellipse_words)
        )
        self.wait()

    def get_circle(self):
        circle = self.circle = Circle(
            radius=self.circle_radius,
            color=self.circle_color
        )
        return circle

    def get_eccentricity_point(self):
        return self.circle.get_center() + self.eccentricity_vector

    def get_lines(self):
        center = self.circle.get_center()
        radius = self.circle.get_width() / 2
        e_point = self.get_eccentricity_point()
        lines = VGroup(*[
            Line(
                e_point,
                center + rotate_vector(radius * RIGHT, angle)
            )
            for angle in np.linspace(0, TAU, self.num_lines)
        ])
        lines.set_stroke(width=self.lines_stroke_width)
        for line in lines:
            line.generate_target()
            line.target.rotate(90 * DEGREES)
        return lines

    def get_ghost_lines(self, lines):
        return lines.copy().set_stroke(
            color=self.ghost_lines_stroke_color,
            width=self.ghost_lines_stroke_width
        )

    def get_ellipse(self):
        center = self.circle.get_center()
        e_point = self.get_eccentricity_point()
        radius = self.circle.get_width() / 2

        # Ellipse parameters
        a = radius / 2
        c = np.linalg.norm(e_point - center) / 2
        b = np.sqrt(a**2 - c**2)

        result = Circle(radius=b, color=self.ellipse_color)
        result.stretch(a / b, 0)
        result.move_to(Line(center, e_point))
        return result


class FeynmanAndOrbitingPlannetOnEllipseDiagram(ShowEmergingEllipse):
    def construct(self):
        circle = self.get_circle()
        lines = self.get_lines()
        ghost_lines = self.get_ghost_lines(lines)
        for line in lines:
            MoveToTarget(line).update(1)
        ellipse = self.get_ellipse()
        e_dot = Dot(self.get_eccentricity_point())
        e_dot.set_color(YELLOW)

        comet = ImageMobject("earth")
        comet.scale_to_fit_width(0.3)

        feynman = ImageMobject("Feynman")
        feynman.scale_to_fit_height(6)
        feynman.next_to(ORIGIN, LEFT)
        feynman.to_edge(UP)
        feynman_name = TextMobject("Richard Feynman")
        feynman_name.next_to(feynman, DOWN)
        feynman.save_state()
        feynman.shift(2 * DOWN)
        feynman_rect = BackgroundRectangle(
            feynman, fill_opacity=1
        )

        group = VGroup(circle, ghost_lines, lines, e_dot, ellipse)

        self.add(group)
        self.add(Orbiting(comet, e_dot, ellipse))
        self.add_foreground_mobjects(comet)
        self.wait()
        self.play(
            feynman.restore,
            MaintainPositionRelativeTo(feynman_rect, feynman),
            VFadeOut(feynman_rect),
            group.to_edge, RIGHT,
        )
        self.play(Write(feynman_name))
        self.wait()
        self.wait(10)


class FeynmanFame(Scene):
    def construct(self):
        books = VGroup(
            ImageMobject("Feynman_QED_cover"),
            ImageMobject("Surely_Youre_Joking_cover"),
            ImageMobject("Feynman_Lectures_cover"),
        )
        for book in books:
            book.scale_to_fit_height(6)
            book.move_to(FRAME_WIDTH * LEFT / 4)

        feynman_diagram = self.get_feynman_diagram()
        feynman_diagram.next_to(ORIGIN, RIGHT)
        fd_parts = VGroup(*reversed(feynman_diagram.family_members_with_points()))

        # As a physicist
        self.play(self.get_book_intro(books[0]))
        self.play(LaggedStart(
            Write, feynman_diagram,
            run_time=4
        ))
        self.wait()
        self.play(
            self.get_book_intro(books[1]),
            self.get_book_outro(books[0]),
            LaggedStart(
                ApplyMethod, fd_parts,
                lambda m: (m.scale, 0),
                run_time=1
            ),
        )
        self.remove(feynman_diagram)
        self.wait()

        # As a public figure
        safe = SVGMobject(file_name="safe", height=2)
        safe_rect = SurroundingRectangle(safe, buff=0)
        safe_rect.set_stroke(width=0)
        safe_rect.set_fill(DARK_GREY, 1)
        safe.add_to_back(safe_rect)

        bongo = SVGMobject(file_name="bongo")
        bongo.scale_to_fit_height(1)
        bongo.set_color(WHITE)
        bongo.next_to(safe, RIGHT, LARGE_BUFF)

        objects = VGroup(safe, bongo)

        feynman_smile = ImageMobject("Feynman_Los_Alamos")
        feynman_smile.match_width(objects)
        feynman_smile.next_to(objects, DOWN)

        VGroup(objects, feynman_smile).next_to(ORIGIN, RIGHT)

        joke = TextMobject(
            "``Science is the belief \\\\ in the ignorance of \\\\ experts.''"
        )
        joke.move_to(objects)

        self.play(LaggedStart(
            DrawBorderThenFill, objects,
            lag_ratio=0.75
        ))
        self.play(self.get_book_intro(feynman_smile))
        self.wait()
        self.play(
            objects.shift, 2 * UP,
            VFadeOut(objects)
        )
        self.play(Write(joke))
        self.wait(2)

        self.play(
            self.get_book_intro(books[2]),
            self.get_book_outro(books[1]),
            LaggedStart(FadeOut, joke, run_time=1),
            ApplyMethod(
                feynman_smile.shift, FRAME_HEIGHT * DOWN,
                remover=True
            )
        )

        # As a teacher
        feynman_teacher = ImageMobject("Feynman_teaching")
        feynman_teacher.scale_to_fit_width(FRAME_WIDTH / 2 - 1)
        feynman_teacher.next_to(ORIGIN, RIGHT)

        self.play(self.get_book_intro(feynman_teacher))
        self.wait(3)

    def get_book_animation(self, book,
                           initial_shift,
                           animated_shift,
                           opacity_func
                           ):
        rect = BackgroundRectangle(book, fill_opacity=1)
        book.shift(initial_shift)

        return AnimationGroup(
            ApplyMethod(book.shift, animated_shift),
            UpdateFromAlphaFunc(
                rect, lambda r, a: r.move_to(book).set_fill(
                    opacity=opacity_func(a)
                ),
                remover=True
            )
        )

    def get_book_intro(self, book):
        return self.get_book_animation(
            book, 2 * DOWN, 2 * UP, lambda a: 1 - a
        )

    def get_book_outro(self, book):
        return ApplyMethod(book.shift, FRAME_HEIGHT * UP, remover=True)

    def get_feynman_diagram(self):
        x_min = -1.5
        x_max = 1.5
        arrow = Arrow(LEFT, RIGHT, buff=0, use_rectangular_stem=False)
        arrow.tip.move_to(arrow.get_center())
        arrows = VGroup(*[
            arrow.copy().rotate(angle).next_to(point, vect, buff=0)
            for (angle, point, vect) in [
                (-45 * DEGREES, x_min * RIGHT, UL),
                (-135 * DEGREES, x_min * RIGHT, DL),
                (-135 * DEGREES, x_max * RIGHT, UR),
                (-45 * DEGREES, x_max * RIGHT, DR),
            ]
        ])
        labels = VGroup(*[
            TexMobject(tex)
            for tex in ["e^-", "e^+", "\\text{\\=q}", "q"]
        ])
        vects = [UR, DR, UL, DL]
        for arrow, label, vect in zip(arrows, labels, vects):
            label.next_to(arrow.get_center(), vect, buff=SMALL_BUFF)

        wave = FunctionGraph(
            lambda x: 0.2 * np.sin(2 * TAU * x),
            x_min=x_min,
            x_max=x_max,
        )
        wave_label = TexMobject("\\gamma")
        wave_label.next_to(wave, UP, SMALL_BUFF)
        labels.add(wave_label)

        squiggle = ParametricFunction(
            lambda t: np.array([
                t + 0.5 * np.sin(TAU * t),
                0.5 * np.cos(TAU * t),
                0,
            ]),
            t_min=0,
            t_max=4,
        )
        squiggle.scale(0.25)
        squiggle.set_color(BLUE)
        squiggle.rotate(-30 * DEGREES)
        squiggle.next_to(
            arrows[2].point_from_proportion(0.75),
            DR, buff=0
        )
        squiggle_label = TexMobject("g")
        squiggle_label.next_to(squiggle, UR, buff=-MED_SMALL_BUFF)
        labels.add(squiggle_label)

        return VGroup(arrows, wave, squiggle, labels)


class FeynmanLecturesScreenCaptureFrame(Scene):
    def construct(self):
        url = TextMobject("http://www.feynmanlectures.caltech.edu/")
        url.to_edge(UP)

        screen_rect = ScreenRectangle(height=6)
        screen_rect.next_to(url, DOWN)

        self.add(url)
        self.play(ShowCreation(screen_rect))
        self.wait()


class TheMotionOfPlanets(Scene):
    CONFIG = {
        "camera_config": {"background_opacity": 1},
        "random_seed": 2,
    }

    def construct(self):
        self.add_title()
        self.setup_orbits()

    def add_title(self):
        title = TextMobject("``The motion of planets around the sun''")
        title.set_color(YELLOW)
        title.to_edge(UP)
        title.add_to_back(title.copy().set_stroke(BLACK, 5))
        self.add(title)
        self.title = title

    def setup_orbits(self):
        sun = ImageMobject("sun")
        sun.scale_to_fit_height(0.7)
        planets, ellipses, orbits = self.get_planets_ellipses_and_orbits(sun)

        archivist_words = TextMobject(
            "Judith Goodstein (Caltech archivist)"
        )
        archivist_words.to_corner(UL)
        archivist_words.shift(1.5 * DOWN)
        archivist_words.add_background_rectangle()
        alt_name = TextMobject("David Goodstein (Caltech physicist)")
        alt_name.next_to(archivist_words, DOWN, aligned_edge=LEFT)
        alt_name.add_background_rectangle()

        book = ImageMobject("Lost_Lecture_cover")
        book.scale_to_fit_height(4)
        book.next_to(alt_name, DOWN)

        self.add(SunAnimation(sun))
        self.add(ellipses, planets)
        self.add(self.title)
        self.add(*orbits)
        self.add_foreground_mobjects(planets)
        self.wait(10)
        self.play(
            VGroup(ellipses, sun).shift, 3 * RIGHT,
            FadeInFromDown(archivist_words),
            Animation(self.title)
        )
        self.add_foreground_mobjects(archivist_words)
        self.wait(3)
        self.play(FadeInFromDown(alt_name))
        self.add_foreground_mobjects(alt_name)
        self.wait()
        self.play(FadeInFromDown(book))
        self.wait(15)

    def get_planets_ellipses_and_orbits(self, sun):
        planets = VGroup(
            ImageMobject("mercury"),
            ImageMobject("venus"),
            ImageMobject("earth"),
            ImageMobject("mars"),
            ImageMobject("comet")
        )
        sizes = [0.383, 0.95, 1.0, 0.532, 0.3]
        orbit_radii = [0.254, 0.475, 0.656, 1.0, 3.0]
        orbit_eccentricies = [0.206, 0.006, 0.0167, 0.0934, 0.967]

        for planet, size in zip(planets, sizes):
            planet.scale_to_fit_height(0.5)
            planet.scale(size)

        ellipses = VGroup(*[
            Circle(radius=r, color=WHITE, stroke_width=1)
            for r in orbit_radii
        ])
        for circle, ec in zip(ellipses, orbit_eccentricies):
            a = circle.get_height() / 2
            c = ec * a
            b = np.sqrt(a**2 - c**2)
            circle.stretch(b / a, 1)
            c = np.sqrt(a**2 - b**2)
            circle.shift(c * RIGHT)
        for circle in ellipses:
            circle.rotate(
                TAU * np.random.random(),
                about_point=ORIGIN
            )

        ellipses.scale(3.5, about_point=ORIGIN)

        orbits = [
            Orbiting(
                planet, sun, circle,
                rate=0.25 * r**(2 / 3)
            )
            for planet, circle, r in zip(planets, ellipses, orbit_radii)
        ]
        orbits[-1].proportion = 0.15
        orbits[-1].rate = 0.5

        return planets, ellipses, orbits


class AskAboutEllipses(TheMotionOfPlanets):
    CONFIG = {
        "camera_config": {"background_opacity": 1},
        "animate_sun": True,
    }

    def construct(self):
        self.add_title()
        self.add_sun()
        self.add_orbit()
        self.add_focus_lines()
        self.add_force_labels()
        self.comment_on_imperfections()
        self.set_up_differential_equations()

    def add_title(self):
        title = Title("Why are orbits ellipses?")
        self.add(title)
        self.title = title

    def add_sun(self):
        sun = ImageMobject("sun", height=0.5)
        self.sun = sun
        self.add(sun)
        if self.animate_sun:
            self.add(SunAnimation(sun))

    def add_orbit(self):
        sun = self.sun
        comet = ImageMobject("comet")
        comet.scale_to_fit_height(0.2)
        ellipse = self.get_ellipse()
        orbit = Orbiting(comet, sun, ellipse)

        self.add(ellipse)
        self.add(orbit)

        self.ellipse = ellipse
        self.comet = comet
        self.orbit = orbit

    def add_focus_lines(self):
        f1, f2 = self.focus_points
        comet = self.comet
        lines = VGroup(Line(LEFT, RIGHT), Line(LEFT, RIGHT))
        lines.set_stroke(LIGHT_GREY, 1)

        def update_lines(lines):
            l1, l2 = lines
            P = comet.get_center()
            l1.put_start_and_end_on(f1, P)
            l2.put_start_and_end_on(f2, P)
            return lines

        animation = ContinualUpdateFromFunc(
            lines, update_lines
        )
        self.add(animation)
        self.wait(8)

        self.focus_lines = lines
        self.focus_lines_animation = animation

    def add_force_labels(self):
        radial_line = self.focus_lines[0]

        # Radial line measurement
        radius_measurement_kwargs = {
            "num_decimal_places": 3,
            "color": BLUE,
        }
        radius_measurement = DecimalNumber(1, **radius_measurement_kwargs)

        def update_radial_measurement(measurement):
            angle = -radial_line.get_angle() + np.pi
            radial_line.rotate(angle, about_point=ORIGIN)
            new_decimal = DecimalNumber(
                radial_line.get_length(),
                **radius_measurement_kwargs
            )
            max_width = 0.6 * radial_line.get_width()
            if new_decimal.get_width() > max_width:
                new_decimal.scale_to_fit_width(max_width)
            new_decimal.next_to(radial_line, UP, SMALL_BUFF)
            VGroup(new_decimal, radial_line).rotate(
                -angle, about_point=ORIGIN
            )
            Transform(measurement, new_decimal).update(1)

        radius_measurement_animation = ContinualUpdateFromFunc(
            radius_measurement, update_radial_measurement
        )

        # Force equation
        force_equation = TexMobject(
            "F = {GMm \\over (0.000)^2}",
            tex_to_color_map={
                "F": YELLOW,
                "0.000": BLACK,
            }
        )
        force_equation.next_to(self.title, DOWN)
        force_equation.to_edge(RIGHT)
        radius_in_denominator_ref = force_equation.get_part_by_tex("0.000")
        radius_in_denominator = DecimalNumber(
            0, **radius_measurement_kwargs
        )
        radius_in_denominator.scale(0.95)
        update_radius_in_denominator = ContinualChangingDecimal(
            radius_in_denominator,
            lambda a: radial_line.get_length(),
            position_update_func=lambda mob: mob.move_to(
                radius_in_denominator_ref, LEFT
            )
        )

        # Force arrow
        force_arrow = Arrow(LEFT, RIGHT, color=YELLOW)

        def update_force_arrow(arrow):
            radius = radial_line.get_length()
            # target_length = 1 / radius**2
            target_length = 1 / radius  # Lies!
            arrow.scale(
                target_length / arrow.get_length()
            )
            arrow.rotate(
                np.pi + radial_line.get_angle() - arrow.get_angle()
            )
            arrow.shift(
                radial_line.get_end() - arrow.get_start()
            )
        force_arrow_animation = ContinualUpdateFromFunc(
            force_arrow, update_force_arrow
        )

        inverse_square_law_words = TextMobject(
            "``Inverse square law''"
        )
        inverse_square_law_words.next_to(force_equation, DOWN, MED_LARGE_BUFF)
        inverse_square_law_words.to_edge(RIGHT)
        force_equation.next_to(inverse_square_law_words, UP, MED_LARGE_BUFF)

        def v_fade_in(mobject):
            return UpdateFromAlphaFunc(
                mobject,
                lambda mob, alpha: mob.set_fill(opacity=alpha)
            )

        self.add(update_radius_in_denominator)
        self.add(radius_measurement_animation)
        self.play(
            FadeIn(force_equation),
            v_fade_in(radius_in_denominator),
            v_fade_in(radius_measurement)
        )
        self.add(force_arrow_animation)
        self.play(v_fade_in(force_arrow))
        self.wait(8)
        self.play(Write(inverse_square_law_words))
        self.wait(9)

        self.force_equation = force_equation
        self.inverse_square_law_words = inverse_square_law_words
        self.force_arrow = force_arrow
        self.radius_measurement = radius_measurement

    def comment_on_imperfections(self):
        planets, ellipses, orbits = self.get_planets_ellipses_and_orbits(self.sun)
        orbits.pop(-1)
        ellipses.submobjects.pop(-1)
        planets.submobjects.pop(-1)

        scale_factor = 20
        center = self.sun.get_center()
        ellipses.save_state()
        ellipses.scale(scale_factor, about_point=center)

        self.add(*orbits)
        self.play(ellipses.restore, Animation(planets))
        self.wait(7)
        self.play(
            ellipses.scale, scale_factor, {"about_point": center},
            Animation(planets)
        )
        self.remove(*orbits)
        self.remove(planets, ellipses)
        self.wait(2)

    def set_up_differential_equations(self):
        d_dt = TexMobject("{d \\over dt}")
        in_vect = Matrix(np.array([
            "x(t)",
            "y(t)",
            "\\dot{x}(t)",
            "\\dot{y}(t)",
        ]))
        equals = TexMobject("=")
        out_vect = Matrix(np.array([
            "\\dot{x}(t)",
            "\\dot{y}(t)",
            "-x(t) / (x(t)^2 + y(t)^2)^{3/2}",
            "-y(t) / (x(t)^2 + y(t)^2)^{3/2}",
        ]), element_alignment_corner=ORIGIN)

        equation = VGroup(d_dt, in_vect, equals, out_vect)
        equation.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
        equation.scale_to_fit_width(6)

        equation.to_corner(DR, buff=MED_LARGE_BUFF)
        cross = Cross(equation)

        self.play(Write(equation))
        self.wait(6)
        self.play(ShowCreation(cross))
        self.wait(6)

    # Helpers
    def get_ellipse(self):
        a = 7.0
        b = 4.0
        c = np.sqrt(a**2 - b**2)
        ellipse = Circle(radius=a / 2)
        ellipse.set_stroke(WHITE, 1)
        ellipse.stretch(b / a, dim=1)
        ellipse.move_to(
            self.sun.get_center() + c * LEFT / 2
        )
        self.focus_points = [
            self.sun.get_center(),
            self.sun.get_center() + c * LEFT,
        ]
        return ellipse


class FeynmanElementaryQuote(Scene):
    def construct(self):
        quote_text = """
            \\large
            I am going to give what I will call an
            \\emph{elementary} demonstration.  But elementary
            does not mean easy to understand.  Elementary
            means that very little is required
            to know ahead of time in order to understand it,
            except to have an infinite amount of intelligence.
        """
        quote_parts = filter(lambda s: s, quote_text.split(" "))
        quote = TextMobject(
            *quote_parts,
            tex_to_color_map={
                "\\emph{elementary}": BLUE,
                "elementary": BLUE,
                "Elementary": BLUE,
                "infinite": YELLOW,
                "amount": YELLOW,
                "of": YELLOW,
                "intelligence": YELLOW,
                "very": RED,
                "little": RED,
            },
            alignment=""
        )
        quote[-1].shift(2 * SMALL_BUFF * LEFT)
        quote.scale_to_fit_width(FRAME_WIDTH - 1)
        quote.to_edge(UP)
        quote.get_part_by_tex("of").set_color(WHITE)

        nothing = TextMobject("nothing")
        nothing.scale(0.9)
        very = quote.get_part_by_tex("very")
        nothing.shift(very[0].get_left() - nothing[0].get_left())
        nothing.set_color(RED)

        for word in quote:
            if word is very:
                self.add_foreground_mobjects(nothing)
                self.play(ShowWord(nothing))
                self.wait(0.2)
                nothing.sort_submobjects(lambda p: -p[0])
                self.play(LaggedStart(
                    FadeOut, nothing,
                    run_time=1
                ))
                self.remove_foreground_mobject(nothing)
            back_word = word.copy().set_stroke(BLACK, 5)
            self.add_foreground_mobjects(back_word, word)
            self.play(
                ShowWord(back_word),
                ShowWord(word),
            )
            self.wait(0.005 * len(word)**1.5)


class LostLecturePicture(TODOStub):
    CONFIG = {"camera_config": {"background_opacity": 1}}

    def construct(self):
        picture = ImageMobject("Feynman_teaching")
        picture.scale_to_fit_height(FRAME_WIDTH)
        picture.to_corner(UL, buff=0)
        picture.fade(0.5)

        self.play(
            picture.to_corner, DR, {"buff": 0},
            picture.shift, 1.5 * DOWN,
            path_arc=60 * DEGREES,
            run_time=20,
            rate_func=bezier([0, 0, 1, 1])
        )


class AskAboutInfiniteIntelligence(TeacherStudentsScene):
    def construct(self):
        self.student_says(
            "Infinite intelligence?",
            target_mode="confused"
        )
        self.play(
            self.get_student_changes("horrified", "confused", "sad"),
            self.teacher.change, "happy",
        )
        self.wait()
        self.teacher_says(
            "It's not too bad, \\\\ but stay focused",
            added_anims=[self.get_student_changes(*["happy"] * 3)]
        )
        self.wait()
        self.look_at(self.screen)
        self.wait(5)


class ShowEllipseDefiningProperty(Scene):
    CONFIG = {
        "ellipse_color": BLUE,
        "a": 4.0,
        "b": 3.0,
    }

    def construct(self):
        self.add_ellipse()
        self.add_focal_lines()
        self.add_distance_labels()
        self.show_constant_sum()
        self.label_foci()
        self.label_focal_sum()

    def add_ellipse(self):
        a = self.a
        b = self.b
        c = np.sqrt(a**2 - b**2)
        ellipse = Circle(radius=a, color=self.ellipse_color)
        ellipse.stretch(fdiv(b, a), dim=1)
        self.foci = [c * LEFT, c * RIGHT]
        self.ellipse = ellipse
        self.add(ellipse)

    def add_focal_lines(self):
        pass

    def add_distance_labels(self):
        pass

    def show_constant_sum(self):
        pass

    def label_foci(self):
        pass

    def label_focal_sum(self):
        pass