3b1b-manim/active_projects/WindingNumber_G.py

from helpers import *

from mobject.tex_mobject import TexMobject
from mobject import Mobject
from mobject.image_mobject import ImageMobject
from mobject.vectorized_mobject 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 *
from mobject.svg_mobject import *
from mobject.tex_mobject import *
from topics.graph_scene import *

from active_projects.WindingNumber import *

class AltTeacherStudentScene(TeacherStudentsScene):
    def setup(self):
        TeacherStudentsScene.setup(self)
        self.teacher.set_color(YELLOW_E)

###############


class TestColorMap(ColorMappedObjectsScene):
    CONFIG = {
        "func" : example_plane_func,
    }
    def construct(self):
        ColorMappedObjectsScene.construct(self)
        circle = Circle(color = WHITE)
        circle.color_using_background_image(self.background_image_file)

        self.play(ShowCreation(circle))
        self.play(circle.scale, 2)
        self.wait()
        self.play(circle.set_fill, {"opacity" : 0.2})
        for corner in standard_rect:
            self.play(circle.to_corner, corner, run_time = 2)


class PiCreaturesAreIntrigued(AltTeacherStudentScene):
    def construct(self):
        self.teacher_says(
            "You can extend \\\\ this to 2d",
            bubble_kwargs = {"width" : 4, "height" : 3}
        )
        self.change_student_modes("pondering", "confused", "erm")
        self.look_at(self.screen)
        self.wait(3)

class RewriteEquationWithTeacher(AltTeacherStudentScene):
    def construct(self):
        equations = VGroup(
            TexMobject(
                "f(\\text{2d input})", "", "=", 
                "g(\\text{2d input})", ""
            ),
            TexMobject(
                "f(\\text{2d input})", "-", 
                "g(\\text{2d input})", "=", "0"
            ),
        )
        specific_equations = VGroup(
            TexMobject("x^2", "", "=", "2", ""),
            TexMobject("x^2", "-", "2", "=", "0"),
        )
        for equation in it.chain(equations, specific_equations):
            equation.sort_submobjects_alphabetically()
            for part in equation.get_parts_by_tex("text"):
                part[2:-1].highlight(YELLOW)
                part[2:-1].scale(0.9)
            equation.move_to(self.hold_up_spot, DOWN)

        self.teacher_holds_up(specific_equations[0])
        self.play(Transform(*specific_equations, path_arc = TAU/4))
        self.play(self.get_student_changes(*["pondering"]*3))
        self.play(FadeOut(specific_equations[0]), FadeIn(equations[0]))
        self.wait()
        self.play(Transform(*equations, path_arc = TAU/4))
        self.change_student_modes(*["happy"]*3)

        # 2d plane
        plane = NumberPlane(x_radius = 2.5, y_radius = 2.5)
        plane.scale(0.8)
        plane.to_corner(UP+LEFT)
        plane.add_coordinates()

        dot = Dot(color = YELLOW)
        label = TextMobject("Sign?")
        label.add_background_rectangle()
        label.scale(0.5)
        label.next_to(dot, UP, SMALL_BUFF)
        dot.add(label)
        dot.move_to(plane.coords_to_point(1, 1))
        dot.save_state()
        dot.fade(1)
        dot.center()

        question = TextMobject(
            "Wait...what would \\\\", "+", "and", "\\textminus", " \\, be in 2d?",
        )
        question.highlight_by_tex_to_color_map({
            "+" : "green", 
            "textminus" : "red"
        })

        self.student_says(
            question,
            target_mode = "sassy",
            student_index = 2,
            added_anims = [
                equations[0].to_corner, UP+RIGHT,
                self.teacher.change, "plain",
            ],
            bubble_kwargs = {"direction" : LEFT},
            run_time = 1,
        )
        self.play(
            Write(plane, run_time = 1),
            self.students[0].change, "confused",
            self.students[1].change, "confused",
        )
        self.play(dot.restore)
        for coords in (-1, 1), (1, -1), (0, -2), (-2, 1):
            self.wait(0.5)
            self.play(dot.move_to, plane.coords_to_point(*coords))
        self.wait()

class DotsHoppingToColor(Scene):
    CONFIG = {
        "dot_radius" : 0.05,
        "plane_width" : 6,
        "plane_height" : 6,
        "x_shift" : SPACE_WIDTH/2,
        "y_shift" : MED_LARGE_BUFF,
        "output_scalar" : 10,
    }
    def construct(self):
        input_coloring, output_coloring = self.get_colorings()
        input_plane, output_plane = self.get_planes()

        v_line = Line(UP, DOWN).scale(SPACE_HEIGHT)
        v_line.set_stroke(WHITE, 5)

        dots = self.get_dots(input_plane, output_plane)

        right_half_block = Rectangle(
            height = 2*SPACE_HEIGHT,
            width = SPACE_WIDTH - SMALL_BUFF,
            stroke_width = 0,
            fill_color = BLACK,
            fill_opacity = 0.8,
        )
        right_half_block.to_edge(RIGHT, buff = 0)

        #Introduce parts
        self.add(input_plane, output_plane, v_line)
        self.play(
            FadeIn(output_coloring), 
            Animation(output_plane),
            output_plane.white_parts.highlight, BLACK,
            output_plane.lines_to_fade.set_stroke, {"width" : 0},
        )
        self.wait()
        self.play(LaggedStart(GrowFromCenter, dots, run_time = 3))
        self.wait()

        #Hop over and back
        self.play(LaggedStart(
            MoveToTarget, dots, 
            path_arc = -TAU/4,
            run_time = 3,
        ))
        self.wait()
        self.play(LaggedStart(
            ApplyMethod, dots,
            lambda d : (d.set_fill, d.target_color),
        ))
        self.wait()
        self.play(LaggedStart(
            ApplyMethod, dots,
            lambda d : (d.move_to, d.original_position),
            path_arc = TAU/4,
            run_time = 3,
        ))
        self.wait()
        self.play(
            FadeIn(input_coloring),
            Animation(input_plane),
            input_plane.white_parts.highlight, BLACK,
            input_plane.lines_to_fade.set_stroke, {"width" : 0},
            LaggedStart(
                ApplyFunction, dots,
                lambda dot : (lambda d : d.set_stroke(width = 0).scale(0.25), dot)
            ),
        )
        self.wait()

        #Cover output half
        right_half_block.save_state()
        right_half_block.next_to(SPACE_WIDTH*RIGHT, RIGHT)
        self.play(right_half_block.restore)
        self.wait()
        self.play(LaggedStart(
            ApplyMethod, dots,
            lambda d : (d.shift, SMALL_BUFF*UP),
            rate_func = wiggle,
        ))
        self.wait()

    ###

    def func(self, coord_pair):
        out_coords = np.array(example_plane_func(coord_pair))
        out_norm = np.linalg.norm(out_coords)
        if out_norm > 0.5:
            angle = angle_of_vector(out_coords)
            factor = 0.5-0.1*np.cos(4*angle)
            target_norm = factor*np.log(out_norm)
            out_coords *= target_norm / out_norm
        return tuple(out_coords)

    def get_colorings(self):
        in_cmos = ColorMappedObjectsScene(
            func = lambda p : self.func(
                (p[0]+self.x_shift, p[1]+self.y_shift)
            )
        )
        scalar = self.output_scalar
        out_cmos = ColorMappedObjectsScene(
            func = lambda p : (
                scalar*(p[0]-self.x_shift), scalar*(p[1]+self.y_shift)
            )
        )

        input_coloring = Rectangle(
            height = self.plane_height,
            width = self.plane_width,
            stroke_width = 0,
            fill_color = WHITE,
            fill_opacity = 1,
        )
        output_coloring = input_coloring.copy()
        colorings = [input_coloring, output_coloring]
        vects = [LEFT, RIGHT]
        cmos_pair = [in_cmos, out_cmos]
        for coloring, vect, cmos in zip(colorings, vects, cmos_pair):
            coloring.move_to(self.x_shift*vect + self.y_shift*DOWN)
            coloring.color_using_background_image(cmos.background_image_file)
        return colorings

    def get_planes(self):
        input_plane = NumberPlane(
            x_radius = self.plane_width/2.0,
            y_radius = self.plane_height/2.0,
        )
        output_plane = input_plane.copy()
        planes = [input_plane, output_plane]
        vects = [LEFT, RIGHT]
        label_texts = ["Input", "Output"]
        label_colors = [GREEN, RED]
        for plane, vect, text, color in zip(planes, vects, label_texts, label_colors):
            plane.stretch_to_fit_width(self.plane_width)
            plane.add_coordinates(x_vals = range(-2, 3), y_vals = range(-2, 3))
            plane.white_parts = VGroup(plane.axes, plane.coordinate_labels)
            plane.lines_to_fade = VGroup(plane.main_lines, plane.secondary_lines)
            plane.move_to(vect*SPACE_WIDTH/2 + self.y_shift*DOWN)
            label = TextMobject(text)
            label.scale(1.5)
            label.add_background_rectangle()
            label.move_to(plane)
            label.to_edge(UP, buff = MED_SMALL_BUFF)
            plane.add(label)
            plane.label = label
            for submob in plane.submobject_family():
                if isinstance(submob, TexMobject) and hasattr(submob, "background_rectangle"):
                    submob.remove(submob.background_rectangle)


        return planes

    def get_dots(self, input_plane, output_plane):
        step = 0.25
        x_min = -3.0
        x_max = 3.0
        y_min = -3.0
        y_max = 3.0
        dots = VGroup()
        for x in np.arange(x_min, x_max + step, step):
            for y in np.arange(y_min, y_max + step, step):
                out_coords = self.func((x, y))
                dot = Dot(radius = self.dot_radius)
                dot.set_stroke(BLACK, 1)
                dot.move_to(input_plane.coords_to_point(x, y))
                dot.original_position = dot.get_center()
                dot.generate_target()
                dot.target.move_to(output_plane.coords_to_point(*out_coords))
                dot.target_color = rgba_to_color(point_to_rgba(
                    tuple(self.output_scalar*np.array(out_coords))
                ))
                dots.add(dot)
        return dots