3b1b-manim/active_projects/fourier.py

from helpers import *


from animation.animation import Animation
from animation.transform import *
from animation.simple_animations import *
from animation.playground import *
from animation.continual_animation import *
from topics.geometry import *
from topics.characters import *
from topics.functions import *
from topics.fractals import *
from topics.number_line import *
from topics.combinatorics import *
from topics.numerals import *
from topics.three_dimensions import *
from topics.objects import *
from topics.probability import *
from topics.complex_numbers import *
from scene import Scene
from scene.reconfigurable_scene import ReconfigurableScene
from scene.zoomed_scene import *
from camera import Camera
from mobject import *
from mobject.image_mobject import *
from mobject.vectorized_mobject import *
from mobject.svg_mobject import *
from mobject.tex_mobject import *
from topics.graph_scene import *

#revert_to_original_skipping_status

class AddingPureFrequencies(PiCreatureScene):
    CONFIG = {
        "A_frequency" : 2.1,
        "A_color" : YELLOW,
        "D_color" : PINK,
        "sum_color" : GREEN,
        "equilibrium_height" : 1.5,
    }
    def construct(self):
        self.force_skipping()

        self.add_speaker()
        self.play_A440()
        self.measure_air_pressure()
        self.play_lower_pitch()
        self.play_mix()
        self.separate_out_parts()
        self.draw_sum_at_single_point()
        self.draw_full_sum()
        self.add_more_notes()

    def add_speaker(self):
        speaker = SVGMobject(file_name = "speaker")
        speaker.to_edge(DOWN)

        self.add(speaker)
        self.speaker = speaker

    def play_A440(self):
        randy = self.pi_creature
        A_label = TextMobject("A440")
        A_label.highlight(self.A_color)
        A_label.next_to(self.speaker, UP)

        self.broadcast(
            FadeIn(A_label),
            randy.change, "pondering"
        )
        self.dither()

        self.set_variables_as_attrs(A_label)

    def measure_air_pressure(self):
        randy = self.pi_creature
        axes = Axes(
            y_min = -2, y_max = 2,
            x_min = 0, x_max = 10,
            number_line_config = {"include_tip" : False},
        )
        axes.stretch_to_fit_height(2)
        axes.to_corner(UP+LEFT)
        axes.shift(LARGE_BUFF*DOWN)
        eh = self.equilibrium_height
        equilibrium_line = DashedLine(
            axes.coords_to_point(0, eh),
            axes.coords_to_point(axes.x_max, eh),
            stroke_width = 2,
            stroke_color = LIGHT_GREY
        )

        frequency = self.A_frequency
        graph = self.get_wave_graph(frequency, axes)
        func = graph.underlying_function
        graph.highlight(self.A_color)
        pressure = TextMobject("Pressure")
        time = TextMobject("Time")
        for label in pressure, time:
            label.scale_in_place(0.8)
        pressure.next_to(axes.y_axis, UP)
        pressure.to_edge(LEFT, buff = MED_SMALL_BUFF)
        time.next_to(axes.x_axis.get_right(), DOWN+LEFT)
        axes.labels = VGroup(pressure, time)

        n = 10
        brace = Brace(Line(
            axes.coords_to_point(n/frequency, func(n/frequency)),
            axes.coords_to_point((n+1)/frequency, func((n+1)/frequency)),
        ), UP)
        words = brace.get_text("Imagine 440 per second", buff = SMALL_BUFF)
        words.scale(0.8, about_point = words.get_bottom())

        self.play(
            FadeIn(pressure),
            ShowCreation(axes.y_axis)
        )
        self.play(
            Write(time),
            ShowCreation(axes.x_axis)
        )
        self.dither()
        self.broadcast(
            randy.change, "erm", graph,
            ShowCreation(graph, run_time = 4, rate_func = None),
            ShowCreation(equilibrium_line),
        )
        axes.add(equilibrium_line)
        self.play(
            GrowFromCenter(brace),
            Write(words)
        )
        self.dither(2)
        graph.save_state()
        self.play(
            FadeOut(brace),
            FadeOut(words),
            VGroup(axes, graph, axes.labels).shift, 0.8*UP,
            graph.fade, 0.85,
            graph.shift, 0.8*UP,
        )

        graph.saved_state.move_to(graph)
        self.set_variables_as_attrs(axes, A_graph = graph)

    def play_lower_pitch(self):
        axes = self.axes
        randy = self.pi_creature

        frequency = self.A_frequency*(2.0/3.0)
        graph = self.get_wave_graph(frequency, axes)
        graph.set_color(self.D_color)

        D_label = TextMobject("D294")
        D_label.highlight(self.D_color)
        D_label.move_to(self.A_label)

        self.play(
            FadeOut(self.A_label),
            GrowFromCenter(D_label),
        )
        self.broadcast(
            ShowCreation(graph, run_time = 4, rate_func = None),
            randy.change, "happy",
            n_circles = 6,
        )
        self.play(randy.change, "confused", graph)
        self.dither(2)

        self.set_variables_as_attrs(
            D_label,
            D_graph = graph
        )

    def play_mix(self):
        self.A_graph.restore()
        self.broadcast(
            self.get_broadcast_animation(n_circles = 6),
            self.pi_creature.change, "thinking",
            *[
                ShowCreation(graph, run_time = 4, rate_func = None)
                for graph in self.A_graph, self.D_graph
            ]
        )
        self.dither()

    def separate_out_parts(self):
        axes = self.axes
        speaker = self.speaker
        randy = self.pi_creature

        A_axes = axes.deepcopy()
        A_graph = self.A_graph
        A_label = self.A_label
        D_axes = axes.deepcopy()
        D_graph = self.D_graph
        D_label = self.D_label
        movers = [A_axes, A_graph, A_label, D_axes, D_graph, D_label]
        for mover in movers:
            mover.generate_target()
        D_target_group = VGroup(D_axes.target, D_graph.target)
        A_target_group = VGroup(A_axes.target, A_graph.target)
        D_target_group.next_to(axes, DOWN, MED_LARGE_BUFF)
        A_target_group.next_to(D_target_group, DOWN, MED_LARGE_BUFF)
        A_label.fade(1)
        A_label.target.next_to(A_graph.target, UP)
        D_label.target.next_to(D_graph.target, UP)

        self.play(*it.chain(
            map(MoveToTarget, movers),
            [
                ApplyMethod(mob.shift, SPACE_HEIGHT*DOWN, remover = True)
                for mob in  randy, speaker
            ]
        ))
        self.dither()

        self.set_variables_as_attrs(A_axes, D_axes)

    def draw_sum_at_single_point(self):
        axes = self.axes
        A_axes = self.A_axes
        D_axes = self.D_axes
        A_graph = self.A_graph
        D_graph = self.D_graph

        x = 2.85
        A_line = self.get_A_graph_v_line(x)
        D_line = self.get_D_graph_v_line(x)
        lines = VGroup(A_line, D_line)
        sum_lines = lines.copy()
        sum_lines.generate_target()
        self.stack_v_lines(x, sum_lines.target)

        top_axes_point = axes.coords_to_point(x, self.equilibrium_height)
        x_point = np.array(top_axes_point)
        x_point[1] = 0
        l_rect, r_rect = rects = VGroup(*[
            FullScreenFadeRectangle().next_to(x_point, vect, SMALL_BUFF)
            for vect in LEFT, RIGHT
        ])
        rects.save_state()
        for rect, vect in zip(rects, [LEFT, RIGHT]):
            rect.next_to(SPACE_WIDTH*vect, vect)

        self.play(rects.restore)
        self.play(*map(ShowCreation, lines))
        self.dither()
        self.play(MoveToTarget(sum_lines, path_arc = np.pi/4))
        self.dither(2)
        self.play(
            l_rect.next_to, SPACE_WIDTH*LEFT, LEFT,
            r_rect.next_to, SPACE_WIDTH*RIGHT, RIGHT,
            *[
                Transform(
                    line, 
                    VectorizedPoint(axes.coords_to_point(0, self.equilibrium_height)),
                    remover = True
                )
                for line, axes in [
                    (A_line, A_axes),
                    (D_line, D_axes),
                    (sum_lines, axes),
                ]
            ]
        )

    def draw_full_sum(self):
        axes = self.axes

        def new_func(x):
            result = self.A_graph.underlying_function(x)
            result += self.D_graph.underlying_function(x)
            result -= self.equilibrium_height
            return result

        graph = axes.get_graph(new_func)
        graph.highlight(self.sum_color)
        graph_copy = graph.deepcopy()

        all_v_lines = VGroup(
            self.get_A_graph_v_line(0),
            self.get_D_graph_v_line(0),
            self.get_graph_v_line(0, axes, graph)
        )
        x_max = axes.x_max
        def update_all_v_lines(v_lines, alpha):
            A_line, D_line, sum_line = v_lines
            x = alpha*x_max
            Transform(A_line, self.get_A_graph_v_line(x)).update(1)
            Transform(D_line, self.get_D_graph_v_line(x)).update(1)
            Transform(
                sum_line, 
                self.get_graph_v_line(x, axes, graph_copy)
            ).update(1)
            return v_lines

        self.play(
            UpdateFromAlphaFunc(all_v_lines, update_all_v_lines),
            ShowCreation(graph),
            run_time = 15,
            rate_func = None
        )
        self.dither()

    def add_more_notes(self):
        axes = self.axes
        A_label = self.A_label
        D_label = self.D_label
        
        A_group = VGroup(self.A_axes, self.A_graph)
        D_group = VGroup(self.D_axes, self.D_graph)


    ####

    def broadcast(self, *added_anims, **kwargs):
        self.play(self.get_broadcast_animation(**kwargs), *added_anims)

    def get_broadcast_animation(self, **kwargs):
        kwargs["run_time"] = kwargs.get("run_time", 5)
        kwargs["n_circles"] = kwargs.get("n_circles", 10)
        return Broadcast(self.speaker[1], **kwargs)

    def get_wave_graph(self, frequency, axes):
        tail_len = 3.0
        x_min, x_max = axes.x_min, axes.x_max
        def func(x):
            value = 0.7*np.cos(2*np.pi*frequency*x)
            if x - x_min < tail_len:
                value *= smooth((x-x_min)/tail_len)
            if x_max - x < tail_len:
                value *= smooth((x_max - x )/tail_len)
            return value + self.equilibrium_height
        ngp = 2*(x_max - x_min)*frequency + 1
        graph = axes.get_graph(func, num_graph_points = ngp)
        return graph

    def get_A_graph_v_line(self, x):
        return self.get_graph_v_line(x, self.A_axes, self.A_graph)

    def get_D_graph_v_line(self, x):
        return self.get_graph_v_line(x, self.D_axes, self.D_graph)

    def get_graph_v_line(self, x, axes, graph):
        result = Line(
            axes.coords_to_point(x, self.equilibrium_height),
            # axes.coords_to_point(x, graph.underlying_function(x)),
            graph.point_from_proportion(float(x)/axes.x_max),
            color = WHITE,
            buff = 0,
        )
        return result
    
    def stack_v_lines(self, x, lines):
        point = self.axes.coords_to_point(x, self.equilibrium_height)
        A_line, D_line = lines
        A_line.shift(point - A_line.get_start())
        D_line.shift(A_line.get_end()-D_line.get_start())
        A_line.highlight(self.A_color)
        D_line.highlight(self.D_color)
        return lines

    def create_pi_creature(self):
        return Randolph().to_corner(DOWN+LEFT)