3b1b-manim/brachistochrone/wordplay.py

import numpy as np
import itertools as it
import os

from helpers import *

from mobject.tex_mobject import TexMobject, TextMobject, Brace
from mobject import Mobject
from mobject.image_mobject import \
    ImageMobject, MobjectFromPixelArray
from topics.three_dimensions import Stars

from animation import Animation
from animation.transform import *
from animation.simple_animations import *
from animation.playground import TurnInsideOut, Vibrate
from topics.geometry import *
from topics.characters import Randolph, Mathematician
from topics.functions import ParametricFunction, FunctionGraph
from topics.number_line import NumberPlane
from mobject.region import  Region, region_from_polygon_vertices
from scene import Scene
from generate_logo import LogoGeneration
from brachistochrone.drawing_images import sort_by_color

class Intro(Scene):
    def construct(self):
        logo = ImageMobject("LogoGeneration", invert = False)
        name_mob = TextMobject("3Blue1Brown").center()
        name_mob.highlight("grey")
        name_mob.shift(2*DOWN)
        self.add(name_mob, logo)

        new_text = TextMobject(["with ", "Steven Strogatz"])
        new_text.next_to(name_mob, DOWN)
        self.play(*[
            ShimmerIn(part)
            for part in new_text.split()
        ])
        self.dither()
        with_word, steve = new_text.split()
        steve_copy = steve.copy().center().to_edge(UP)
        # logo.sort_points(lambda p : -np.linalg.norm(p))
        sort_by_color(logo)
        self.play(
            Transform(steve, steve_copy),
            DelayByOrder(Transform(logo, Point())),
            FadeOut(with_word),
            FadeOut(name_mob),
            run_time = 3
        )


class IntroduceSteve(Scene):
    def construct(self):
        name = TextMobject("Steven Strogatz")
        name.to_edge(UP)
        contributions = TextMobject("Frequent Contributions")
        contributions.scale(0.5).to_edge(RIGHT).shift(2*UP)
        books_word = TextMobject("Books")
        books_word.scale(0.5).to_edge(LEFT).shift(2*UP)
        radio_lab, sci_fri, cornell, book2, book3, book4 = [
            ImageMobject(filename, invert = False, filter_color = WHITE)
            for filename in [
                "radio_lab",
                "science_friday",
                "cornell",
                "strogatz_book2",
                "strogatz_book3",
                "strogatz_book4",
            ]
        ]
        book1 = ImageMobject("strogatz_book1", invert = False)
        nyt = ImageMobject("new_york_times")
        logos = [radio_lab, nyt, sci_fri]
        books = [book1, book2, book3, book4]

        sample_size = Square(side_length = 2)
        last = contributions        
        for image in logos:
            image.replace(sample_size)
            image.next_to(last, DOWN)
            last = image
        sci_fri.scale_in_place(0.9)
        shift_val = 0
        sample_size.scale(0.75)
        for book in books:
            book.replace(sample_size)
            book.next_to(books_word, DOWN)
            book.shift(shift_val*(RIGHT+DOWN))
            shift_val += 0.5
        sample_size.scale(2)
        cornell.replace(sample_size)
        cornell.next_to(name, DOWN)

        self.add(name)
        self.play(FadeIn(cornell))
        self.play(ShimmerIn(books_word))
        for book in books:
            book.shift(5*LEFT)
            self.play(ApplyMethod(book.shift, 5*RIGHT))
        self.play(ShimmerIn(contributions))
        for logo in logos:
            self.play(FadeIn(logo))
        self.dither()

class ShowTweets(Scene):
    def construct(self):
        tweets = [
            ImageMobject("tweet%d"%x, invert = False)
            for x in range(1, 4)
        ]
        for tweet in tweets:
            tweet.scale(0.4)
        tweets[0].to_corner(UP+LEFT)
        tweets[1].next_to(tweets[0], RIGHT, aligned_edge = UP)
        tweets[2].next_to(tweets[1], DOWN)

        self.play(GrowFromCenter(tweets[0]))
        for x in 1, 2:
            self.play(
                Transform(Point(tweets[x-1].get_center()), tweets[x]),
                Animation(tweets[x-1])
            )
        self.dither()

class LetsBeHonest(Scene):
    def construct(self):
        self.play(ShimmerIn(TextMobject("""
            Let's be honest about who benefits 
            from this collaboration...
        """)))
        self.dither()


class DisectBrachistochroneWord(Scene):
    def construct(self):
        word = TextMobject(["Bra", "chis", "to", "chrone"])
        original_word = word.copy()
        dots = []
        for part in word.split():
            if dots:
                part.next_to(dots[-1], buff = 0.06)
            dot = TexMobject("\\cdot")
            dot.next_to(part, buff = 0.06)
            dots.append(dot)
        dots = Mobject(*dots[:-1])
        dots.shift(0.1*DOWN)
        Mobject(word, dots).center()
        overbrace1 = Brace(Mobject(*word.split()[:-1]), UP)
        overbrace2 = Brace(word.split()[-1], UP)
        shortest = TextMobject("Shortest")
        shortest.next_to(overbrace1, UP)
        shortest.highlight(YELLOW)
        time = TextMobject("Time")
        time.next_to(overbrace2, UP)
        time.highlight(YELLOW)
        chrono_example = TextMobject("""
            As in ``Chronological'' \\\\
            or ``Synchronize''
        """)
        chrono_example.scale(0.5)
        chrono_example.to_edge(RIGHT)
        chrono_example.shift(2*UP)
        chrono_example.highlight(BLUE_D)
        chrono_arrow = Arrow(
            word.get_right(), 
            chrono_example.get_bottom(), 
            color = BLUE_D
        )
        brachy_example = TextMobject("As in . . . brachydactyly?")
        brachy_example.scale(0.5)
        brachy_example.to_edge(LEFT)
        brachy_example.shift(2*DOWN)
        brachy_example.highlight(GREEN)
        brachy_arrow = Arrow(
            word.get_left(),
            brachy_example.get_top(), 
            color = GREEN
        )

        pronunciation = TextMobject(["/br", "e", "kist","e","kr$\\bar{o}$n/"])
        pronunciation.split()[1].rotate_in_place(np.pi)
        pronunciation.split()[3].rotate_in_place(np.pi) 
        pronunciation.scale(0.7)
        pronunciation.shift(DOWN)

        latin = TextMobject(list("Latin"))
        greek = TextMobject(list("Greek"))
        for mob in latin, greek:
            mob.to_edge(LEFT)
        question_mark = TextMobject("?").next_to(greek, buff = 0.1)
        stars = Stars().highlight(BLACK)
        stars.scale(0.5).shift(question_mark.get_center())

        self.play(Transform(original_word, word), ShowCreation(dots))
        self.play(ShimmerIn(pronunciation))
        self.dither()
        self.play(
            GrowFromCenter(overbrace1),
            GrowFromCenter(overbrace2)
        )
        self.dither()
        self.play(ShimmerIn(latin))
        self.play(FadeIn(question_mark))
        self.play(Transform(
            latin, greek,
            path_func = counterclockwise_path()
        ))
        self.dither()
        self.play(Transform(question_mark, stars))
        self.remove(stars)
        self.dither()
        self.play(ShimmerIn(shortest))
        self.play(ShimmerIn(time))
        for ex, ar in [(chrono_example, chrono_arrow), (brachy_example, brachy_arrow)]:
            self.play(
                ShowCreation(ar),
                ShimmerIn(ex)
            )
        self.dither()

class OneSolutionTwoInsights(Scene):
    def construct(self):
        one_solution = TextMobject(["One ", "solution"])
        two_insights = TextMobject(["Two ", " insights"])
        two, insights = two_insights.split()        
        johann = ImageMobject("Johann_Bernoulli2", invert = False)
        mark = ImageMobject("Mark_Levi", invert = False)
        for mob in johann, mark:
            mob.scale(0.4)
        johann.next_to(insights, LEFT)
        mark.next_to(johann, RIGHT)
        name = TextMobject("Mark Levi").to_edge(UP)

        self.play(*map(ShimmerIn, one_solution.split()))
        self.dither()
        for pair in zip(one_solution.split(), two_insights.split()):
            self.play(Transform(*pair, path_func = path_along_arc(np.pi)))
        self.dither()
        self.clear()
        self.add(two, insights)
        for word, man in [(two, johann), (insights, mark)]:
            self.play(
                Transform(word, Point(word.get_left())),                
                GrowFromCenter(man)
            )
            self.dither()
        self.clear()
        self.play(ApplyMethod(mark.center))
        self.play(ShimmerIn(name))
        self.dither()

class CircleOfIdeas(Scene):
    def construct(self):
        words = map(TextMobject, [
            "optics", "calculus", "mechanics", "geometry", "history"
        ])
        words[0].highlight(YELLOW)
        words[1].highlight(BLUE_D)
        words[2].highlight(GREY)
        words[3].highlight(GREEN)
        words[4].highlight(MAROON)
        brachistochrone = TextMobject("Brachistochrone")
        displayed_words = []
        for word in words:
            anims = self.get_spinning_anims(displayed_words)
            word.shift(3*RIGHT)
            point = Point()
            anims.append(Transform(point, word))
            self.play(*anims)
            self.remove(point)
            self.add(word)
            displayed_words.append(word)
        self.play(*self.get_spinning_anims(displayed_words))
        self.play(*[
            Transform(
                word, word.copy().highlight(BLACK).center().scale(0.1),
                path_func = path_along_arc(np.pi),
                rate_func = None,
                run_time = 2
            )
            for word in displayed_words
        ]+[
            GrowFromCenter(brachistochrone)
        ])
        self.dither()

    def get_spinning_anims(self, words, angle = np.pi/6):
        anims = []
        for word in words:
            old_center = word.get_center()
            new_center = rotate_vector(old_center, angle)
            vect = new_center-old_center
            anims.append(ApplyMethod(
                word.shift, vect,
                path_func = path_along_arc(angle), 
                rate_func = None
            ))
        return anims


class FermatsPrincipleStatement(Scene):
    def construct(self):
        words = TextMobject([
            "Fermat's principle:",
            """
            If a beam of light travels
            from point $A$ to $B$, it does so along the 
            fastest path possible.
            """
        ])
        words.split()[0].highlight(BLUE)
        everything = MobjectFromRegion(Region())
        everything.scale(0.9)
        angles = np.apply_along_axis(
            angle_of_vector, 1, everything.points
        )
        norms = np.apply_along_axis(
            np.linalg.norm, 1, everything.points
        )
        norms -= np.min(norms)
        norms /= np.max(norms)
        alphas = 0.25 + 0.75 * norms * (1 + np.sin(12*angles))/2
        everything.rgbs = alphas.repeat(3).reshape((len(alphas), 3))

        Mobject(everything, words).show()

        everything.sort_points(np.linalg.norm)        
        self.add(words)
        self.play(
            DelayByOrder(FadeIn(everything, run_time = 3)),
            Animation(words)
        )
        self.play(
            ApplyMethod(everything.highlight, WHITE),
        )
        self.dither()

class VideoProgression(Scene):
    def construct(self):
        all_topics = [
            TextMobject(word, size = "\\Huge")
            for word in [
                "Brachistochrone",
                "Light through \\\\ multilayered glass",
                "Light from \\\\ air into glass",
                "Lifeguard problem",
                "Springs and rod",
                "Snell's Law",
                "Cycloid",
                "Mark Levi's cleverness",
            ]
        ]
        brachy, multi_glass, bi_glass, lifeguard, springs, \
        snell, cycloid, levi = all_topics
        positions = [
            (multi_glass, brachy, DOWN, "both"),
            (bi_glass, multi_glass, LEFT, "to"),
            (lifeguard, bi_glass, UP, "both"),
            (springs, bi_glass, DOWN, "both"),
            (snell, springs, RIGHT, "from"),
            (cycloid, multi_glass, RIGHT, "from"),
            (cycloid, snell, UP+RIGHT, "from"),
            (levi, cycloid, UP, "to"),
        ]
        arrows = []
        for mob1, mob2, direction, arrow_type in positions:
            hasarrow = hasattr(mob1, "arrow")
            if not hasarrow:
                mob1.next_to(mob2, direction, buff = 3)
            arrow = Arrow(mob1, mob2)
            if arrow_type in ["to", "from"]:
                arrow.highlight(GREEN)
            if arrow_type == "from":
                arrow.rotate_in_place(np.pi)
            elif arrow_type == "both":
                arrow.highlight(BLUE_D)
                arrow.add(arrow.copy().rotate_in_place(np.pi))
            arrows.append(arrow)
            if hasarrow:
                mob1.arrow.add(arrow)
            else:
                mob1.arrow = arrow
        everything = Mobject(*all_topics+arrows)
        everything.scale(0.7)
        everything.center()
        everything.to_edge(UP)
        everything.show()

        self.add(brachy)
        for mob in all_topics[1:]:
            self.play(ApplyMethod(mob.highlight, YELLOW))
            self.play(ShowCreation(mob.arrow))
            self.dither()
            mob.highlight(WHITE)



class BalanceCompetingFactors(Scene):
    args_list = [
        ("Short", "Steep"),
        ("Minimal time \\\\ in water", "Short path")
    ]

    # For subclasses to turn args in the above  
    # list into stings which can be appended to the name
    @staticmethod
    def args_to_string(*words):
        return "".join([word.split(" ")[0] for word in words])
        
    @staticmethod
    def string_to_args(string):
        raise Exception("string_to_args Not Implemented!")

    def construct(self, *words):
        factor1, factor2 = [
            TextMobject("Factor %d"%x).highlight(c)
            for x, c in [
                (1, RED_D),
                (2, BLUE_D)
            ]
        ]
        real_factor1, real_factor2 = map(TextMobject, words)  
        for word in factor1, factor2, real_factor1, real_factor2:
            word.shift(0.2*UP-word.get_bottom())
        for f1 in factor1, real_factor1:
            f1.highlight(RED_D)
            f1.shift(2*LEFT)
        for f2 in factor2, real_factor2:
            f2.highlight(BLUE_D)
            f2.shift(2*RIGHT)      
        line = Line(
            factor1.get_left(),
            factor2.get_right()
        )
        line.center()
        self.balancers = Mobject(factor1, factor2, line)
        self.hidden_balancers = Mobject(real_factor1, real_factor2)

        triangle = Polygon(RIGHT, np.sqrt(3)*UP, LEFT)
        triangle.next_to(line, DOWN, buff = 0)

        self.add(triangle, self.balancers)
        self.rotate(1)
        self.rotate(-2)
        self.dither()
        self.play(Transform(
            factor1, real_factor1, 
            path_func = path_along_arc(np.pi/4)
        ))
        self.rotate(2)
        self.dither()
        self.play(Transform(
            factor2, real_factor2,
            path_func = path_along_arc(np.pi/4)
        ))
        self.rotate(-2)
        self.dither()
        self.rotate(1)

    def rotate(self, factor):
        angle = np.pi/11
        self.play(Rotate(
            self.balancers, 
            factor*angle,
            run_time = abs(factor)
        ))
        self.hidden_balancers.rotate(factor*angle)