mirror of
https://github.com/3b1b/manim.git
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370 lines
11 KiB
Python
370 lines
11 KiB
Python
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#!/usr/bin/env python
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import numpy as np
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import itertools as it
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from copy import deepcopy
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import sys
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from animation import *
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from mobject import *
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from constants import *
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from region import *
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from scene import Scene
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from script_wrapper import command_line_create_scene
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MOVIE_PREFIX = "inventing_math/"
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DIVERGENT_SUM_TEXT = [
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"1",
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"+2",
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"+4",
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"+8", "+\\cdots",
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"+2^n",
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"+\\cdots",
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"= -1",
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]
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CONVERGENT_SUM_TEXT = [
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"\\frac{1}{2}",
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"+\\frac{1}{4}",
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"+\\frac{1}{8}",
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"+\\frac{1}{16}",
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"+\\cdots+",
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"\\frac{1}{2^n}",
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"+\\cdots",
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"=1",
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]
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NUM_WRITTEN_TERMS = 4
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INTERVAL_RADIUS = 5
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NUM_INTERVAL_TICKS = 16
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def divergent_sum():
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return tex_mobject(DIVERGENT_SUM_TEXT, size = "\\large").scale(2)
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def convergent_sum():
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return tex_mobject(CONVERGENT_SUM_TEXT, size = "\\large").scale(2)
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def underbrace():
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return tex_mobject("\\underbrace{%s}"%(8*"\\quad"))
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def zero_to_one_interval():
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interval = NumberLine(
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radius = INTERVAL_RADIUS,
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interval_size = 2.0*INTERVAL_RADIUS/NUM_INTERVAL_TICKS
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)
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interval.elongate_tick_at(-INTERVAL_RADIUS, 4)
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interval.elongate_tick_at(INTERVAL_RADIUS, 4)
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zero = tex_mobject("0").shift(INTERVAL_RADIUS*LEFT+DOWN)
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one = tex_mobject("1").shift(INTERVAL_RADIUS*RIGHT+DOWN)
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return CompoundMobject(interval, zero, one)
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def draw_you():
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result = PiCreature()
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result.give_straight_face().highlight("grey")
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result.to_corner(LEFT+DOWN)
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result.rewire_part_attributes()
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return result
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class FlipThroughNumbers(Animation):
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def __init__(self, function = lambda x : x,
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start = 0, end = 10,
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start_center = ORIGIN,
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end_center = ORIGIN,
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**kwargs):
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self.function = function
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self.start = start
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self.end = end
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self.start_center = start_center
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self.end_center = end_center
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self.current_number = function(start)
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mobject = tex_mobject(str(self.current_number)).shift(start_center)
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Animation.__init__(self, mobject, **kwargs)
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def update_mobject(self, alpha):
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new_number = self.function(
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self.start + int(alpha *(self.end-self.start))
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)
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if new_number != self.current_number:
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self.current_number = new_number
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self.mobject = tex_mobject(str(new_number)).shift(self.start_center)
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if not all(self.start_center == self.end_center):
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self.mobject.center().shift(
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(1-alpha)*self.start_center + alpha*self.end_center
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)
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######################################
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class IntroduceDivergentSum(Scene):
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def construct(self):
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equation = divergent_sum().split()
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sum_value = None
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brace = underbrace().shift(0.75*DOWN)
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min_x_coord = min(equation[0].points[:,0])
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for x in range(NUM_WRITTEN_TERMS):
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self.add(equation[x])
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if x == 0:
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self.dither(0.75)
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continue
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brace.stretch_to_fit_width(
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max(equation[x].points[:,0]) - min_x_coord
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)
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brace.to_edge(LEFT, buff = SPACE_WIDTH+min_x_coord)
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if sum_value:
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self.remove(sum_value)
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sum_value = tex_mobject(str(2**(x+1) - 1))
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sum_value.shift(brace.get_center() + 0.5*DOWN)
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self.add(brace, sum_value)
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self.dither(0.75)
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self.remove(sum_value)
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ellipses = CompoundMobject(
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*[equation[NUM_WRITTEN_TERMS + i] for i in range(3)]
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)
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end_brace = deepcopy(brace).stretch_to_fit_width(
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max(ellipses.points[:,0])-min_x_coord
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).to_edge(LEFT, buff = SPACE_WIDTH+min_x_coord)
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kwargs = {"run_time" : 5.0, "alpha_func" : rush_into}
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flip_through = FlipThroughNumbers(
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lambda x : 2**(x+1)-1,
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start = NUM_WRITTEN_TERMS-1,
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end = 40,
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start_center = brace.get_center() + 0.5*DOWN,
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end_center = end_brace.get_center() + 0.5*DOWN,
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**kwargs
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)
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self.add(ellipses)
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self.animate(
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Transform(brace, end_brace, **kwargs),
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flip_through,
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)
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kwargs = {"run_time" : 0.5, "alpha_func" : rush_from}
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self.clear()
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self.add(CompoundMobject(*equation[:-1]))
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self.animate(
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Transform(
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flip_through.mobject,
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equation[-1],
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**kwargs
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),
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FadeOut(brace, **kwargs),
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)
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self.dither()
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class ClearlyNonsense(Scene):
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def construct(self):
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number_line = NumberLine().add_numbers()
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div_sum = divergent_sum()
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this_way = text_mobject("Sum goes this way...")
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this_way.to_edge(LEFT).shift(RIGHT*(SPACE_WIDTH+1) + DOWN)
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how_here = text_mobject("How does it end up here?")
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how_here.shift(1.5*UP+LEFT)
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neg_1_arrow = Arrow(
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(-1, 0.3, 0),
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tail=how_here.get_center()+0.5*DOWN
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)
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right_arrow = Arrow(
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(SPACE_WIDTH-0.5)*RIGHT + DOWN,
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tail = (max(this_way.points[:,0]), -1, 0)
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)
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how_here.highlight("red")
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neg_1_arrow.highlight("red")
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this_way.highlight("yellow")
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right_arrow.highlight("yellow")
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self.animate(Transform(
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div_sum,
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deepcopy(div_sum).scale(0.5).shift(3*UP)
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))
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self.animate(ShowCreation(number_line))
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self.dither()
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self.add(how_here)
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self.animate(ShowCreation(neg_1_arrow))
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self.dither()
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self.add(this_way)
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self.animate(ShowCreation(right_arrow))
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self.dither()
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class ReasonsForMakingVideo(Scene):
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def construct(self):
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text = text_mobject([
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"""
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\\begin{itemize}
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\\item Understand what ``$
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""",
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"".join(DIVERGENT_SUM_TEXT),
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"""
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$'' is saying.
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""",
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"""
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\\item Nonsense-Driven Construction
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\\end{itemize}
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"""
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], size = "\\Small")
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text.scale(1.5).to_edge(LEFT).shift(UP).highlight("white")
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text.highlight("green", lambda (x, y, z) : x < -SPACE_WIDTH + 1)
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line_one_first, equation, line_one_last, line_two = text.split()
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line_two.shift(2*DOWN)
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div_sum = divergent_sum().scale(0.5).shift(3*UP)
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self.add(div_sum)
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self.animate(
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ApplyMethod(div_sum.replace, equation),
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FadeIn(line_one_first),
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FadeIn(line_one_last)
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)
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self.dither()
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self.add(line_two)
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self.dither()
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class YouAsMathematician(Scene):
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def construct(self):
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you = draw_you()
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explanation = text_mobject(
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"You as a (questionably accurate portrayal of a) mathematician.",
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size = "\\small"
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).shift([2, you.get_center()[1], 0])
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arrow = Arrow(you.get_center(), direction = LEFT)
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arrow.nudge(you.get_width())
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for mob in arrow, explanation:
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mob.highlight("yellow")
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bubble = ThoughtBubble()
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bubble.stretch_to_fit_width(10)
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bubble.pin_to(you)
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equation = convergent_sum()
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bubble.add_content(equation)
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equation.shift(0.5*RIGHT)
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bubble.clear()
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dot_pair = [
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Dot(density = 3*DEFAULT_POINT_DENSITY_1D).shift(x+UP)
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for x in LEFT, RIGHT
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]
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self.add(you, explanation)
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self.animate(
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ShowCreation(arrow),
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BlinkPiCreature(you)
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)
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self.dither()
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self.animate(ShowCreation(bubble))
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self.animate(ShowCreation(equation, run_time = 2.0))
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self.dither()
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self.animate(
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BlinkPiCreature(you),
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FadeOut(explanation),
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FadeOut(arrow)
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)
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self.animate(Transform(equation, CompoundMobject(*dot_pair)))
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self.remove(equation)
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self.add(*dot_pair)
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two_arrows = [
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Arrow(x, direction = x).shift(UP).nudge()
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for x in LEFT, RIGHT
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]
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self.animate(*[ShowCreation(a) for a in two_arrows])
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self.animate(BlinkPiCreature(you))
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self.remove(*dot_pair+two_arrows)
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everything = CompoundMobject(*self.mobjects)
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self.clear()
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self.animate(
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ApplyFunction(
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everything,
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lambda p : 3*SPACE_WIDTH*p/np.linalg.norm(p)
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),
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*[
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Transform(dot, deepcopy(dot).shift(DOWN).scale(3))
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for dot in dot_pair
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],
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run_time = 2.0
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)
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self.dither()
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class DotsGettingCloser(Scene):
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def construct(self):
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dots = [
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Dot(radius = 3*Dot.DEFAULT_RADIUS).shift(3*x)
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for x in LEFT, RIGHT
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]
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self.add(*dots)
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self.dither()
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for x in range(10):
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distance = min(dots[1].points[:,0])-max(dots[0].points[:,0])
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self.animate(ApplyMethod(dots[0].shift, 0.5*distance*RIGHT))
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class ZoomInOnInterval(Scene):
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def construct(self):
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number_line = NumberLine(density = 10*DEFAULT_POINT_DENSITY_1D)
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number_line.add_numbers()
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interval = zero_to_one_interval().split()
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new_line = deepcopy(number_line)
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new_line.highlight("black", lambda (x,y,z) : x < 0 or x > 1 or y < -0.2)
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# height = new_line.get_height()
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new_line.scale(2*INTERVAL_RADIUS)
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new_line.shift(INTERVAL_RADIUS*LEFT)
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# new_line.stretch_to_fit_height(height)
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self.add(number_line)
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self.dither()
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self.animate(Transform(number_line, new_line))
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self.clear()
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squish = lambda p : (p[0], 0, 0)
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self.animate(
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ApplyMethod(new_line.apply_function, squish),
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ApplyMethod(
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interval[0].apply_function, squish,
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alpha_func = lambda t : 1-t
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),
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*[FadeIn(interval[x]) for x in [1, 2]]
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)
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self.clear()
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self.add(*interval)
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self.dither()
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class DanceDotOnInterval(Scene):
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def construct(self):
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interval = zero_to_one_interval()
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dots = [
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Dot(radius = 3*Dot.DEFAULT_RADIUS).shift(INTERVAL_RADIUS*x+UP)
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for x in LEFT, RIGHT
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]
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color_range = Color("green").range_to("grey", NUM_WRITTEN_TERMS)
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conv_sum = convergent_sum().split()
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self.add(interval)
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self.animate(*[
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ApplyMethod(dot.shift, DOWN)
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for dot in dots
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])
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self.dither()
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for count in range(NUM_WRITTEN_TERMS):
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shift_val = RIGHT*INTERVAL_RADIUS/(2.0**count)
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start = dots[0].get_center()
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line = Line(start, start + shift_val*RIGHT)
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line.highlight(color_range.next())
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self.animate(
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ApplyMethod(dots[0].shift, shift_val),
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ShowCreation(line)
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)
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num = conv_sum[count]
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num.shift(RIGHT*(line.get_center()[0]-num.get_center()[0]))
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if num.get_width() > line.get_length():
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num.stretch_to_fit_width(line.get_length())
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num.shift(3*DOWN)
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self.animate(
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ApplyMethod(line.shift, 2*DOWN),
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FadeIn(num)
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)
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self.dither()
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self.animate(FadeIn(conv_sum[NUM_WRITTEN_TERMS]))
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if __name__ == "__main__":
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command_line_create_scene(MOVIE_PREFIX)
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