mirror of
https://github.com/3b1b/manim.git
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Reorganized files for 3b1b videos into a 3b1b_projects folder
This commit is contained in:
Grant Sanderson
495
3b1b_projects/old/brachistochrone/misc.py
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495
3b1b_projects/old/brachistochrone/misc.py
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@ -0,0 +1,495 @@
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import numpy as np
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import itertools as it
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from manimlib.imports import *
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from old_projects.brachistochrone.curves import Cycloid
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class PhysicalIntuition(Scene):
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def construct(self):
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n_terms = 4
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def func(xxx_todo_changeme):
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(x, y, ignore) = xxx_todo_changeme
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z = complex(x, y)
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if (np.abs(x%1 - 0.5)<0.01 and y < 0.01) or np.abs(z)<0.01:
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return ORIGIN
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out_z = 1./(2*np.tan(np.pi*z)*(z**2))
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return out_z.real*RIGHT - out_z.imag*UP
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arrows = Mobject(*[
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Arrow(ORIGIN, np.sqrt(2)*point)
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for point in compass_directions(4, RIGHT+UP)
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])
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arrows.set_color(YELLOW)
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arrows.ingest_submobjects()
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all_arrows = Mobject(*[
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arrows.copy().scale(0.3/(x)).shift(x*RIGHT)
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for x in range(1, n_terms+2)
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])
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terms = TexMobject([
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"\\dfrac{1}{%d^2} + "%(x+1)
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for x in range(n_terms)
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]+["\\cdots"])
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terms.shift(2*UP)
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plane = NumberPlane(color = BLUE_E)
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axes = Mobject(NumberLine(), NumberLine().rotate(np.pi/2))
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axes.set_color(WHITE)
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for term in terms.split():
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self.play(ShimmerIn(term, run_time = 0.5))
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self.wait()
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self.play(ShowCreation(plane), ShowCreation(axes))
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self.play(*[
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Transform(*pair)
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for pair in zip(terms.split(), all_arrows.split())
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])
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self.play(PhaseFlow(
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func, plane,
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run_time = 5,
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virtual_time = 8
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))
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class TimeLine(Scene):
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def construct(self):
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dated_events = [
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{
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"date" : 1696,
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"text": "Johann Bernoulli poses Brachistochrone problem",
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"picture" : "Johann_Bernoulli2"
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},
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{
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"date" : 1662,
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"text" : "Fermat states his principle of least time",
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"picture" : "Pierre_de_Fermat"
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}
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]
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speical_dates = [2016] + [
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obj["date"] for obj in dated_events
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]
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centuries = list(range(1600, 2100, 100))
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timeline = NumberLine(
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numerical_radius = 300,
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number_at_center = 1800,
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unit_length_to_spatial_width = FRAME_X_RADIUS/100,
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tick_frequency = 10,
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numbers_with_elongated_ticks = centuries
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)
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timeline.add_numbers(*centuries)
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centers = [
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Point(timeline.number_to_point(year))
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for year in speical_dates
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]
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timeline.add(*centers)
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timeline.shift(-centers[0].get_center())
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self.add(timeline)
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self.wait()
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run_times = iter([3, 1])
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for point, event in zip(centers[1:], dated_events):
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self.play(ApplyMethod(
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timeline.shift, -point.get_center(),
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run_time = next(run_times)
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))
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picture = ImageMobject(event["picture"], invert = False)
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picture.set_width(2)
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picture.to_corner(UP+RIGHT)
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event_mob = TextMobject(event["text"])
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event_mob.shift(2*LEFT+2*UP)
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date_mob = TexMobject(str(event["date"]))
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date_mob.scale(0.5)
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date_mob.shift(0.6*UP)
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line = Line(event_mob.get_bottom(), 0.2*UP)
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self.play(
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ShimmerIn(event_mob),
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ShowCreation(line),
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ShimmerIn(date_mob)
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)
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self.play(FadeIn(picture))
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self.wait(3)
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self.play(*list(map(FadeOut, [event_mob, date_mob, line, picture])))
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class StayedUpAllNight(Scene):
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def construct(self):
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clock = Circle(radius = 2, color = WHITE)
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clock.add(Dot(ORIGIN))
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ticks = Mobject(*[
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Line(1.8*vect, 2*vect, color = GREY)
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for vect in compass_directions(12)
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])
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clock.add(ticks)
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hour_hand = Line(ORIGIN, UP)
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minute_hand = Line(ORIGIN, 1.5*UP)
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clock.add(hour_hand, minute_hand)
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clock.to_corner(UP+RIGHT)
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hour_hand.get_center = lambda : clock.get_center()
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minute_hand.get_center = lambda : clock.get_center()
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solution = ImageMobject(
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"Newton_brachistochrone_solution2",
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use_cache = False
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)
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solution.stroke_width = 3
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solution.set_color(GREY)
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solution.set_width(5)
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solution.to_corner(UP+RIGHT)
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newton = ImageMobject("Old_Newton", invert = False)
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newton.scale(0.8)
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phil_trans = TextMobject("Philosophical Transactions")
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rect = Rectangle(height = 6, width = 4.5, color = WHITE)
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rect.to_corner(UP+RIGHT)
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rect.shift(DOWN)
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phil_trans.set_width(0.8*rect.get_width())
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phil_trans.next_to(Point(rect.get_top()), DOWN)
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new_solution = solution.copy()
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new_solution.set_width(phil_trans.get_width())
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new_solution.next_to(phil_trans, DOWN, buff = 1)
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not_newton = TextMobject("-Totally not by Newton")
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not_newton.set_width(2.5)
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not_newton.next_to(new_solution, DOWN, aligned_edge = RIGHT)
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phil_trans.add(rect)
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newton_complaint = TextMobject([
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"``I do not love to be",
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" \\emph{dunned} ",
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"and teased by foreigners''"
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], size = "\\small")
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newton_complaint.to_edge(UP, buff = 0.2)
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dunned = newton_complaint.split()[1]
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dunned.set_color()
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dunned_def = TextMobject("(old timey term for making \\\\ demands on someone)")
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dunned_def.scale(0.7)
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dunned_def.next_to(phil_trans, LEFT)
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dunned_def.shift(2*UP)
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dunned_arrow = Arrow(dunned_def, dunned)
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johann = ImageMobject("Johann_Bernoulli2", invert = False)
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johann.scale(0.4)
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johann.to_edge(LEFT)
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johann.shift(DOWN)
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johann_quote = TextMobject("``I recognize the lion by his claw''")
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johann_quote.next_to(johann, UP, aligned_edge = LEFT)
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self.play(ApplyMethod(newton.to_edge, LEFT))
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self.play(ShowCreation(clock))
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kwargs = {
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"axis" : OUT,
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"rate_func" : smooth
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}
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self.play(
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Rotating(hour_hand, radians = -2*np.pi, **kwargs),
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Rotating(minute_hand, radians = -12*2*np.pi, **kwargs),
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run_time = 5
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)
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self.wait()
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self.clear()
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self.add(newton)
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clock.ingest_submobjects()
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self.play(Transform(clock, solution))
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self.remove(clock)
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self.add(solution)
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self.wait()
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self.play(
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FadeIn(phil_trans),
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Transform(solution, new_solution)
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)
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self.wait()
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self.play(ShimmerIn(not_newton))
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phil_trans.add(solution, not_newton)
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self.wait()
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self.play(*list(map(ShimmerIn, newton_complaint.split())))
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self.wait()
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self.play(
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ShimmerIn(dunned_def),
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ShowCreation(dunned_arrow)
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)
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self.wait()
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self.remove(dunned_def, dunned_arrow)
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self.play(FadeOut(newton_complaint))
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self.remove(newton_complaint)
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self.play(
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FadeOut(newton),
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GrowFromCenter(johann)
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)
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self.remove(newton)
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self.wait()
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self.play(ShimmerIn(johann_quote))
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self.wait()
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class ThetaTGraph(Scene):
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def construct(self):
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t_axis = NumberLine()
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theta_axis = NumberLine().rotate(np.pi/2)
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theta_mob = TexMobject("\\theta(t)")
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t_mob = TexMobject("t")
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theta_mob.next_to(theta_axis, RIGHT)
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theta_mob.to_edge(UP)
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t_mob.next_to(t_axis, UP)
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t_mob.to_edge(RIGHT)
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graph = ParametricFunction(
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lambda t : 4*t*RIGHT + 2*smooth(t)*UP
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)
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line = Line(graph.points[0], graph.points[-1], color = WHITE)
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q_mark = TextMobject("?")
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q_mark.next_to(Point(graph.get_center()), LEFT)
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stars = Stars(color = BLACK)
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stars.scale(0.1).shift(q_mark.get_center())
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squiggle = ParametricFunction(
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lambda t : t*RIGHT + 0.2*t*(5-t)*(np.sin(t)**2)*UP,
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start = 0,
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end = 5
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)
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self.play(
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ShowCreation(t_axis),
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ShowCreation(theta_axis),
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ShimmerIn(theta_mob),
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ShimmerIn(t_mob)
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)
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self.play(
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ShimmerIn(q_mark),
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ShowCreation(graph)
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)
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self.wait()
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self.play(
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Transform(q_mark, stars),
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Transform(graph, line)
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)
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self.wait()
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self.play(Transform(graph, squiggle))
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self.wait()
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class SolutionsToTheBrachistochrone(Scene):
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def construct(self):
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r_range = np.arange(0.5, 2, 0.25)
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cycloids = Mobject(*[
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Cycloid(radius = r, end_theta=2*np.pi)
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for r in r_range
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])
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lower_left = 2*DOWN+6*LEFT
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lines = Mobject(*[
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Line(
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lower_left,
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lower_left+5*r*np.cos(np.arctan(r))*RIGHT+2*r*np.sin(np.arctan(r))*UP
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)
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for r in r_range
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])
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nl = NumberLine(numbers_with_elongated_ticks = [])
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x_axis = nl.copy().shift(3*UP)
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y_axis = nl.copy().rotate(np.pi/2).shift(6*LEFT)
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t_axis = nl.copy().shift(2*DOWN)
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x_label = TexMobject("x")
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x_label.next_to(x_axis, DOWN)
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x_label.to_edge(RIGHT)
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y_label = TexMobject("y")
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y_label.next_to(y_axis, RIGHT)
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y_label.shift(2*DOWN)
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t_label = TexMobject("t")
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t_label.next_to(t_axis, UP)
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t_label.to_edge(RIGHT)
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theta_label = TexMobject("\\theta")
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theta_label.next_to(y_axis, RIGHT)
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theta_label.to_edge(UP)
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words = TextMobject("Boundary conditions?")
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words.next_to(lines, RIGHT)
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words.shift(2*UP)
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self.play(ShowCreation(x_axis), ShimmerIn(x_label))
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self.play(ShowCreation(y_axis), ShimmerIn(y_label))
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self.play(ShowCreation(cycloids))
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self.wait()
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self.play(
|
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Transform(cycloids, lines),
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Transform(x_axis, t_axis),
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Transform(x_label, t_label),
|
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Transform(y_label, theta_label),
|
||||
run_time = 2
|
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)
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self.wait()
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self.play(ShimmerIn(words))
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self.wait()
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class VideoLayout(Scene):
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def construct(self):
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left, right = 5*LEFT, 5*RIGHT
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top_words = TextMobject("The next 15 minutes of your life:")
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top_words.to_edge(UP)
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line = Line(left, right, color = BLUE_D)
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for a in np.arange(0, 4./3, 1./3):
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vect = interpolate(left, right, a)
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line.add_line(vect+0.2*DOWN, vect+0.2*UP)
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left_brace = Brace(
|
||||
Mobject(
|
||||
Point(left),
|
||||
Point(interpolate(left, right, 2./3))
|
||||
),
|
||||
DOWN
|
||||
)
|
||||
right_brace = Brace(
|
||||
Mobject(
|
||||
Point(interpolate(left, right, 2./3)),
|
||||
Point(right)
|
||||
),
|
||||
UP
|
||||
)
|
||||
left_brace.words = list(map(TextMobject, [
|
||||
"Problem statement",
|
||||
"History",
|
||||
"Johann Bernoulli's cleverness"
|
||||
]))
|
||||
curr = left_brace
|
||||
right_brace.words = list(map(TextMobject, [
|
||||
"Challenge",
|
||||
"Mark Levi's cleverness",
|
||||
]))
|
||||
for brace in left_brace, right_brace:
|
||||
curr = brace
|
||||
direction = DOWN if brace is left_brace else UP
|
||||
for word in brace.words:
|
||||
word.next_to(curr, direction)
|
||||
curr = word
|
||||
right_brace.words.reverse()
|
||||
|
||||
self.play(ShimmerIn(top_words))
|
||||
self.play(ShowCreation(line))
|
||||
for brace in left_brace, right_brace:
|
||||
self.play(GrowFromCenter(brace))
|
||||
self.wait()
|
||||
for word in brace.words:
|
||||
self.play(ShimmerIn(word))
|
||||
self.wait()
|
||||
|
||||
|
||||
|
||||
|
||||
class ShortestPathProblem(Scene):
|
||||
def construct(self):
|
||||
point_a, point_b = 3*LEFT, 3*RIGHT
|
||||
dots = []
|
||||
for point, char in [(point_a, "A"), (point_b, "B")]:
|
||||
dot = Dot(point)
|
||||
letter = TexMobject(char)
|
||||
letter.next_to(dot, UP+LEFT)
|
||||
dot.add(letter)
|
||||
dots.append(dot)
|
||||
|
||||
path = ParametricFunction(
|
||||
lambda t : (t/2 + np.cos(t))*RIGHT + np.sin(t)*UP,
|
||||
start = -2*np.pi,
|
||||
end = 2*np.pi
|
||||
)
|
||||
path.scale(6/(2*np.pi))
|
||||
path.shift(point_a - path.points[0])
|
||||
path.set_color(RED)
|
||||
line = Line(point_a, point_b)
|
||||
words = TextMobject("Shortest path from $A$ to $B$")
|
||||
words.to_edge(UP)
|
||||
|
||||
self.play(
|
||||
ShimmerIn(words),
|
||||
*list(map(GrowFromCenter, dots))
|
||||
)
|
||||
self.play(ShowCreation(path))
|
||||
self.play(Transform(
|
||||
path, line,
|
||||
path_func = path_along_arc(np.pi)
|
||||
))
|
||||
self.wait()
|
||||
|
||||
|
||||
class MathBetterThanTalking(Scene):
|
||||
def construct(self):
|
||||
mathy = Mathematician()
|
||||
mathy.to_corner(DOWN+LEFT)
|
||||
bubble = ThoughtBubble()
|
||||
bubble.pin_to(mathy)
|
||||
bubble.write("Math $>$ Talking about math")
|
||||
|
||||
self.add(mathy)
|
||||
self.play(ShowCreation(bubble))
|
||||
self.play(ShimmerIn(bubble.content))
|
||||
self.wait()
|
||||
self.play(ApplyMethod(
|
||||
mathy.blink,
|
||||
rate_func = squish_rate_func(there_and_back, 0.4, 0.6)
|
||||
))
|
||||
|
||||
|
||||
class DetailsOfProofBox(Scene):
|
||||
def construct(self):
|
||||
rect = Rectangle(height = 4, width = 6, color = WHITE)
|
||||
words = TextMobject("Details of proof")
|
||||
words.to_edge(UP)
|
||||
|
||||
self.play(
|
||||
ShowCreation(rect),
|
||||
ShimmerIn(words)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
|
||||
class TalkedAboutSnellsLaw(Scene):
|
||||
def construct(self):
|
||||
randy = Randolph()
|
||||
randy.to_corner(DOWN+LEFT)
|
||||
morty = Mortimer()
|
||||
morty.to_edge(DOWN+RIGHT)
|
||||
randy.bubble = SpeechBubble().pin_to(randy)
|
||||
morty.bubble = SpeechBubble().pin_to(morty)
|
||||
|
||||
phrases = [
|
||||
"Let's talk about Snell's law",
|
||||
"I love Snell's law",
|
||||
"It's like running from \\\\ a beach into the ocean",
|
||||
"It's like two constant \\\\ tension springs",
|
||||
]
|
||||
|
||||
self.add(randy, morty)
|
||||
talkers = it.cycle([randy, morty])
|
||||
for talker, phrase in zip(talkers, phrases):
|
||||
talker.bubble.write(phrase)
|
||||
self.play(
|
||||
FadeIn(talker.bubble),
|
||||
ShimmerIn(talker.bubble.content)
|
||||
)
|
||||
self.play(ApplyMethod(
|
||||
talker.blink,
|
||||
rate_func = squish_rate_func(there_and_back)
|
||||
))
|
||||
self.wait()
|
||||
self.remove(talker.bubble, talker.bubble.content)
|
||||
|
||||
|
||||
class YetAnotherMarkLevi(Scene):
|
||||
def construct(self):
|
||||
words = TextMobject("Yet another bit of Mark Levi cleverness")
|
||||
words.to_edge(UP)
|
||||
levi = ImageMobject("Mark_Levi", invert = False)
|
||||
levi.set_width(6)
|
||||
levi.show()
|
||||
|
||||
self.add(levi)
|
||||
self.play(ShimmerIn(words))
|
||||
self.wait(2)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user