Merge pull request #479 from 3b1b/ode

Ode

active_projects/eola2/cramer.py

@@ -2268,7 +2268,8 @@ class Thumbnail(TransformingAreasYCoord, MovingCameraScene):
         ip = self.get_input_parallelogram(vect)
         self.add_transformable_mobject(ip)
         self.apply_transposed_matrix([[2, -0.5], [1, 2]])
-        # self.square.set_fill(YELLOW, 0.7)
+        self.square.set_fill(opacity=0.7)
+        self.square.set_sheen(0.75, UR)
         self.camera_frame.shift(UP)
 
         words = TextMobject("Cramer's", "rule")

active_projects/ode/all_part1_scenes.py

@@ -1,6 +1,22 @@
 from active_projects.ode.part1.pendulum import *
+from active_projects.ode.part1.staging import *
+from active_projects.ode.part1.pi_scenes import *
 
 OUTPUT_DIRECTORY = "ode/part1"
 ALL_SCENE_CLASSES = [
-    PendulumTest
+    IntroducePendulum,
+    MultiplePendulumsOverlayed,
+    FormulasAreLies,
+    MediumAnglePendulum,
+    MediumHighAnglePendulum,
+    HighAnglePendulum,
+    LowAnglePendulum,
+    SomeOfYouWatching,
+    SmallAngleApproximationTex,
+    VeryLowAnglePendulum,
+    FollowThisThread,
+    StrogatzQuote,
+    # Something...
+    ShowGravityAcceleration,
+    BuildUpEquation,
 ]

active_projects/ode/part1/pendulum.py

@@ -1,4 +1,5 @@
 from big_ol_pile_of_manim_imports import *
+from active_projects.ode.part1.shared_constructs import *
 
 
 class Pendulum(VGroup):
@@ -19,9 +20,12 @@ class Pendulum(VGroup):
         "weight_style": {
             "stroke_width": 0,
             "fill_opacity": 1,
-            "fill_color": DARK_GREY,
+            "fill_color": GREY_BROWN,
             "sheen_direction": UL,
             "sheen_factor": 0.5,
+            "background_stroke_color": BLACK,
+            "background_stroke_width": 3,
+            "background_stroke_opacity": 0.5,
         },
         "dashed_line_config": {
             "num_dashes": 25,
@@ -36,7 +40,8 @@ class Pendulum(VGroup):
         "velocity_vector_config": {
             "color": RED,
         },
-        "n_steps_per_frame": 10,
+        "theta_label_height": 0.25,
+        "n_steps_per_frame": 100,
     }
 
     def __init__(self, **kwargs):
@@ -47,12 +52,15 @@ class Pendulum(VGroup):
         self.rotating_group = VGroup(self.rod, self.weight)
         self.create_dashed_line()
         self.create_angle_arc()
+        self.add_theta_label()
 
         self.set_theta(self.initial_theta)
         self.update()
 
     def create_fixed_point(self):
         self.fixed_point_tracker = VectorizedPoint(self.top_point)
+        self.add(self.fixed_point_tracker)
+        return self
 
     def create_rod(self):
         rod = self.rod = Line(UP, DOWN)
@@ -87,11 +95,33 @@ class Pendulum(VGroup):
 
     def add_velocity_vector(self):
         def make_vector():
-            vector = Vector(0.5 * self.get_omega() * RIGHT)
+            omega = self.get_omega()
+            theta = self.get_theta()
+            vector = Vector(
+                0.5 * omega * RIGHT,
+                **self.velocity_vector_config,
+            )
+            vector.rotate(theta, about_point=ORIGIN)
+            vector.shift(self.rod.get_end())
+            return vector
+
         self.velocity_vector = always_redraw(make_vector)
         self.add(self.velocity_vector)
         return self
 
+    def add_theta_label(self):
+        label = self.theta_label = TexMobject("\\theta")
+        label.set_height(self.theta_label_height)
+
+        def update_label(l):
+            top = self.get_fixed_point()
+            arc_center = self.angle_arc.point_from_proportion(0.5)
+            vect = arc_center - top
+            vect = normalize(vect) * (1 + self.theta_label_height)
+            l.move_to(top + vect)
+        label.add_updater(update_label)
+        self.add(label)
+
     #
     def get_theta(self):
         theta = self.rod.get_angle() - self.dashed_line.get_angle()
@@ -141,11 +171,816 @@ class Pendulum(VGroup):
         return self
 
 
-class PendulumTest(Scene):
+class GravityVector(Vector):
-    def construct(self):
+    CONFIG = {
-        pendulum = Pendulum(
+        "color": YELLOW,
-            initial_theta=150 * DEGREES,
+        "length_multiple": 1 / 9.8,
+        # TODO, continually update the length based
+        # on the pendulum's gravity?
+    }
+
+    def __init__(self, pendulum, **kwargs):
+        super().__init__(DOWN, **kwargs)
+        self.pendulum = pendulum
+        self.scale(self.length_multiple * pendulum.gravity)
+        self.attach_to_pendulum(pendulum)
+
+    def attach_to_pendulum(self, pendulum):
+        self.add_updater(lambda m: m.shift(
+            pendulum.weight.get_center() - self.get_start(),
+        ))
+
+    def add_component_lines(self):
+        self.component_lines = always_redraw(self.create_component_lines)
+        self.add(self.component_lines)
+
+    def create_component_lines(self):
+        theta = self.pendulum.get_theta()
+        x_new = rotate(RIGHT, theta)
+        base = self.get_start()
+        tip = self.get_end()
+        vect = tip - base
+        corner = base + x_new * np.dot(vect, x_new)
+        kw = {"dash_length": 0.025}
+        return VGroup(
+            DashedLine(base, corner, **kw),
+            DashedLine(corner, tip, **kw),
         )
-        self.add(pendulum)
+
+
+class ThetaValueDisplay(VGroup):
+    CONFIG = {
+
+    }
+
+    def __init__(self, **kwargs):
+        super().__init__(**kwargs)
+
+
+class ThetaVsTAxes(Axes):
+    CONFIG = {
+        "x_min": 0,
+        "x_max": 8,
+        "y_min": -PI / 2,
+        "y_max": PI / 2,
+        "y_axis_config": {
+            "tick_frequency": PI / 8,
+            "unit_size": 1.5,
+        },
+        "number_line_config": {
+            "color": "#EEEEEE",
+            "stroke_width": 2,
+            "include_tip": False,
+        },
+        "graph_style": {
+            "stroke_color": GREEN,
+            "stroke_width": 3,
+            "fill_opacity": 0,
+        },
+    }
+
+    def __init__(self, **kwargs):
+        super().__init__(**kwargs)
+        self.add_labels()
+
+    def add_axes(self):
+        self.axes = Axes(**self.axes_config)
+        self.add(self.axes)
+
+    def add_labels(self):
+        x_axis = self.get_x_axis()
+        y_axis = self.get_y_axis()
+
+        t_label = self.t_label = TexMobject("t")
+        t_label.next_to(x_axis.get_right(), UP, MED_SMALL_BUFF)
+        x_axis.label = t_label
+        x_axis.add(t_label)
+        theta_label = self.theta_label = TexMobject("\\theta(t)")
+        theta_label.next_to(y_axis.get_top(), UP, SMALL_BUFF)
+        y_axis.label = theta_label
+        y_axis.add(theta_label)
+
+        x_axis.add_numbers()
+        y_axis.add(self.get_y_axis_coordinates(y_axis))
+
+    def get_y_axis_coordinates(self, y_axis):
+        texs = [
+            # "\\pi \\over 4",
+            # "\\pi \\over 2",
+            # "3 \\pi \\over 4",
+            # "\\pi",
+            "\\pi / 4",
+            "\\pi / 2",
+            "3 \\pi / 4",
+            "\\pi",
+        ]
+        values = np.arange(1, 5) * PI / 4
+        labels = VGroup()
+        for pos_tex, pos_value in zip(texs, values):
+            neg_tex = "-" + pos_tex
+            neg_value = -1 * pos_value
+            for tex, value in (pos_tex, pos_value), (neg_tex, neg_value):
+                if value > self.y_max or value < self.y_min:
+                    continue
+                symbol = TexMobject(tex)
+                symbol.scale(0.5)
+                point = y_axis.number_to_point(value)
+                symbol.next_to(point, LEFT, MED_SMALL_BUFF)
+                labels.add(symbol)
+        return labels
+
+    def get_live_drawn_graph(self, pendulum,
+                             t_max=None,
+                             t_step=1.0 / 60,
+                             **style):
+        style = merge_dicts_recursively(self.graph_style, style)
+        if t_max is None:
+            t_max = self.x_max
+
+        graph = VMobject()
+        graph.set_style(**style)
+
+        graph.all_coords = [(0, pendulum.get_theta())]
+        graph.time = 0
+        graph.time_of_last_addition = 0
+
+        def update_graph(graph, dt):
+            graph.time += dt
+            if graph.time > t_max:
+                graph.remove_updater(update_graph)
+                return
+            new_coords = (graph.time, pendulum.get_theta())
+            if graph.time - graph.time_of_last_addition >= t_step:
+                graph.all_coords.append(new_coords)
+                graph.time_of_last_addition = graph.time
+            points = [
+                self.coords_to_point(*coords)
+                for coords in [*graph.all_coords, new_coords]
+            ]
+            graph.set_points_smoothly(points)
+
+        graph.add_updater(update_graph)
+        return graph
+
+
+# Scenes
+class IntroducePendulum(PiCreatureScene, MovingCameraScene):
+    CONFIG = {
+        "pendulum_config": {
+            "length": 3,
+            "top_point": 4 * RIGHT,
+            "weight_diameter": 0.35,
+        },
+        "theta_vs_t_axes_config": {
+            "y_max": PI / 4,
+            "y_min": -PI / 4,
+            "y_axis_config": {
+                "tick_frequency": PI / 16,
+                "unit_size": 2,
+                "tip_length": 0.3,
+            },
+            "number_line_config": {
+                "stroke_width": 2,
+            }
+        },
+    }
+
+    def setup(self):
+        MovingCameraScene.setup(self)
+        PiCreatureScene.setup(self)
+
+    def construct(self):
+        self.add_pendulum()
+        self.label_pi_creatures()
+        self.label_pendulum()
+        self.add_graph()
+        self.show_graph_period()
+        self.show_length_and_gravity()
+        self.tweak_length_and_gravity()
+
+    def create_pi_creatures(self):
+        randy = Randolph(color=BLUE_C)
+        morty = Mortimer(color=MAROON_E)
+        creatures = VGroup(randy, morty)
+        creatures.scale(0.5)
+        creatures.arrange(RIGHT, buff=2.5)
+        creatures.to_corner(DR)
+        return creatures
+
+    def add_pendulum(self):
+        pendulum = self.pendulum = Pendulum(**self.pendulum_config)
         pendulum.start_swinging()
+        frame = self.camera_frame
+        frame.save_state()
+        frame.scale(0.5)
+        frame.move_to(pendulum.dashed_line)
+
+        self.add(pendulum, frame)
+
+    def label_pi_creatures(self):
+        randy, morty = self.pi_creatures
+        randy_label = TextMobject("Physics\\\\", "student")
+        morty_label = TextMobject("Physics\\\\", "teacher")
+        labels = VGroup(randy_label, morty_label)
+        labels.scale(0.5)
+        randy_label.next_to(randy, UP, LARGE_BUFF)
+        morty_label.next_to(morty, UP, LARGE_BUFF)
+
+        for label, pi in zip(labels, self.pi_creatures):
+            label.arrow = Arrow(
+                label.get_bottom(), pi.eyes.get_top()
+            )
+            label.arrow.set_color(WHITE)
+            label.arrow.set_stroke(width=5)
+
+        morty.labels = VGroup(
+            morty_label,
+            morty_label.arrow,
+        )
+
+        self.play(
+            FadeInFromDown(randy_label),
+            GrowArrow(randy_label.arrow),
+            randy.change, "hooray",
+        )
+        self.play(
+            Animation(self.pendulum.fixed_point_tracker),
+            TransformFromCopy(randy_label[0], morty_label[0]),
+            FadeIn(morty_label[1]),
+            GrowArrow(morty_label.arrow),
+            morty.change, "raise_right_hand",
+        )
+        self.wait()
+
+    def label_pendulum(self):
+        pendulum = self.pendulum
+        randy, morty = self.pi_creatures
+        label = pendulum.theta_label
+        rect = SurroundingRectangle(label, buff=0.5 * SMALL_BUFF)
+        rect.add_updater(lambda r: r.move_to(label))
+
+        self.add(rect)
+        self.play(
+            ShowCreationThenFadeOut(rect),
+            ShowCreationThenDestruction(
+                label.copy().set_style(
+                    fill_opacity=0,
+                    stroke_color=PINK,
+                    stroke_width=2,
+                )
+            ),
+            randy.change, "pondering",
+            morty.change, "pondering",
+        )
+        self.wait()
+
+    def add_graph(self):
+        axes = self.axes = ThetaVsTAxes(**self.theta_vs_t_axes_config)
+        axes.y_axis.label.next_to(axes.y_axis, UP, buff=0)
+        axes.to_corner(UL)
+
+        self.play(
+            Restore(self.camera_frame),
+            DrawBorderThenFill(
+                axes,
+                rate_func=squish_rate_func(smooth, 0.5, 1),
+                lag_ratio=0.9,
+            ),
+            Transform(
+                self.pendulum.theta_label.copy().clear_updaters(),
+                axes.y_axis.label.copy(),
+                remover=True,
+                rate_func=squish_rate_func(smooth, 0, 0.8),
+            ),
+            run_time=3,
+        )
+        self.wait(2)
+        self.graph = axes.get_live_drawn_graph(self.pendulum)
+
+        self.add(self.graph)
+        self.wait(4)
+
+    def show_graph_period(self):
+        pendulum = self.pendulum
+        axes = self.axes
+
+        period = self.period = TAU * np.sqrt(
+            pendulum.length / pendulum.gravity
+        )
+        amplitude = pendulum.initial_theta
+
+        line = Line(
+            axes.coords_to_point(0, amplitude),
+            axes.coords_to_point(period, amplitude),
+        )
+        line.shift(SMALL_BUFF * RIGHT)
+        brace = Brace(line, UP, buff=SMALL_BUFF)
+        brace.add_to_back(brace.copy().set_style(BLACK, 10))
+        formula = TexMobject(
+            "\\sqrt{\\,", "2\\pi", "L", "/", "g", "}",
+            tex_to_color_map={
+                "L": BLUE,
+                "g": YELLOW,
+            }
+        )
+        formula.next_to(brace, UP, SMALL_BUFF)
+
+        self.period_formula = formula
+        self.period_brace = brace
+
+        self.play(
+            GrowFromCenter(brace),
+            FadeInFromDown(formula),
+        )
+        self.wait(2)
+
+    def show_length_and_gravity(self):
+        formula = self.period_formula
+        L = formula.get_part_by_tex("L")
+        g = formula.get_part_by_tex("g")
+
+        rod = self.pendulum.rod
+        new_rod = rod.copy()
+        new_rod.set_stroke(BLUE, 7)
+        new_rod.add_updater(lambda r: r.put_start_and_end_on(
+            *rod.get_start_and_end()
+        ))
+
+        g_vect = GravityVector(
+            self.pendulum,
+            length_multiple=0.5 / 9.8,
+        )
+
+        self.play(ShowCreationThenDestructionAround(L))
+        dot = Dot(fill_opacity=0.25)
+        dot.move_to(L)
+        self.play(
+            ShowCreation(new_rod),
+            dot.move_to, new_rod,
+            dot.fade, 1,
+        )
+        self.remove(dot)
+        self.play(FadeOut(new_rod))
+        self.wait()
+
+        self.play(ShowCreationThenDestructionAround(g))
+        dot.move_to(g)
+        dot.set_fill(opacity=0.5)
+        self.play(
+            GrowArrow(g_vect),
+            dot.move_to, g_vect,
+            dot.fade, 1,
+        )
+        self.remove(dot)
+        self.wait(2)
+
+        self.gravity_vector = g_vect
+
+    def tweak_length_and_gravity(self):
+        pendulum = self.pendulum
+        axes = self.axes
+        graph = self.graph
+        brace = self.period_brace
+        formula = self.period_formula
+        g_vect = self.gravity_vector
+        randy, morty = self.pi_creatures
+
+        graph.clear_updaters()
+        period2 = self.period * np.sqrt(2)
+        period3 = self.period / np.sqrt(2)
+        amplitude = pendulum.initial_theta
+        graph2, graph3 = [
+            axes.get_graph(
+                lambda t: amplitude * np.cos(TAU * t / p),
+                color=RED,
+            )
+            for p in (period2, period3)
+        ]
+        formula.add_updater(lambda m: m.next_to(
+            brace, UP, SMALL_BUFF
+        ))
+
+        new_pendulum_config = dict(self.pendulum_config)
+        new_pendulum_config["length"] *= 2
+        new_pendulum_config["top_point"] += 3.5 * UP
+        # new_pendulum_config["initial_theta"] = pendulum.get_theta()
+        new_pendulum = Pendulum(**new_pendulum_config)
+
+        down_vectors = VGroup(*[
+            Vector(0.5 * DOWN)
+            for x in range(10 * 150)
+        ])
+        down_vectors.arrange_in_grid(10, 150, buff=MED_SMALL_BUFF)
+        down_vectors.set_color_by_gradient(BLUE, RED)
+        # for vect in down_vectors:
+        #     vect.shift(0.1 * np.random.random(3))
+        down_vectors.to_edge(RIGHT)
+
+        self.play(randy.change, "happy")
+        self.play(
+            ReplacementTransform(pendulum, new_pendulum),
+            morty.change, "horrified",
+            morty.shift, 3 * RIGHT,
+            morty.labels.shift, 3 * RIGHT,
+        )
+        self.remove(morty, morty.labels)
+        g_vect.attach_to_pendulum(new_pendulum)
+        new_pendulum.start_swinging()
+        self.play(
+            ReplacementTransform(graph, graph2),
+            brace.stretch, np.sqrt(2), 0, {"about_edge": LEFT},
+        )
+        self.add(g_vect)
+        self.wait(3)
+
+        new_pendulum.gravity *= 4
+        g_vect.scale(2)
+        self.play(
+            FadeOut(graph2),
+            LaggedStart(*[
+                GrowArrow(v, rate_func=there_and_back)
+                for v in down_vectors
+            ], lag_ratio=0.0005, run_time=2, remover=True)
+        )
+        self.play(
+            FadeIn(graph3),
+            brace.stretch, 0.5, 0, {"about_edge": LEFT},
+        )
+        self.wait(6)
+
+
+class MultiplePendulumsOverlayed(Scene):
+    CONFIG = {
+        "initial_thetas": [
+            150 * DEGREES,
+            90 * DEGREES,
+            60 * DEGREES,
+            30 * DEGREES,
+            10 * DEGREES,
+        ],
+        "weight_colors": [
+            PINK, RED, GREEN, BLUE, GREY,
+        ],
+        "pendulum_config": {
+            "top_point": ORIGIN,
+            "length": 3,
+        },
+    }
+
+    def construct(self):
+        pendulums = VGroup(*[
+            Pendulum(
+                initial_theta=theta,
+                weight_style={
+                    "fill_color": wc,
+                    "fill_opacity": 0.5,
+                },
+                **self.pendulum_config,
+            )
+            for theta, wc in zip(
+                self.initial_thetas,
+                self.weight_colors,
+            )
+        ])
+        for pendulum in pendulums:
+            pendulum.start_swinging()
+            pendulum.remove(pendulum.theta_label)
+
+        randy = Randolph(color=BLUE_C)
+        randy.to_corner(DL)
+        randy.add_updater(lambda r: r.look_at(pendulums[0].weight))
+
+        axes = ThetaVsTAxes(
+            x_max=20,
+            y_axis_config={
+                "unit_size": 0.5,
+                "tip_length": 0.3,
+            },
+        )
+        axes.to_corner(UL)
+        graphs = VGroup(*[
+            axes.get_live_drawn_graph(
+                pendulum,
+                stroke_color=pendulum.weight.get_color(),
+                stroke_width=1,
+            )
+            for pendulum in pendulums
+        ])
+
+        self.add(pendulums)
+        self.add(axes, *graphs)
+        self.play(randy.change, "sassy")
+        self.wait(2)
+        self.play(Blink(randy))
+        self.wait(5)
+        self.play(randy.change, "angry")
+        self.play(Blink(randy))
         self.wait(10)
+
+
+class LowAnglePendulum(Scene):
+    CONFIG = {
+        "pendulum_config": {
+            "initial_theta": 20 * DEGREES,
+            "length": 2.0,
+            "damping": 0,
+            "top_point": ORIGIN,
+        },
+        "axes_config": {
+            "y_axis_config": {"unit_size": 0.75},
+            "x_axis_config": {
+                "unit_size": 0.5,
+                "numbers_to_show": range(2, 25, 2),
+                "number_scale_val": 0.5,
+            },
+            "x_max": 25,
+            "number_line_config": {
+                "tip_length": 0.3,
+                "stroke_width": 2,
+            }
+        },
+        "axes_corner": UL,
+    }
+
+    def construct(self):
+        pendulum = Pendulum(**self.pendulum_config)
+        axes = ThetaVsTAxes(**self.axes_config)
+        axes.center()
+        axes.to_corner(self.axes_corner, buff=LARGE_BUFF)
+        graph = axes.get_live_drawn_graph(pendulum)
+
+        L = pendulum.length
+        g = pendulum.gravity
+        theta0 = pendulum.initial_theta
+        prediction = axes.get_graph(
+            lambda t: theta0 * np.cos(t * np.sqrt(g / L))
+        )
+        dashed_prediction = DashedVMobject(prediction, num_dashes=300)
+        dashed_prediction.set_stroke(WHITE, 1)
+        prediction_formula = TexMobject(
+            "\\theta_0", "\\cos(\\sqrt{g / L} \\cdot t)"
+        )
+        prediction_formula.scale(0.75)
+        prediction_formula.next_to(
+            dashed_prediction, UP, SMALL_BUFF,
+        )
+
+        theta0 = prediction_formula.get_part_by_tex("\\theta_0")
+        theta0_brace = Brace(theta0, UP, buff=SMALL_BUFF)
+        theta0_brace.stretch(0.5, 1, about_edge=DOWN)
+        theta0_label = Integer(
+            pendulum.initial_theta * 180 / PI,
+            unit="^\\circ"
+        )
+        theta0_label.scale(0.75)
+        theta0_label.next_to(theta0_brace, UP, SMALL_BUFF)
+
+        group = VGroup(theta0_brace, theta0_label, prediction_formula)
+        group.shift_onto_screen(buff=MED_SMALL_BUFF)
+
+        self.add(axes, dashed_prediction, pendulum)
+        self.play(
+            ShowCreation(dashed_prediction, run_time=2),
+            FadeInFromDown(prediction_formula),
+            FadeInFromDown(theta0_brace),
+            FadeInFromDown(theta0_label),
+        )
+        self.play(
+            ShowCreationThenFadeAround(theta0_label),
+            ShowCreationThenFadeAround(pendulum.theta_label),
+        )
+        self.wait()
+
+        pendulum.start_swinging()
+        self.add(graph)
+        self.wait(30)
+
+
+class ApproxWordsLowAnglePendulum(Scene):
+    def construct(self):
+        period = TexMobject(
+            "\\text{Period}", "\\approx",
+            "2\\pi \\sqrt{\\,{L} / {g}}",
+            **Lg_formula_config
+        )
+        checkmark = TexMobject("\\checkmark")
+        checkmark.set_color(GREEN)
+        checkmark.scale(2)
+        checkmark.next_to(period, RIGHT, MED_LARGE_BUFF)
+
+        self.add(period, checkmark)
+
+
+class MediumAnglePendulum(LowAnglePendulum):
+    CONFIG = {
+        "pendulum_config": {
+            "initial_theta": 50 * DEGREES,
+            "n_steps_per_frame": 1000,
+        },
+        "axes_config": {
+            "y_axis_config": {"unit_size": 0.75},
+            "y_max": PI / 2,
+            "y_min": -PI / 2,
+            "number_line_config": {
+                "tip_length": 0.3,
+                "stroke_width": 2,
+            }
+        },
+        "pendulum_shift_vect": 1 * RIGHT,
+    }
+
+
+class MediumHighAnglePendulum(MediumAnglePendulum):
+    CONFIG = {
+        "pendulum_config": {
+            "initial_theta": 90 * DEGREES,
+            "n_steps_per_frame": 1000,
+        },
+    }
+
+
+class HighAnglePendulum(LowAnglePendulum):
+    CONFIG = {
+        "pendulum_config": {
+            "initial_theta": 175 * DEGREES,
+            "n_steps_per_frame": 1000,
+            "top_point": 1.5 * DOWN,
+            "length": 2,
+        },
+        "axes_config": {
+            "y_axis_config": {"unit_size": 0.5},
+            "y_max": PI,
+            "y_min": -PI,
+            "number_line_config": {
+                "tip_length": 0.3,
+                "stroke_width": 2,
+            }
+        },
+        "pendulum_shift_vect": 1 * RIGHT,
+    }
+
+
+class VeryLowAnglePendulum(LowAnglePendulum):
+    CONFIG = {
+        "pendulum_config": {
+            "initial_theta": 10 * DEGREES,
+            "n_steps_per_frame": 1000,
+            "top_point": ORIGIN,
+            "length": 3,
+        },
+        "axes_config": {
+            "y_axis_config": {"unit_size": 2},
+            "y_max": PI / 4,
+            "y_min": -PI / 4,
+            "number_line_config": {
+                "tip_length": 0.3,
+                "stroke_width": 2,
+            }
+        },
+        "pendulum_shift_vect": 1 * RIGHT,
+    }
+
+
+class BuildUpEquation(MovingCameraScene):
+    CONFIG = {
+        "pendulum_config": {
+            "length": 5,
+            "top_point": 3 * UP,
+            "initial_theta": 45 * DEGREES,
+        },
+        "g_vect_config": {
+            "length_multiple": 0.25,
+        },
+        "tan_line_color": BLUE,
+        "perp_line_color": PINK,
+    }
+
+    def construct(self):
+        self.add_pendulum()
+        self.show_constraint()
+        self.break_g_vect_into_components()
+        self.show_angle_geometry()
+        self.show_gsin_formula()
+        self.show_acceleration_at_different_angles()
+        self.ask_about_what_to_do()
+        self.show_velocity_and_position()
+        self.show_derivatives()
+        self.show_equation()
+        self.talk_about_sine_component()
+        self.add_air_resistance()
+
+    def add_pendulum(self):
+        self.pendulum = Pendulum(**self.pendulum_config)
+        self.add(self.pendulum)
+
+    def show_constraint(self):
+        pendulum = self.pendulum
+        weight = pendulum.weight
+
+        g_vect = self.g_vect = GravityVector(
+            pendulum, **self.g_vect_config,
+        )
+        g_word = self.g_word = TextMobject("Gravity")
+        g_word.rotate(-90 * DEGREES)
+        g_word.scale(0.75)
+        g_word.add_updater(lambda m: m.next_to(
+            g_vect, RIGHT, buff=-SMALL_BUFF,
+        ))
+
+        theta_tracker = ValueTracker(pendulum.get_theta())
+
+        p = weight.get_center()
+        path = CubicBezier([p, p + 3 * DOWN, p + 3 * UP, p])
+
+        g_word.suspend_updating()
+        self.play(
+            GrowArrow(g_vect),
+            FadeInFrom(g_word, UP, lag_ratio=0.1),
+        )
+        g_word.resume_updating()
+
+        self.play(MoveAlongPath(weight, path, run_time=2))
+        self.wait()
+
+        pendulum.add_updater(lambda p: p.set_theta(
+            theta_tracker.get_value()
+        ))
+        arcs = VGroup()
+        for u in [-1, 2, -1]:
+            d_theta = 40 * DEGREES * u
+            arc = Arc(
+                start_angle=pendulum.get_theta() - 90 * DEGREES,
+                angle=d_theta,
+                radius=pendulum.length,
+                arc_center=pendulum.get_fixed_point(),
+                stroke_width=2,
+                stroke_color=RED,
+                stroke_opacity=0.5,
+            )
+            self.play(
+                theta_tracker.increment_value, d_theta,
+                ShowCreation(arc)
+            )
+            arcs.add(arc)
+        pendulum.clear_updaters()
+        self.wait()
+        self.play(FadeOut(arc))
+
+    def break_g_vect_into_components(self):
+        g_vect = self.g_vect
+        g_vect.component_lines = always_redraw(
+            g_vect.create_component_lines
+        )
+        tan_line, perp_line = g_vect.component_lines
+        g_vect.tangent = always_redraw(lambda: Arrow(
+            tan_line.get_start(),
+            tan_line.get_end(),
+            buff=0,
+            color=self.tan_line_color,
+        ))
+        g_vect.perp = always_redraw(lambda: Arrow(
+            perp_line.get_start(),
+            perp_line.get_end(),
+            buff=0,
+            color=self.perp_line_color,
+        ))
+
+        self.play(
+            ShowCreation(g_vect.component_lines),
+        )
+        self.play(GrowArrow(g_vect.tangent))
+        self.wait()
+        self.play(GrowArrow(g_vect.perp))
+        self.wait()
+
+    def show_angle_geometry(self):
+        g_vect = self.g_vect
+
+    def show_gsin_formula(self):
+        pass
+
+    def show_acceleration_at_different_angles(self):
+        pass
+
+    def ask_about_what_to_do(self):
+        pass
+
+    def show_velocity_and_position(self):
+        pass
+
+    def show_derivatives(self):
+        pass
+
+    def show_equation(self):
+        pass
+
+    def talk_about_sine_component(self):
+        pass
+
+    def add_air_resistance(self):
+        pass
+
+
+class NewSceneName(Scene):
+    def construct(self):
+        pass

active_projects/ode/part1/pi_scenes.py

@@ -0,0 +1,108 @@
+from big_ol_pile_of_manim_imports import *
+from active_projects.ode.part1.shared_constructs import *
+
+
+class SomeOfYouWatching(TeacherStudentsScene):
+    CONFIG = {
+        "camera_config": {
+            "background_color": DARKER_GREY,
+        }
+    }
+
+    def construct(self):
+        screen = self.screen
+        screen.scale(1.25, about_edge=UL)
+        screen.set_fill(BLACK, 1)
+        self.add(screen)
+
+        self.teacher.change("raise_right_hand")
+        for student in self.students:
+            student.change("pondering", screen)
+
+        self.student_says(
+            "Well...yeah",
+            target_mode="tease"
+        )
+        self.wait(3)
+
+
+class FormulasAreLies(PiCreatureScene):
+    def construct(self):
+        you = self.pi_creature
+        t2c = {
+            "{L}": BLUE,
+            "{g}": YELLOW,
+            "\\theta_0": WHITE,
+            "\\sqrt{\\,": WHITE,
+        }
+        kwargs = {"tex_to_color_map": t2c}
+        period_eq = TexMobject(
+            "\\text{Period} = 2\\pi \\sqrt{\\,{L} / {g}}",
+            **kwargs
+        )
+        theta_eq = TexMobject(
+            "\\theta(t) = \\theta_0 \\cos\\left("
+            "\\sqrt{\\,{L} / {g}} \\cdot t"
+            "\\right)",
+            **kwargs
+        )
+        equations = VGroup(theta_eq, period_eq)
+        equations.arrange(DOWN, buff=LARGE_BUFF)
+
+        for eq in period_eq, theta_eq:
+            i = eq.index_of_part_by_tex("\\sqrt")
+            eq.sqrt_part = eq[i:i + 4]
+
+        theta0 = theta_eq.get_part_by_tex("\\theta_0")
+        theta0_words = TextMobject("Starting angle")
+        theta0_words.next_to(theta0, UL)
+        theta0_words.shift(UP + 0.5 * RIGHT)
+        arrow = Arrow(
+            theta0_words.get_bottom(),
+            theta0,
+            color=WHITE,
+            tip_length=0.25,
+        )
+
+        bubble = SpeechBubble()
+        bubble.pin_to(you)
+        bubble.write("Lies!")
+        bubble.content.scale(2)
+        bubble.resize_to_content()
+
+        self.add(period_eq)
+        you.change("pondering", period_eq)
+        self.wait()
+        theta_eq.remove(*theta_eq.sqrt_part)
+        self.play(
+            TransformFromCopy(
+                period_eq.sqrt_part,
+                theta_eq.sqrt_part,
+            ),
+            FadeIn(theta_eq)
+        )
+        theta_eq.add(*theta_eq.sqrt_part)
+        self.play(
+            FadeInFrom(theta0_words, LEFT),
+            GrowArrow(arrow),
+        )
+        self.wait()
+        self.play(you.change, "confused")
+        self.wait(0)
+        self.play(
+            you.change, "angry",
+            ShowCreation(bubble),
+            FadeInFromPoint(bubble.content, you.mouth),
+            equations.to_edge, LEFT,
+            FadeOut(arrow),
+            FadeOut(theta0_words),
+        )
+        self.wait()
+
+    def create_pi_creature(self):
+        return You().flip().to_corner(DR)
+
+
+class NewSceneName(Scene):
+    def construct(self):
+        pass

active_projects/ode/part1/shared_constructs.py

@@ -0,0 +1,16 @@
+from big_ol_pile_of_manim_imports import *
+
+
+Lg_formula_config = {
+    "tex_to_color_map": {
+        "\\theta_0": WHITE,
+        "{L}": BLUE,
+        "{g}": YELLOW,
+    },
+}
+
+
+class You(PiCreature):
+    CONFIG = {
+        "color": BLUE_C,
+    }

active_projects/ode/part1/staging.py

@@ -0,0 +1,414 @@
+from big_ol_pile_of_manim_imports import *
+from active_projects.ode.part1.shared_constructs import *
+
+
+def pendulum_vector_field(point, mu=0.1, g=9.8, L=3):
+    theta, omega = point[:2]
+    return np.array([
+        omega,
+        -np.sqrt(g / L) * np.sin(theta) - mu * omega,
+        0,
+    ])
+
+
+# Scenes
+
+
+class VectorFieldTest(Scene):
+    def construct(self):
+        plane = NumberPlane(
+            # axis_config={"unit_size": 2}
+        )
+        mu_tracker = ValueTracker(1)
+        field = VectorField(
+            lambda p: pendulum_vector_field(
+                plane.point_to_coords(p),
+                mu=mu_tracker.get_value()
+            ),
+            delta_x=0.5,
+            delta_y=0.5,
+            max_magnitude=4,
+            opacity=0.5,
+            # length_func=lambda norm: norm,
+        )
+        stream_lines = StreamLines(
+            field.func,
+            delta_x=0.5,
+            delta_y=0.5,
+        )
+        animated_stream_lines = AnimatedStreamLines(
+            stream_lines,
+            line_anim_class=ShowPassingFlashWithThinningStrokeWidth,
+        )
+
+        self.add(plane, field, animated_stream_lines)
+        self.wait(10)
+
+
+class SmallAngleApproximationTex(Scene):
+    def construct(self):
+        approx = TexMobject(
+            "\\sin", "(", "\\theta", ") \\approx \\theta",
+            tex_to_color_map={"\\theta": RED},
+            arg_separator="",
+        )
+
+        implies = TexMobject("\\Downarrow")
+        period = TexMobject(
+            "\\text{Period}", "\\approx",
+            "2\\pi \\sqrt{\\,{L} / {g}}",
+            **Lg_formula_config,
+        )
+        group = VGroup(approx, implies, period)
+        group.arrange(DOWN)
+
+        approx_brace = Brace(approx, UP, buff=SMALL_BUFF)
+        approx_words = TextMobject(
+            "For small $\\theta$",
+            tex_to_color_map={"$\\theta$": RED},
+        )
+        approx_words.scale(0.75)
+        approx_words.next_to(approx_brace, UP, SMALL_BUFF)
+
+        self.add(approx, approx_brace, approx_words)
+        self.play(
+            Write(implies),
+            FadeInFrom(period, LEFT)
+        )
+        self.wait()
+
+
+class FollowThisThread(Scene):
+    CONFIG = {
+        "screen_rect_style": {
+            "stroke_width": 2,
+            "stroke_color": WHITE,
+            "fill_opacity": 1,
+            "fill_color": DARKER_GREY,
+        }
+    }
+
+    def construct(self):
+        self.show_thumbnails()
+        self.show_words()
+
+    def show_thumbnails(self):
+        # TODO, replace each of these with a picture?
+        thumbnails = self.thumbnails = VGroup(
+            ScreenRectangle(**self.screen_rect_style),
+            ScreenRectangle(**self.screen_rect_style),
+            ScreenRectangle(**self.screen_rect_style),
+            ScreenRectangle(**self.screen_rect_style),
+            ScreenRectangle(**self.screen_rect_style),
+        )
+        n = len(thumbnails)
+        thumbnails.set_height(1.5)
+
+        line = self.line = CubicBezier([
+            [-5, 3, 0],
+            [3, 3, 0],
+            [-3, -3, 0],
+            [5, -3, 0],
+        ])
+        for thumbnail, a in zip(thumbnails, np.linspace(0, 1, n)):
+            thumbnail.move_to(line.point_from_proportion(a))
+
+        self.play(
+            ShowCreation(
+                line,
+                rate_func=lambda t: np.clip(t * (n + 1) / n, 0, 1)
+            ),
+            LaggedStart(*[
+                GrowFromCenter(
+                    thumbnail,
+                    rate_func=squish_rate_func(
+                        smooth,
+                        0, 0.7,
+                    )
+                )
+                for thumbnail in thumbnails
+            ], lag_ratio=1),
+            run_time=5
+        )
+
+    def show_words(self):
+        words = VGroup(
+            TextMobject("Generalize"),
+            TextMobject("Put in context"),
+            TextMobject("Modify"),
+        )
+        # words.arrange(DOWN, aligned_edge=LEFT, buff=LARGE_BUFF)
+        words.scale(1.5)
+        words.to_corner(UR)
+        words.add_to_back(VectorizedPoint(words.get_center()))
+        words.add(VectorizedPoint(words.get_center()))
+
+        diffEq = TextMobject("Differential\\\\equations")
+        diffEq.scale(1.5)
+        diffEq.to_corner(DL, buff=LARGE_BUFF)
+
+        for word1, word2 in zip(words, words[1:]):
+            self.play(
+                FadeInFromDown(word2),
+                FadeOutAndShift(word1, UP),
+            )
+            self.wait()
+        self.play(
+            ReplacementTransform(
+                VGroup(self.thumbnails).copy().fade(1),
+                diffEq,
+                lag_ratio=0.01,
+            )
+        )
+        self.wait()
+
+
+class StrogatzQuote(Scene):
+    def construct(self):
+        law_words = "laws of physics"
+        language_words = "language of differential equations"
+        author = "-Steven Strogatz"
+        quote = TextMobject(
+            """
+            \\Large
+            ``Since Newton, mankind has come to realize
+            that the laws of physics are always expressed
+            in the language of differential equations.''\\\\
+            """ + author,
+            alignment="",
+            arg_separator=" ",
+            substrings_to_isolate=[law_words, language_words, author]
+        )
+        law_part = quote.get_part_by_tex(law_words)
+        language_part = quote.get_part_by_tex(language_words)
+        author_part = quote.get_part_by_tex(author)
+        quote.set_width(12)
+        quote.to_edge(UP)
+        quote[-2].shift(SMALL_BUFF * LEFT)
+        author_part.shift(RIGHT + 0.5 * DOWN)
+        author_part.scale(1.2, about_edge=UL)
+
+        movers = VGroup(*quote[:-1].family_members_with_points())
+        for mover in movers:
+            mover.save_state()
+            disc = Circle(radius=0.05)
+            disc.set_stroke(width=0)
+            disc.set_fill(BLACK, 0)
+            disc.move_to(mover)
+            mover.become(disc)
+        self.play(
+            FadeInFrom(author_part, LEFT),
+            LaggedStartMap(
+                # FadeInFromLarge,
+                # quote[:-1].family_members_with_points(),
+                Restore, movers,
+                lag_ratio=0.005,
+                run_time=2,
+            )
+            # FadeInFromDown(quote[:-1]),
+            # lag_ratio=0.01,
+        )
+        self.wait()
+        self.play(
+            Write(law_part.copy().set_color(YELLOW)),
+            run_time=1,
+        )
+        self.wait()
+        self.play(
+            Write(language_part.copy().set_color(BLUE)),
+            run_time=1.5,
+        )
+        self.wait(2)
+
+
+class ShowGravityAcceleration(Scene):
+    def construct(self):
+        self.add_gravity_field()
+        self.add_title()
+        self.pulse_gravity_down()
+        self.show_trajectory()
+        self.combine_v_vects()
+
+    def add_gravity_field(self):
+        gravity_field = self.gravity_field = VectorField(
+            lambda p: DOWN,
+            # delta_x=2,
+            # delta_y=2,
+        )
+        gravity_field.set_opacity(0.5)
+        gravity_field.sort_submobjects(
+            lambda p: -p[1],
+        )
+        self.add(gravity_field)
+
+    def add_title(self):
+        title = self.title = TextMobject("Gravitational acceleration")
+        title.scale(1.5)
+        title.to_edge(UP)
+        g_eq = self.g_eq = TexMobject(
+            "{g}", "=", "-9.8", "\\frac{\\text{m/s}}{\\text{s}}",
+            **Lg_formula_config
+        )
+        g_eq.next_to(title, DOWN)
+        for mob in title, g_eq:
+            mob.add_background_rectangle_to_submobjects(
+                buff=0.05,
+                opacity=1,
+            )
+        self.add(title, g_eq)
+
+    def pulse_gravity_down(self):
+        field = self.gravity_field
+        self.play(LaggedStart(*[
+            ApplyFunction(
+                lambda v: v.set_opacity(1).scale(1.2),
+                vector,
+                rate_func=there_and_back,
+            )
+            for vector in field
+        ]), run_time=2, lag_ratio=0.001)
+        self.add(self.title, self.g_eq)
+
+    def show_trajectory(self):
+        ball = Circle(
+            stroke_width=1,
+            stroke_color=WHITE,
+            fill_color=GREY,
+            fill_opacity=1,
+            sheen_factor=1,
+            sheen_direction=UL,
+            radius=0.25,
+        )
+        randy = Randolph(mode="pondering")
+        randy.eyes.set_stroke(BLACK, 0.5)
+        randy.match_height(ball)
+        randy.scale(0.75)
+        randy.move_to(ball)
+        ball.add(randy)
+
+        total_time = 6
+
+        p0 = 3 * DOWN + 5 * LEFT
+        v0 = 2.8 * UP + 1.5 * RIGHT
+        g = 0.9 * DOWN
+        graph = ParametricFunction(
+            lambda t: p0 + v0 * t + 0.5 * g * t**2,
+            t_min=0,
+            t_max=total_time,
+        )
+        # graph.center().to_edge(DOWN)
+        dashed_graph = DashedVMobject(graph, num_dashes=60)
+        dashed_graph.set_stroke(WHITE, 1)
+
+        ball.move_to(graph.get_start())
+        randy.add_updater(
+            lambda m, dt: m.rotate(dt).move_to(ball)
+        )
+        times = np.arange(0, total_time + 1)
+
+        velocity_graph = ParametricFunction(
+            lambda t: v0 + g * t,
+            t_min=0, t_max=total_time,
+        )
+        v_point = VectorizedPoint()
+        v_point.move_to(velocity_graph.get_start())
+
+        def get_v_vect():
+            result = Vector(
+                v_point.get_location(),
+                color=RED,
+                tip_length=0.2,
+            )
+            result.scale(0.5, about_point=result.get_start())
+            result.shift(ball.get_center())
+            result.set_stroke(width=2, family=False)
+            return result
+        v_vect = always_redraw(get_v_vect)
+        self.add(v_vect)
+
+        flash_rect = FullScreenRectangle(
+            stroke_width=0,
+            fill_color=WHITE,
+            fill_opacity=0.2,
+        )
+        flash = FadeOut(
+            flash_rect,
+            rate_func=squish_rate_func(smooth, 0, 0.1)
+        )
+
+        ball_copies = VGroup()
+        v_vect_copies = VGroup()
+        self.add(dashed_graph, ball)
+        for t1, t2 in zip(times, times[1:]):
+            v_vect_copy = v_vect.copy()
+            v_vect_copies.add(v_vect_copy)
+            self.add(v_vect_copy)
+            ball_copy = ball.copy()
+            ball_copy.clear_updaters()
+            ball_copies.add(ball_copy)
+            self.add(ball_copy)
+
+            dashed_graph.save_state()
+            kw = {
+                "rate_func": lambda alpha: interpolate(
+                    t1 / total_time,
+                    t2 / total_time,
+                    alpha
+                )
+            }
+            self.play(
+                ShowCreation(dashed_graph, **kw),
+                MoveAlongPath(ball, graph, **kw),
+                MoveAlongPath(v_point, velocity_graph, **kw),
+                flash,
+                run_time=1,
+            )
+            dashed_graph.restore()
+        randy.clear_updaters()
+        self.wait()
+
+        self.v_vects = v_vect_copies
+
+    def combine_v_vects(self):
+        v_vects = self.v_vects.copy()
+        v_vects.generate_target()
+        new_center = 2 * DOWN + 2 * LEFT
+        for vect in v_vects.target:
+            vect.scale(1.5)
+            vect.set_stroke(width=2)
+            vect.shift(new_center - vect.get_start())
+
+        self.play(MoveToTarget(v_vects))
+
+        delta_vects = VGroup(*[
+            Arrow(
+                v1.get_end(),
+                v2.get_end(),
+                buff=0.01,
+                color=YELLOW,
+            ).set_opacity(0.5)
+            for v1, v2 in zip(v_vects, v_vects[1:])
+        ])
+        brace = Brace(Line(ORIGIN, UP), RIGHT)
+        braces = VGroup(*[
+            brace.copy().match_height(arrow).next_to(
+                arrow, RIGHT, buff=0.2 * SMALL_BUFF
+            )
+            for arrow in delta_vects
+        ])
+        amounts = VGroup(*[
+            TextMobject("9.8 m/s").scale(0.5).next_to(
+                brace, RIGHT, SMALL_BUFF
+            )
+            for brace in braces
+        ])
+
+        self.play(
+            FadeOut(self.gravity_field),
+            FadeIn(delta_vects, lag_ratio=0.1),
+        )
+        self.play(
+            LaggedStartMap(GrowFromCenter, braces),
+            LaggedStartMap(FadeInFrom, amounts, lambda m: (m, LEFT)),
+        )
+        self.wait()

big_ol_pile_of_manim_imports.py

@@ -55,6 +55,7 @@ from manimlib.mobject.types.point_cloud_mobject import *
 from manimlib.mobject.types.vectorized_mobject import *
 from manimlib.mobject.mobject_update_utils import *
 from manimlib.mobject.value_tracker import *
+from manimlib.mobject.vector_field import *
 
 from manimlib.for_3b1b_videos.common_scenes import *
 from manimlib.for_3b1b_videos.pi_creature import *

manimlib/animation/fading.py

@@ -97,6 +97,18 @@ class FadeOutAndShiftDown(FadeOutAndShift):
     }
 
 
+class FadeInFromPoint(FadeIn):
+    def __init__(self, mobject, point, **kwargs):
+        self.point = point
+        super().__init__(mobject, **kwargs)
+
+    def create_starting_mobject(self):
+        start = super().create_starting_mobject()
+        start.scale(0)
+        start.move_to(self.point)
+        return start
+
+
 class FadeInFromLarge(FadeIn):
     CONFIG = {
         "scale_factor": 2,

manimlib/animation/growing.py

@@ -1,4 +1,3 @@
-from manimlib.mobject.types.vectorized_mobject import VectorizedPoint
 from manimlib.animation.transform import Transform
 # from manimlib.utils.paths import counterclockwise_path
 from manimlib.constants import PI

manimlib/animation/indication.py

@@ -1,5 +1,3 @@
-from functools import reduce
-
 import numpy as np
 
 from manimlib.constants import *
@@ -9,12 +7,8 @@ from manimlib.animation.composition import AnimationGroup
 from manimlib.animation.composition import Succession
 from manimlib.animation.creation import ShowCreation
 from manimlib.animation.creation import ShowPartial
-from manimlib.animation.fading import FadeIn
 from manimlib.animation.fading import FadeOut
 from manimlib.animation.transform import Transform
-from manimlib.animation.update import UpdateFromAlphaFunc
-from manimlib.mobject.mobject_update_utils import always_redraw
-from manimlib.mobject.mobject import Mobject
 from manimlib.mobject.types.vectorized_mobject import VMobject
 from manimlib.mobject.geometry import Circle
 from manimlib.mobject.geometry import Dot
@@ -23,9 +17,6 @@ from manimlib.mobject.types.vectorized_mobject import VGroup
 from manimlib.mobject.geometry import Line
 from manimlib.utils.bezier import interpolate
 from manimlib.utils.config_ops import digest_config
-from manimlib.utils.rate_functions import linear
-from manimlib.utils.rate_functions import smooth
-from manimlib.utils.rate_functions import squish_rate_func
 from manimlib.utils.rate_functions import there_and_back
 from manimlib.utils.rate_functions import wiggle
 

manimlib/animation/movement.py

@@ -1,5 +1,4 @@
 from manimlib.animation.animation import Animation
-from manimlib.utils.config_ops import digest_config
 from manimlib.utils.rate_functions import linear
 
 

manimlib/constants.py

@@ -214,6 +214,8 @@ COLOR_MAP = {
     "GREY": "#888888",
     "DARK_GREY": "#444444",
     "DARK_GRAY": "#444444",
+    "DARKER_GREY": "#222222",
+    "DARKER_GRAY": "#222222",
     "GREY_BROWN": "#736357",
     "PINK": "#D147BD",
     "GREEN_SCREEN": "#00FF00",

manimlib/for_3b1b_videos/pi_creature_scene.py

@@ -148,12 +148,12 @@ class PiCreatureScene(Scene):
         self.pi_creature_thinks(
             self.get_primary_pi_creature(), *content, **kwargs)
 
-    def compile_play_args_to_animation_list(self, *args):
+    def compile_play_args_to_animation_list(self, *args, **kwargs):
         """
         Add animations so that all pi creatures look at the
         first mobject being animated with each .play call
         """
-        animations = Scene.compile_play_args_to_animation_list(self, *args)
+        animations = Scene.compile_play_args_to_animation_list(self, *args, **kwargs)
         if not self.any_pi_creatures_on_screen():
             return animations
 
@@ -211,21 +211,24 @@ class PiCreatureScene(Scene):
         ])
         return self
 
-    def wait(self, time=1, blink=True):
+    def wait(self, time=1, blink=True, **kwargs):
+        if "stop_condition" in kwargs:
+            self.non_blink_wait(time, **kwargs)
+            return
         while time >= 1:
             time_to_blink = self.total_wait_time % self.seconds_to_blink == 0
             if blink and self.any_pi_creatures_on_screen() and time_to_blink:
                 self.blink()
             else:
-                self.non_blink_wait()
+                self.non_blink_wait(**kwargs)
             time -= 1
             self.total_wait_time += 1
         if time > 0:
-            self.non_blink_wait(time)
+            self.non_blink_wait(time, **kwargs)
         return self
 
-    def non_blink_wait(self, time=1):
+    def non_blink_wait(self, time=1, **kwargs):
-        Scene.wait(self, time)
+        Scene.wait(self, time, **kwargs)
         return self
 
     def change_mode(self, mode):

manimlib/mobject/geometry.py

@@ -542,7 +542,7 @@ class Arrow(Line):
         "stroke_width": 6,
         "buff": MED_SMALL_BUFF,
         "tip_width_to_length_ratio": 1,
-        "max_tip_length_to_length_ratio": 0.2,
+        "max_tip_length_to_length_ratio": 0.25,
         "max_stroke_width_to_length_ratio": 6,
         "preserve_tip_size_when_scaling": True,
         "rectangular_stem_width": 0.05,
@@ -560,15 +560,17 @@ class Arrow(Line):
         has_tip = self.has_tip()
         has_start_tip = self.has_start_tip()
         if has_tip or has_start_tip:
-            self.pop_tips()
+            old_tips = self.pop_tips()
 
         VMobject.scale(self, factor, **kwargs)
         self.set_stroke_width_from_length()
 
         if has_tip:
             self.add_tip()
+            self.tip.match_style(old_tips[0])
         if has_start_tip:
             self.add_tip(at_start=True)
+            self.start_tip.match_style(old_tips[1])
         return self
 
     def get_normal_vector(self):
@@ -588,10 +590,13 @@ class Arrow(Line):
 
     def set_stroke_width_from_length(self):
         max_ratio = self.max_stroke_width_to_length_ratio
-        self.set_stroke(width=min(
+        self.set_stroke(
+            width=min(
                 self.initial_stroke_width,
                 max_ratio * self.get_length(),
-        ))
+            ),
+            family=False,
+        )
         return self
 
     # TODO, should this be the default for everything?

manimlib/mobject/mobject.py

@@ -4,6 +4,7 @@ import itertools as it
 import operator as op
 import os
 import random
+import sys
 
 from colour import Color
 import numpy as np

manimlib/mobject/number_line.py

@@ -97,7 +97,7 @@ class NumberLine(Line):
     def get_tick_numbers(self):
         return np.arange(
             self.leftmost_tick,
-            self.x_max - self.tick_frequency / 2,
+            self.x_max + self.tick_frequency / 2,
             self.tick_frequency
         )
 

manimlib/mobject/svg/drawings.py

@@ -446,7 +446,10 @@ class Bubble(SVGMobject):
         return self.get_center() + factor * self.get_height() * UP
 
     def move_tip_to(self, point):
-        VGroup(self, self.content).shift(point - self.get_tip())
+        mover = VGroup(self)
+        if self.content is not None:
+            mover.add(self.content)
+        mover.shift(point - self.get_tip())
         return self
 
     def flip(self):

manimlib/mobject/types/vectorized_mobject.py

@@ -202,6 +202,7 @@ class VMobject(Mobject):
             )
         if background_image_file:
             self.color_using_background_image(background_image_file)
+        return self
 
     def get_style(self):
         return {
@@ -209,8 +210,10 @@ class VMobject(Mobject):
             "fill_opacity": self.get_fill_opacities(),
             "stroke_color": self.get_stroke_colors(),
             "stroke_width": self.get_stroke_width(),
+            "stroke_opacity": self.get_stroke_opacity(),
             "background_stroke_color": self.get_stroke_colors(background=True),
             "background_stroke_width": self.get_stroke_width(background=True),
+            "background_stroke_opacity": self.get_stroke_opacity(background=True),
             "sheen_factor": self.get_sheen_factor(),
             "sheen_direction": self.get_sheen_direction(),
             "background_image_file": self.get_background_image_file(),
@@ -835,6 +838,8 @@ class VMobject(Mobject):
         upper_index, upper_residue = integer_interpolate(0, num_cubics, b)
 
         self.clear_points()
+        if num_cubics == 0:
+            return self
         if lower_index == upper_index:
             self.append_points(partial_bezier_points(
                 bezier_quads[lower_index],

manimlib/mobject/vector_field.py

@@ -0,0 +1,341 @@
+import numpy as np
+import os
+import itertools as it
+from PIL import Image
+import random
+
+from manimlib.constants import *
+
+from manimlib.animation.composition import AnimationGroup
+from manimlib.animation.indication import ShowPassingFlash
+from manimlib.mobject.geometry import Vector
+from manimlib.mobject.types.vectorized_mobject import VGroup
+from manimlib.mobject.types.vectorized_mobject import VMobject
+from manimlib.utils.bezier import inverse_interpolate
+from manimlib.utils.bezier import interpolate
+from manimlib.utils.color import color_to_rgb
+from manimlib.utils.color import rgb_to_color
+from manimlib.utils.config_ops import digest_config
+from manimlib.utils.rate_functions import linear
+from manimlib.utils.simple_functions import sigmoid
+from manimlib.utils.space_ops import get_norm
+# from manimlib.utils.space_ops import normalize
+
+
+DEFAULT_SCALAR_FIELD_COLORS = [BLUE_E, GREEN, YELLOW, RED]
+
+
+def get_colored_background_image(scalar_field_func,
+                                 number_to_rgb_func,
+                                 pixel_height=DEFAULT_PIXEL_HEIGHT,
+                                 pixel_width=DEFAULT_PIXEL_WIDTH):
+    ph = pixel_height
+    pw = pixel_width
+    fw = FRAME_WIDTH
+    fh = FRAME_HEIGHT
+    points_array = np.zeros((ph, pw, 3))
+    x_array = np.linspace(-fw / 2, fw / 2, pw)
+    x_array = x_array.reshape((1, len(x_array)))
+    x_array = x_array.repeat(ph, axis=0)
+
+    y_array = np.linspace(fh / 2, -fh / 2, ph)
+    y_array = y_array.reshape((len(y_array), 1))
+    y_array.repeat(pw, axis=1)
+    points_array[:, :, 0] = x_array
+    points_array[:, :, 1] = y_array
+    scalars = np.apply_along_axis(scalar_field_func, 2, points_array)
+    rgb_array = number_to_rgb_func(scalars.flatten()).reshape((ph, pw, 3))
+    return Image.fromarray((rgb_array * 255).astype('uint8'))
+
+
+def get_rgb_gradient_function(min_value=0, max_value=1,
+                              colors=[BLUE, RED],
+                              flip_alphas=True,  # Why?
+                              ):
+    rgbs = np.array(list(map(color_to_rgb, colors)))
+
+    def func(values):
+        alphas = inverse_interpolate(
+            min_value, max_value, np.array(values)
+        )
+        alphas = np.clip(alphas, 0, 1)
+        # if flip_alphas:
+        #     alphas = 1 - alphas
+        scaled_alphas = alphas * (len(rgbs) - 1)
+        indices = scaled_alphas.astype(int)
+        next_indices = np.clip(indices + 1, 0, len(rgbs) - 1)
+        inter_alphas = scaled_alphas % 1
+        inter_alphas = inter_alphas.repeat(3).reshape((len(indices), 3))
+        result = interpolate(rgbs[indices], rgbs[next_indices], inter_alphas)
+        return result
+    return func
+
+
+def get_color_field_image_file(scalar_func,
+                               min_value=0, max_value=2,
+                               colors=DEFAULT_SCALAR_FIELD_COLORS
+                               ):
+    # try_hash
+    np.random.seed(0)
+    sample_inputs = 5 * np.random.random(size=(10, 3)) - 10
+    sample_outputs = np.apply_along_axis(scalar_func, 1, sample_inputs)
+    func_hash = hash(
+        str(min_value) + str(max_value) + str(colors) + str(sample_outputs)
+    )
+    file_name = "%d.png" % func_hash
+    full_path = os.path.join(RASTER_IMAGE_DIR, file_name)
+    if not os.path.exists(full_path):
+        print("Rendering color field image " + str(func_hash))
+        rgb_gradient_func = get_rgb_gradient_function(
+            min_value=min_value,
+            max_value=max_value,
+            colors=colors
+        )
+        image = get_colored_background_image(scalar_func, rgb_gradient_func)
+        image.save(full_path)
+    return full_path
+
+
+def move_along_vector_field(mobject, func):
+    mobject.add_updater(
+        lambda m, dt: m.shift(
+            func(m.get_center()) * dt
+        )
+    )
+    return mobject
+
+
+def move_submobjects_along_vector_field(mobject, func):
+    def apply_nudge(mob, dt):
+        for submob in mob:
+            x, y = submob.get_center()[:2]
+            if abs(x) < FRAME_WIDTH and abs(y) < FRAME_HEIGHT:
+                submob.shift(func(submob.get_center()) * dt)
+
+    mobject.add_updater(apply_nudge)
+    return mobject
+
+
+def move_points_along_vector_field(mobject, func):
+    def apply_nudge(self, dt):
+        self.mobject.apply_function(
+            lambda p: p + func(p) * dt
+        )
+    mobject.add_updater(apply_nudge)
+    return mobject
+
+
+# Mobjects
+
+class VectorField(VGroup):
+    CONFIG = {
+        "delta_x": 0.5,
+        "delta_y": 0.5,
+        "x_min": int(np.floor(-FRAME_WIDTH / 2)),
+        "x_max": int(np.ceil(FRAME_WIDTH / 2)),
+        "y_min": int(np.floor(-FRAME_HEIGHT / 2)),
+        "y_max": int(np.ceil(FRAME_HEIGHT / 2)),
+        "min_magnitude": 0,
+        "max_magnitude": 2,
+        "colors": DEFAULT_SCALAR_FIELD_COLORS,
+        # Takes in actual norm, spits out displayed norm
+        "length_func": lambda norm: 0.45 * sigmoid(norm),
+        "opacity": 1.0,
+        "vector_config": {},
+    }
+
+    def __init__(self, func, **kwargs):
+        VGroup.__init__(self, **kwargs)
+        self.func = func
+        self.rgb_gradient_function = get_rgb_gradient_function(
+            self.min_magnitude,
+            self.max_magnitude,
+            self.colors,
+            flip_alphas=False
+        )
+        x_range = np.arange(
+            self.x_min,
+            self.x_max + self.delta_x,
+            self.delta_x
+        )
+        y_range = np.arange(
+            self.y_min,
+            self.y_max + self.delta_y,
+            self.delta_y
+        )
+        for x, y in it.product(x_range, y_range):
+            point = x * RIGHT + y * UP
+            self.add(self.get_vector(point))
+        self.set_opacity(self.opacity)
+
+    def get_vector(self, point, **kwargs):
+        output = np.array(self.func(point))
+        norm = get_norm(output)
+        if norm == 0:
+            output *= 0
+        else:
+            output *= self.length_func(norm) / norm
+        vector_config = dict(self.vector_config)
+        vector_config.update(kwargs)
+        vect = Vector(output, **vector_config)
+        vect.shift(point)
+        fill_color = rgb_to_color(
+            self.rgb_gradient_function(np.array([norm]))[0]
+        )
+        vect.set_color(fill_color)
+        return vect
+
+
+class StreamLines(VGroup):
+    CONFIG = {
+        # TODO, this is an awkward way to inherit
+        # defaults to a method.
+        "start_points_generator_config": {},
+        # Config for choosing start points
+        "x_min": -8,
+        "x_max": 8,
+        "y_min": -5,
+        "y_max": 5,
+        "delta_x": 0.5,
+        "delta_y": 0.5,
+        "n_repeats": 1,
+        "noise_factor": None,
+        # Config for drawing lines
+        "dt": 0.05,
+        "virtual_time": 3,
+        "n_anchors_per_line": 100,
+        "stroke_width": 1,
+        "stroke_color": WHITE,
+        "color_by_arc_length": True,
+        # Min and max arc lengths meant to define
+        # the color range, should color_by_arc_length be True
+        "min_arc_length": 0,
+        "max_arc_length": 12,
+        "color_by_magnitude": False,
+        # Min and max magnitudes meant to define
+        # the color range, should color_by_magnitude be True
+        "min_magnitude": 0.5,
+        "max_magnitude": 1.5,
+        "colors": DEFAULT_SCALAR_FIELD_COLORS,
+        "cutoff_norm": 15,
+    }
+
+    def __init__(self, func, **kwargs):
+        VGroup.__init__(self, **kwargs)
+        self.func = func
+        dt = self.dt
+
+        start_points = self.get_start_points(
+            **self.start_points_generator_config
+        )
+        for point in start_points:
+            points = [point]
+            for t in np.arange(0, self.virtual_time, dt):
+                last_point = points[-1]
+                points.append(last_point + dt * func(last_point))
+                if get_norm(last_point) > self.cutoff_norm:
+                    break
+            line = VMobject()
+            step = max(1, int(len(points) / self.n_anchors_per_line))
+            line.set_points_smoothly(points[::step])
+            self.add(line)
+
+        self.set_stroke(self.stroke_color, self.stroke_width)
+
+        if self.color_by_arc_length:
+            len_to_rgb = get_rgb_gradient_function(
+                self.min_arc_length,
+                self.max_arc_length,
+                colors=self.colors,
+            )
+            for line in self:
+                arc_length = line.get_arc_length()
+                rgb = len_to_rgb([arc_length])[0]
+                color = rgb_to_color(rgb)
+                line.set_color(color)
+        elif self.color_by_magnitude:
+            image_file = get_color_field_image_file(
+                lambda p: get_norm(func(p)),
+                min_value=self.min_magnitude,
+                max_value=self.max_magnitude,
+                colors=self.colors,
+            )
+            self.color_using_background_image(image_file)
+
+    def get_start_points(self):
+        x_min = self.x_min
+        x_max = self.x_max
+        y_min = self.y_min
+        y_max = self.y_max
+        delta_x = self.delta_x
+        delta_y = self.delta_y
+        n_repeats = self.n_repeats
+        noise_factor = self.noise_factor
+
+        if noise_factor is None:
+            noise_factor = delta_y / 2
+        return np.array([
+            x * RIGHT + y * UP + noise_factor * np.random.random(3)
+            for n in range(n_repeats)
+            for x in np.arange(x_min, x_max + delta_x, delta_x)
+            for y in np.arange(y_min, y_max + delta_y, delta_y)
+        ])
+
+
+# TODO: Make it so that you can have a group of stream_lines
+# varying in response to a changing vector field, and still
+# animate the resulting flow
+class ShowPassingFlashWithThinningStrokeWidth(AnimationGroup):
+    CONFIG = {
+        "n_segments": 10,
+        "time_width": 0.1,
+        "remover": True
+    }
+
+    def __init__(self, vmobject, **kwargs):
+        digest_config(self, kwargs)
+        max_stroke_width = vmobject.get_stroke_width()
+        max_time_width = kwargs.pop("time_width", self.time_width)
+        AnimationGroup.__init__(self, *[
+            ShowPassingFlash(
+                vmobject.deepcopy().set_stroke(width=stroke_width),
+                time_width=time_width,
+                **kwargs
+            )
+            for stroke_width, time_width in zip(
+                np.linspace(0, max_stroke_width, self.n_segments),
+                np.linspace(max_time_width, 0, self.n_segments)
+            )
+        ])
+
+
+# TODO, this is untested after turning it from a
+# ContinualAnimation into a VGroup
+class AnimatedStreamLines(VGroup):
+    CONFIG = {
+        "lag_range": 4,
+        "line_anim_class": ShowPassingFlash,
+        "line_anim_config": {
+            "run_time": 4,
+            "rate_func": linear,
+            "time_width": 0.3,
+        },
+    }
+
+    def __init__(self, stream_lines, **kwargs):
+        VGroup.__init__(self, **kwargs)
+        self.stream_lines = stream_lines
+        for line in stream_lines:
+            line.anim = self.line_anim_class(line, **self.line_anim_config)
+            line.anim.begin()
+            line.time = -self.lag_range * random.random()
+            self.add(line.anim.mobject)
+
+        self.add_updater(lambda m, dt: m.update(dt))
+
+    def update(self, dt):
+        stream_lines = self.stream_lines
+        for line in stream_lines:
+            line.time += dt
+            adjusted_time = max(line.time, 0) % line.anim.run_time
+            line.anim.update(adjusted_time / line.anim.run_time)

manimlib/scene/scene.py

@@ -503,7 +503,7 @@ class Scene(Container):
                 self.update_mobjects(dt)
                 self.update_frame()
                 self.add_frames(self.get_frame())
-                if stop_condition and stop_condition():
+                if stop_condition is not None and stop_condition():
                     time_progression.close()
                     break
         elif self.skip_animations:

manimlib/scene/vector_space_scene.py

@@ -287,6 +287,9 @@ class LinearTransformationScene(VectorScene):
         },
         "background_plane_kwargs": {
             "color": GREY,
+            "axis_config": {
+                "stroke_color": LIGHT_GREY,
+            },
             "number_line_config": {
                 "color": GREY,
             },
@@ -358,7 +361,7 @@ class LinearTransformationScene(VectorScene):
         self.add_special_mobjects(self.moving_mobjects, mobject)
 
     def get_unit_square(self, color=YELLOW, opacity=0.3, stroke_width=3):
-        square = Rectangle(
+        square = self.square = Rectangle(
             color=color,
             width=self.plane.get_x_unit_size(),
             height=self.plane.get_y_unit_size(),

old_projects/div_curl.py

@@ -1,7 +1,6 @@
 
 from big_ol_pile_of_manim_imports import *
 
-DEFAULT_SCALAR_FIELD_COLORS = [BLUE_E, GREEN, YELLOW, RED]
 
 # Quick note to anyone coming to this file with the
 # intent of recreating animations from the video.  Some
@@ -24,22 +23,6 @@ RABBIT_COLOR = "#C6D6EF"
 
 
 # Helper functions
-def get_flow_start_points(x_min=-8, x_max=8,
-                          y_min=-5, y_max=5,
-                          delta_x=0.5, delta_y=0.5,
-                          n_repeats=1,
-                          noise_factor=None
-                          ):
-    if noise_factor is None:
-        noise_factor = delta_y / 2
-    return np.array([
-        x * RIGHT + y * UP + noise_factor * np.random.random(3)
-        for n in range(n_repeats)
-        for x in np.arange(x_min, x_max + delta_x, delta_x)
-        for y in np.arange(y_min, y_max + delta_y, delta_y)
-    ])
-
-
 def joukowsky_map(z):
     if z == 0:
         return 0
@@ -99,77 +82,6 @@ def cylinder_flow_magnitude_field(point):
     return get_norm(cylinder_flow_vector_field(point))
 
 
-def get_colored_background_image(scalar_field_func,
-                                 number_to_rgb_func,
-                                 pixel_height=DEFAULT_PIXEL_HEIGHT,
-                                 pixel_width=DEFAULT_PIXEL_WIDTH,
-                                 ):
-    ph = pixel_height
-    pw = pixel_width
-    fw = FRAME_WIDTH
-    fh = FRAME_HEIGHT
-    points_array = np.zeros((ph, pw, 3))
-    x_array = np.linspace(-fw / 2, fw / 2, pw)
-    x_array = x_array.reshape((1, len(x_array)))
-    x_array = x_array.repeat(ph, axis=0)
-
-    y_array = np.linspace(fh / 2, -fh / 2, ph)
-    y_array = y_array.reshape((len(y_array), 1))
-    y_array.repeat(pw, axis=1)
-    points_array[:, :, 0] = x_array
-    points_array[:, :, 1] = y_array
-    scalars = np.apply_along_axis(scalar_field_func, 2, points_array)
-    rgb_array = number_to_rgb_func(scalars.flatten()).reshape((ph, pw, 3))
-    return Image.fromarray((rgb_array * 255).astype('uint8'))
-
-
-def get_rgb_gradient_function(min_value=0, max_value=1,
-                              colors=[BLUE, RED],
-                              flip_alphas=True,  # Why?
-                              ):
-    rgbs = np.array(list(map(color_to_rgb, colors)))
-
-    def func(values):
-        alphas = inverse_interpolate(min_value, max_value, values)
-        alphas = np.clip(alphas, 0, 1)
-        # if flip_alphas:
-        #     alphas = 1 - alphas
-        scaled_alphas = alphas * (len(rgbs) - 1)
-        indices = scaled_alphas.astype(int)
-        next_indices = np.clip(indices + 1, 0, len(rgbs) - 1)
-        inter_alphas = scaled_alphas % 1
-        inter_alphas = inter_alphas.repeat(3).reshape((len(indices), 3))
-        result = interpolate(rgbs[indices], rgbs[next_indices], inter_alphas)
-        return result
-
-    return func
-
-
-def get_color_field_image_file(scalar_func,
-                               min_value=0, max_value=2,
-                               colors=DEFAULT_SCALAR_FIELD_COLORS
-                               ):
-    # try_hash
-    np.random.seed(0)
-    sample_inputs = 5 * np.random.random(size=(10, 3)) - 10
-    sample_outputs = np.apply_along_axis(scalar_func, 1, sample_inputs)
-    func_hash = hash(
-        str(min_value) + str(max_value) + str(colors) + str(sample_outputs)
-    )
-    file_name = "%d.png" % func_hash
-    full_path = os.path.join(RASTER_IMAGE_DIR, file_name)
-    if not os.path.exists(full_path):
-        print("Rendering color field image " + str(func_hash))
-        rgb_gradient_func = get_rgb_gradient_function(
-            min_value=min_value,
-            max_value=max_value,
-            colors=colors
-        )
-        image = get_colored_background_image(scalar_func, rgb_gradient_func)
-        image.save(full_path)
-    return full_path
-
-
 def vec_tex(s):
     return "\\vec{\\textbf{%s}}" % s
 
@@ -244,204 +156,6 @@ def preditor_prey_vector_field(point):
 
 # Mobjects
 
-
-class StreamLines(VGroup):
-    CONFIG = {
-        "start_points_generator": get_flow_start_points,
-        "start_points_generator_config": {},
-        "dt": 0.05,
-        "virtual_time": 3,
-        "n_anchors_per_line": 100,
-        "stroke_width": 1,
-        "stroke_color": WHITE,
-        "color_lines_by_magnitude": True,
-        "min_magnitude": 0.5,
-        "max_magnitude": 1.5,
-        "colors": DEFAULT_SCALAR_FIELD_COLORS,
-        "cutoff_norm": 15,
-    }
-
-    def __init__(self, func, **kwargs):
-        VGroup.__init__(self, **kwargs)
-        self.func = func
-        dt = self.dt
-
-        start_points = self.start_points_generator(
-            **self.start_points_generator_config
-        )
-        for point in start_points:
-            points = [point]
-            for t in np.arange(0, self.virtual_time, dt):
-                last_point = points[-1]
-                points.append(last_point + dt * func(last_point))
-                if get_norm(last_point) > self.cutoff_norm:
-                    break
-            line = VMobject()
-            step = max(1, int(len(points) / self.n_anchors_per_line))
-            line.set_points_smoothly(points[::step])
-            self.add(line)
-
-        self.set_stroke(self.stroke_color, self.stroke_width)
-
-        if self.color_lines_by_magnitude:
-            image_file = get_color_field_image_file(
-                lambda p: get_norm(func(p)),
-                min_value=self.min_magnitude,
-                max_value=self.max_magnitude,
-                colors=self.colors,
-            )
-            self.color_using_background_image(image_file)
-
-
-class VectorField(VGroup):
-    CONFIG = {
-        "delta_x": 0.5,
-        "delta_y": 0.5,
-        "x_min": int(np.floor(-FRAME_WIDTH / 2)),
-        "x_max": int(np.ceil(FRAME_WIDTH / 2)),
-        "y_min": int(np.floor(-FRAME_HEIGHT / 2)),
-        "y_max": int(np.ceil(FRAME_HEIGHT / 2)),
-        "min_magnitude": 0,
-        "max_magnitude": 2,
-        "colors": DEFAULT_SCALAR_FIELD_COLORS,
-        # Takes in actual norm, spits out displayed norm
-        "length_func": lambda norm: 0.5 * sigmoid(norm),
-        "stroke_color": BLACK,
-        "stroke_width": 0.5,
-        "fill_opacity": 1.0,
-        "vector_config": {},
-    }
-
-    def __init__(self, func, **kwargs):
-        VGroup.__init__(self, **kwargs)
-        self.func = func
-        self.rgb_gradient_function = get_rgb_gradient_function(
-            self.min_magnitude,
-            self.max_magnitude,
-            self.colors,
-            flip_alphas=False
-        )
-        for x in np.arange(self.x_min, self.x_max, self.delta_x):
-            for y in np.arange(self.y_min, self.y_max, self.delta_y):
-                point = x * RIGHT + y * UP
-                self.add(self.get_vector(point))
-
-    def get_vector(self, point, **kwargs):
-        output = np.array(self.func(point))
-        norm = get_norm(output)
-        if norm == 0:
-            output *= 0
-        else:
-            output *= self.length_func(norm) / norm
-        vector_config = dict(self.vector_config)
-        vector_config.update(kwargs)
-        vect = Vector(output, **vector_config)
-        vect.shift(point)
-        fill_color = rgb_to_color(
-            self.rgb_gradient_function(np.array([norm]))[0]
-        )
-        vect.set_color(fill_color)
-        vect.set_fill(opacity=self.fill_opacity)
-        vect.set_stroke(
-            self.stroke_color,
-            self.stroke_width
-        )
-        return vect
-
-
-# Redefining what was once a ContinualAnimation class
-# as a function
-def VectorFieldFlow(mobject, func):
-    mobject.add_updater(
-        lambda m, dt: m.shift(
-            func(m.get_center()) * dt
-        )
-    )
-    return mobject
-
-
-# Redefining what was once a ContinualAnimation class
-# as a function
-def VectorFieldSubmobjectFlow(mobject, func):
-    def apply_nudge(mob, dt):
-        for submob in mob:
-            x, y = submob.get_center()[:2]
-            if abs(x) < FRAME_WIDTH and abs(y) < FRAME_HEIGHT:
-                submob.shift(func(submob.get_center()) * dt)
-
-    mobject.add_updater(apply_nudge)
-    return mobject
-
-
-# Redefining what was once a ContinualAnimation class
-# as a function
-def VectorFieldPointFlow(mobject, func):
-    def apply_nudge(self, dt):
-        self.mobject.apply_function(
-            lambda p: p + func(p) * dt
-        )
-    mobject.add_updater(apply_nudge)
-    return mobject
-
-
-# TODO: Make it so that you can have a group of stream_lines
-# varying in response to a changing vector field, and still
-# animate the resulting flow
-class ShowPassingFlashWithThinningStrokeWidth(AnimationGroup):
-    CONFIG = {
-        "n_segments": 10,
-        "time_width": 0.1,
-        "remover": True
-    }
-
-    def __init__(self, vmobject, **kwargs):
-        digest_config(self, kwargs)
-        max_stroke_width = vmobject.get_stroke_width()
-        max_time_width = kwargs.pop("time_width", self.time_width)
-        AnimationGroup.__init__(self, *[
-            ShowPassingFlash(
-                vmobject.deepcopy().set_stroke(width=stroke_width),
-                time_width=time_width,
-                **kwargs
-            )
-            for stroke_width, time_width in zip(
-                np.linspace(0, max_stroke_width, self.n_segments),
-                np.linspace(max_time_width, 0, self.n_segments)
-            )
-        ])
-
-
-# TODO, this is untested after turning it from a
-# ContinualAnimation into a VGroup
-class AnimatedStreamLines(VGroup):
-    CONFIG = {
-        "lag_range": 4,
-        "line_anim_class": ShowPassingFlash,
-        "line_anim_config": {
-            "run_time": 4,
-            "rate_func": linear,
-            "time_width": 0.3,
-        },
-    }
-
-    def __init__(self, stream_lines, **kwargs):
-        VGroup.__init__(self, **kwargs)
-        self.stream_lines = stream_lines
-        for line in stream_lines:
-            line.anim = self.line_anim_class(line, **self.line_anim_config)
-            line.time = -self.lag_range * random.random()
-            self.add(line.anim.mobject)
-
-        self.add_updater(lambda m, dt: m.update(dt))
-
-    def update(self, dt):
-        stream_lines = self.stream_lines
-        for line in stream_lines:
-            line.time += dt
-            adjusted_time = max(line.time, 0) % line.anim.run_time
-            line.anim.update(adjusted_time / line.anim.run_time)
-
-
 # TODO, this is untested after turning it from a
 # ContinualAnimation into a VGroup
 class JigglingSubmobjects(VGroup):
@@ -3066,7 +2780,7 @@ class ShowTwoPopulations(Scene):
             self.start_num_rabbits * RIGHT +
             self.start_num_foxes * UP
         )
-        self.add(VectorFieldFlow(
+        self.add(move_along_vector_field(
             phase_point,
             preditor_prey_vector_field,
         ))
@@ -3420,7 +3134,7 @@ class PhaseSpaceOfPopulationModel(ShowTwoPopulations, PiCreatureScene, MovingCam
             dot_vector = new_dot_vector
             self.play(dot.move_to, dot_vector.get_end())
 
-        dot_movement = VectorFieldFlow(
+        dot_movement = move_along_vector_field(
             dot, lambda p: 0.3 * vector_field.func(p)
         )
         self.add(dot_movement)

old_projects/turbulence.py

@@ -1,7 +1,7 @@
 from big_ol_pile_of_manim_imports import *
 from old_projects.div_curl import PureAirfoilFlow
-from old_projects.div_curl import VectorFieldSubmobjectFlow
+from old_projects.div_curl import move_submobjects_along_vector_field
-from old_projects.div_curl import VectorFieldPointFlow
+from old_projects.div_curl import move_points_along_vector_field
 from old_projects.div_curl import four_swirls_function
 from old_projects.lost_lecture import ShowWord
 
@@ -836,7 +836,7 @@ class LaminarFlowLabel(Scene):
 
 class HighCurlFieldBreakingLayers(Scene):
     CONFIG = {
-        "flow_anim": VectorFieldSubmobjectFlow,
+        "flow_anim": move_submobjects_along_vector_field,
     }
 
     def construct(self):
@@ -870,7 +870,7 @@ class HighCurlFieldBreakingLayers(Scene):
 
 class HighCurlFieldBreakingLayersLines(HighCurlFieldBreakingLayers):
     CONFIG = {
-        "flow_anim": VectorFieldPointFlow
+        "flow_anim": move_points_along_vector_field
     }
 
     def get_line(self):