mirror of
https://github.com/3b1b/manim.git
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Preliminary end to eoc/chapter2 animations
This commit is contained in:
Grant Sanderson
@ -2582,16 +2582,17 @@ class PatreonThanks(Scene):
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"Kirk Werklund",
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"Ripta Pasay",
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"Felipe Diniz",
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]
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],
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"max_patrons_height" : 2*SPACE_HEIGHT - 1,
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}
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def construct(self):
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morty = Mortimer()
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morty.next_to(ORIGIN, DOWN)
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n_patrons = len(self.specific_patrons)
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special_thanks = TextMobject("Special thanks to:")
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special_thanks = TextMobject("Special thanks")
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special_thanks.highlight(YELLOW)
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special_thanks.shift(2*UP)
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special_thanks.to_edge(UP)
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left_patrons = VGroup(*map(TextMobject,
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self.specific_patrons[:n_patrons/2]
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@ -2599,10 +2600,26 @@ class PatreonThanks(Scene):
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right_patrons = VGroup(*map(TextMobject,
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self.specific_patrons[n_patrons/2:]
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))
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for patrons in left_patrons, right_patrons:
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patrons.arrange_submobjects(
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DOWN, aligned_edge = LEFT,
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buff = 1.5*MED_BUFF
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)
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all_patrons = VGroup(left_patrons, right_patrons)
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if all_patrons.get_height() > self.max_patrons_height:
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all_patrons.scale_to_fit_height(self.max_patrons_height)
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for patrons, vect in (left_patrons, LEFT), (right_patrons, RIGHT):
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patrons.arrange_submobjects(DOWN, aligned_edge = LEFT)
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patrons.next_to(special_thanks, DOWN)
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patrons.to_edge(vect, buff = LARGE_BUFF)
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patrons.to_edge(vect, buff = MED_BUFF)
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# shift_distance = max(
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# 0, 1-SPACE_HEIGHT-all_patrons.get_bottom()[1]
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# )
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# velocity = shift_distance/8
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# def get_shift_anim():
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# return ApplyMethod(
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# all_patrons.shift, velocity*UP,
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# rate_func = None
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# )
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self.play(morty.change_mode, "gracious")
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self.play(Write(special_thanks, run_time = 1))
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@ -2617,7 +2634,9 @@ class PatreonThanks(Scene):
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self.play(Blink(morty))
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for patrons in left_patrons, right_patrons:
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for index in 0, -1:
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self.play(morty.look_at, patrons[index])
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self.play(
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morty.look_at, patrons[index],
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)
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self.dither()
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class Thumbnail(CircleScene):
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487
eoc/chapter2.py
487
eoc/chapter2.py
@ -24,7 +24,7 @@ from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from eoc.chapter1 import OpeningQuote
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from eoc.chapter1 import OpeningQuote, PatreonThanks
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from eoc.graph_scene import *
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DISTANCE_COLOR = BLUE
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@ -172,8 +172,21 @@ class Chapter2OpeningQuote(OpeningQuote):
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class Introduction(TeacherStudentsScene):
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def construct(self):
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goals = TextMobject(
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"Goals: ",
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"1) Learn derivatives",
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", 2) Avoid paradoxes.",
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arg_separator = ""
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)
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goals[1].highlight(MAROON_B)
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goals[2].highlight(RED)
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goals[2][0].highlight(WHITE)
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goals.to_edge(UP)
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self.add(*goals[:2])
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self.student_says(
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"What is a derivative?"
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"What is a derivative?",
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run_time = 2
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)
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self.play(self.get_teacher().change_mode, "happy")
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self.dither()
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@ -183,24 +196,24 @@ class Introduction(TeacherStudentsScene):
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target_mode = "well"
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)
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self.change_student_modes(None, "pondering", "thinking")
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self.dither()
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self.play(Write(goals[2], run_time = 2))
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self.change_student_modes("erm")
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self.student_says(
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"Doesn't the derivative measure\\\\",
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"instantaneous rate of change", "?",
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"Instantaneous rate of change", "?",
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student_index = 0,
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)
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self.dither()
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bubble = self.get_students()[0].bubble
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phrase = bubble.content[1]
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phrase = bubble.content[0]
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bubble.content.remove(phrase)
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self.play(
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FadeOut(bubble),
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FadeOut(bubble.content),
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FadeOut(goals),
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phrase.center,
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phrase.scale, 1.5,
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phrase.to_edge, UP,
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FadeOut(bubble),
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FadeOut(bubble.content),
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*it.chain(*[
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[
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pi.change_mode, mode,
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@ -247,7 +260,7 @@ class Introduction(TeacherStudentsScene):
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clock.copy().next_to, instantaneous_description, DOWN,
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get_clock_anim(3)
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)
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self.play(get_clock_anim(6))
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self.play(get_clock_anim(12))
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class FathersOfCalculus(Scene):
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CONFIG = {
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@ -584,6 +597,7 @@ class GraphCarTrajectory(GraphScene):
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for graph_func in graph_funcs:
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new_graph = self.graph_function(
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graph_func,
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color = DISTANCE_COLOR,
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is_main_graph = False
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)
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self.remove(new_graph)
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@ -1513,6 +1527,18 @@ class SecantLineToTangentLine(GraphCarTrajectory, DefineTrueDerivative):
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self.play(ShowCreation(circle))
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self.dither()
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class UseOfDImpliesApproaching(TeacherStudentsScene):
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def construct(self):
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statement = TextMobject("""
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Using ``$d$''
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announces that
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$dt \\to 0$
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""")
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VGroup(*statement[-4:-2]).highlight(TIME_COLOR)
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self.teacher_says(statement)
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self.change_student_modes(*["pondering"]*3)
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self.dither(4)
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class LeadIntoASpecificExample(TeacherStudentsScene, SecantLineToTangentLine):
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def setup(self):
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TeacherStudentsScene.setup(self)
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@ -1799,10 +1825,10 @@ class TCubedExample(SecantLineToTangentLine):
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new_exp = TexMobject("2").replace(faders[-1], dim_to_match = 1)
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self.play(
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faders.highlight, BLACK,
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run_time = 3,
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submobject_mode = "lagged_start"
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FadeIn(new_exp),
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run_time = 2,
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)
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self.play(FadeIn(new_exp))
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self.dither()
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terms[3].add(new_exp)
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shift_val = 0.4*DOWN
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self.play(
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@ -2020,19 +2046,430 @@ class ContrastConcreteDtWithLimit(Scene):
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r_text = r_brace.get_text("Simple")
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r_text.highlight(GREEN)
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self.add(r_formula, r_brace, r_text, l_formula, l_brace, l_text)
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triplets = [
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(l_formula, l_brace, l_text),
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(r_formula, r_brace, r_text),
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]
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for formula, brace, text in triplets:
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self.play(Write(formula, run_time = 1))
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self.play(
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GrowFromCenter(brace),
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Write(text)
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)
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self.dither(2)
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class TimeForAnActualParadox(TeacherStudentsScene):
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def construct(self):
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words = TextMobject("``Instantaneous rate of change''")
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paradoxes = TextMobject("Paradoxes")
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arrow = Arrow(ORIGIN, DOWN, buff = 0)
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group = VGroup(words, arrow, paradoxes)
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group.arrange_submobjects(DOWN)
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group.to_edge(UP)
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teacher = self.get_teacher()
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self.play(
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teacher.change_mode, "raise_right_hand",
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teacher.look_at, words,
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Write(words)
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)
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self.play(*map(Write, [arrow, paradoxes]))
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self.play(*it.chain(*[
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[pi.change_mode, mode, pi.look_at, words]
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for pi, mode in zip(
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self.get_students(),
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["pondering", "happy", "hesitant"]
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)
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]))
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self.dither(4)
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class ParadoxAtTEquals0(TCubedExample):
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CONFIG = {
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"tangent_line_length" : 20,
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}
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def construct(self):
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self.draw_graph()
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self.ask_question()
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self.show_derivative_text()
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self.show_tangent_line()
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self.if_not_then_when()
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self.single_out_question()
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def draw_graph(self):
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self.setup_axes(animate = False)
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self.x_axis_label_mob.set_fill(opacity = 0)
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graph = self.graph_function(lambda t : t**3, animate = False)
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graph_x_max = 3.0
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graph.pointwise_become_partial(graph, 0, graph_x_max/self.x_max)
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origin = self.coords_to_point(0, 0)
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h_line = Line(LEFT, RIGHT, color = TIME_COLOR)
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v_line = Line(UP, DOWN, color = DISTANCE_COLOR)
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VGroup(h_line, v_line).set_stroke(width = 2)
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def h_line_update(h_line):
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point = graph.point_from_proportion(1)
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y_axis_point = origin[0]*RIGHT + point[1]*UP
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h_line.put_start_and_end_on(y_axis_point, point)
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return h_line
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def v_line_update(v_line):
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point = graph.point_from_proportion(1)
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x_axis_point = point[0]*RIGHT + origin[1]*UP
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v_line.put_start_and_end_on(x_axis_point, point)
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return v_line
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car = Car()
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car.rotate(np.pi/2)
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car.move_to(origin)
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self.add(car)
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#Should be 0, 1, but for some reason I don't know
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#the car was lagging the graph.
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car_target_point = self.coords_to_point(0, 1.15)
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self.play(
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MoveCar(
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car, car_target_point,
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rate_func = lambda t : (t*graph_x_max)**3
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),
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ShowCreation(graph, rate_func = None),
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UpdateFromFunc(h_line, h_line_update),
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UpdateFromFunc(v_line, v_line_update),
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run_time = 5
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)
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self.play(*map(FadeOut, [h_line, v_line]))
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self.label_graph(
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graph,
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label = "s(t) = t^3",
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proportion = 0.8,
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direction = RIGHT,
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buff = SMALL_BUFF
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)
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self.dither()
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self.car = car
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def ask_question(self):
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question = TextMobject(
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"At time $t=0$,",
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"is \\\\ the car moving?"
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)
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VGroup(*question[0][-4:-1]).highlight(RED)
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question.next_to(
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self.coords_to_point(0, 10),
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RIGHT
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)
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origin = self.coords_to_point(0, 0)
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arrow = Arrow(question.get_bottom(), origin)
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self.play(Write(question[0], run_time = 1))
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self.play(MoveCar(self.car, origin))
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self.dither()
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self.play(Write(question[1]))
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self.play(ShowCreation(arrow))
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self.dither(2)
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self.question = question
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def show_derivative_text(self):
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derivative = TexMobject(
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"\\frac{ds}{dt}(t) = 3t^2",
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"= 3(0)^2",
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"= 0",
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"\\frac{\\text{m}}{\\text{s}}",
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)
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VGroup(*derivative[0][:2]).highlight(DISTANCE_COLOR)
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VGroup(*derivative[0][3:5]).highlight(TIME_COLOR)
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derivative[1][3].highlight(RED)
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derivative[-1].scale_in_place(0.7)
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derivative.to_edge(RIGHT, buff = LARGE_BUFF)
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derivative.shift(2*UP)
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self.play(Write(derivative[0]))
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self.dither()
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self.play(FadeIn(derivative[1]))
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self.play(*map(FadeIn, derivative[2:]))
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self.dither(2)
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self.derivative = derivative
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def show_tangent_line(self):
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dot = Dot()
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line = Line(ORIGIN, RIGHT, color = VELOCITY_COLOR)
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line.scale(self.tangent_line_length)
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start_time = 2
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end_time = 0
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def get_time_and_point(alpha):
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time = interpolate(start_time, end_time, alpha)
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point = self.input_to_graph_point(time)
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return time, point
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def dot_update(dot, alpha):
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dot.move_to(get_time_and_point(alpha)[1])
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def line_update(line, alpha):
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time, point = get_time_and_point(alpha)
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line.rotate(
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self.angle_of_tangent(time)-line.get_angle()
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)
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line.move_to(point)
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dot_update(dot, 0)
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line_update(line, 0)
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self.play(
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ShowCreation(line),
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ShowCreation(dot)
|
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)
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self.play(
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UpdateFromAlphaFunc(line, line_update),
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UpdateFromAlphaFunc(dot, dot_update),
|
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run_time = 4
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)
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self.dither(2)
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|
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self.tangent_line = line
|
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def if_not_then_when(self):
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morty = Mortimer()
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morty.scale(0.7)
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morty.to_corner(DOWN+RIGHT)
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||||
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self.play(FadeIn(morty))
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self.play(PiCreatureSays(
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morty, "If not at $t=0$, when?",
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target_mode = "maybe"
|
||||
))
|
||||
self.play(Blink(morty))
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||||
self.play(MoveCar(
|
||||
self.car, self.coords_to_point(0, 1),
|
||||
rate_func = lambda t : (3*t)**3,
|
||||
run_time = 5
|
||||
))
|
||||
self.play(
|
||||
morty.change_mode, "pondering",
|
||||
FadeOut(morty.bubble),
|
||||
FadeOut(morty.bubble.content),
|
||||
)
|
||||
self.play(MoveCar(self.car, self.coords_to_point(0, 0)))
|
||||
self.play(Blink(morty))
|
||||
self.dither(2)
|
||||
|
||||
self.morty = morty
|
||||
|
||||
def single_out_question(self):
|
||||
morty, question = self.morty, self.question
|
||||
|
||||
#Shouldn't need this
|
||||
morty.bubble.content.set_fill(opacity = 0)
|
||||
morty.bubble.set_fill(opacity = 0)
|
||||
morty.bubble.set_stroke(width = 0)
|
||||
|
||||
change_word = VGroup(*question[1][-7:-1])
|
||||
moment_word = question[0]
|
||||
|
||||
brace = Brace(VGroup(*self.derivative[1:]))
|
||||
brace_text = brace.get_text("Best constant \\\\ approximation")
|
||||
|
||||
self.remove(question, morty)
|
||||
pre_everything = Mobject(*self.get_mobjects())
|
||||
everything = Mobject(*pre_everything.family_members_with_points())
|
||||
everything.save_state()
|
||||
|
||||
self.play(
|
||||
everything.fade, 0.8,
|
||||
question.center,
|
||||
morty.change_mode, "confused",
|
||||
morty.look_at, ORIGIN
|
||||
)
|
||||
self.play(Blink(morty))
|
||||
for word in change_word, moment_word:
|
||||
self.play(
|
||||
word.scale_in_place, 1.2,
|
||||
word.highlight, YELLOW,
|
||||
rate_func = there_and_back,
|
||||
run_time = 1.5
|
||||
)
|
||||
self.dither(2)
|
||||
self.play(
|
||||
everything.restore,
|
||||
FadeOut(question),
|
||||
morty.change_mode, "raise_right_hand",
|
||||
morty.look_at, self.derivative
|
||||
)
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
FadeIn(brace_text)
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
self.tangent_line.rotate_in_place, np.pi/24,
|
||||
rate_func = wiggle,
|
||||
run_time = 1
|
||||
)
|
||||
self.play(Blink(morty))
|
||||
self.dither()
|
||||
|
||||
class TinyMovement(ZoomedScene):
|
||||
CONFIG = {
|
||||
"distance" : 0.05,
|
||||
"distance_label" : "(0.1)^3 = 0.001",
|
||||
"time_label" : "0.1",
|
||||
}
|
||||
def construct(self):
|
||||
self.activate_zooming()
|
||||
self.show_initial_motion()
|
||||
self.show_ratios()
|
||||
|
||||
def show_initial_motion(self):
|
||||
car = Car()
|
||||
car.move_to(ORIGIN)
|
||||
car_points = car.get_all_points()
|
||||
lowest_to_highest_indices = np.argsort(car_points[:,1])
|
||||
wheel_point = car_points[lowest_to_highest_indices[2]]
|
||||
target_wheel_point = wheel_point+self.distance*RIGHT
|
||||
|
||||
dots = VGroup(*[
|
||||
Dot(point, radius = self.distance/10)
|
||||
for point in wheel_point, target_wheel_point
|
||||
])
|
||||
brace = Brace(Line(ORIGIN, RIGHT))
|
||||
distance_label = TexMobject(self.distance_label)
|
||||
distance_label.next_to(brace, DOWN)
|
||||
distance_label.highlight(DISTANCE_COLOR)
|
||||
brace.add(distance_label)
|
||||
brace.scale(self.distance)
|
||||
brace.next_to(dots, DOWN, buff = self.distance/5)
|
||||
|
||||
zoom_rect = self.little_rectangle
|
||||
zoom_rect.scale(2)
|
||||
zoom_rect.move_to(wheel_point)
|
||||
|
||||
time_label = TextMobject("Time $t = $")
|
||||
time_label.next_to(car, UP, buff = LARGE_BUFF)
|
||||
start_time = TexMobject("0")
|
||||
end_time = TexMobject(self.time_label)
|
||||
for time in start_time, end_time:
|
||||
time.highlight(TIME_COLOR)
|
||||
time.next_to(time_label, RIGHT)
|
||||
|
||||
self.add(car, time_label, start_time)
|
||||
self.play(
|
||||
zoom_rect.scale_in_place,
|
||||
10*self.distance / zoom_rect.get_width()
|
||||
)
|
||||
self.play(ShowCreation(dots[0]))
|
||||
self.play(Transform(start_time, end_time))
|
||||
self.play(MoveCar(car, self.distance*RIGHT))
|
||||
self.play(ShowCreation(dots[1]))
|
||||
self.play(Write(brace, run_time = 1))
|
||||
self.play(
|
||||
zoom_rect.scale, 0.5,
|
||||
zoom_rect.move_to, brace
|
||||
)
|
||||
self.dither()
|
||||
|
||||
def show_ratios(self):
|
||||
ratios = [
|
||||
self.get_ratio(n)
|
||||
for n in range(1, 5)
|
||||
]
|
||||
ratio = ratios[0]
|
||||
self.play(FadeIn(ratio))
|
||||
self.dither(2)
|
||||
for new_ratio in ratios[1:]:
|
||||
self.play(Transform(ratio, new_ratio))
|
||||
self.dither()
|
||||
|
||||
def get_ratio(self, power = 1):
|
||||
dt = "0.%s1"%("0"*(power-1))
|
||||
ds_dt = "0.%s1"%("0"*(2*power-1))
|
||||
expression = TexMobject("""
|
||||
\\frac{(%s)^3 \\text{ meters}}{%s \\text{ seconds}}
|
||||
= %s \\frac{\\text{meters}}{\\text{second}}
|
||||
"""%(dt, dt, ds_dt))
|
||||
expression.next_to(ORIGIN, DOWN, buff = LARGE_BUFF)
|
||||
lengths = [
|
||||
0,
|
||||
len("("),
|
||||
len(dt),
|
||||
len(")3meters_"),
|
||||
len(dt),
|
||||
len("seconds="),
|
||||
len(ds_dt),
|
||||
len("meters_second")
|
||||
]
|
||||
result = VGroup(*[
|
||||
VGroup(*expression[i1:i2])
|
||||
for i1, i2 in zip(
|
||||
np.cumsum(lengths),
|
||||
np.cumsum(lengths)[1:],
|
||||
)
|
||||
])
|
||||
result[1].highlight(DISTANCE_COLOR)
|
||||
result[3].highlight(TIME_COLOR)
|
||||
result[5].highlight(VELOCITY_COLOR)
|
||||
|
||||
return result
|
||||
|
||||
class NextVideos(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
series = VideoSeries()
|
||||
series.scale_to_fit_width(2*SPACE_WIDTH - 1)
|
||||
series.to_edge(UP)
|
||||
series[1].highlight(YELLOW)
|
||||
self.add(series)
|
||||
|
||||
brace = Brace(VGroup(*series[2:6]))
|
||||
brace_text = brace.get_text("More derivative stuffs")
|
||||
|
||||
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
self.get_teacher().change_mode, "raise_right_hand"
|
||||
)
|
||||
self.play(
|
||||
Write(brace_text),
|
||||
*it.chain(*[
|
||||
[pi.look_at, brace]
|
||||
for pi in self.get_students()
|
||||
])
|
||||
)
|
||||
self.dither(2)
|
||||
self.change_student_modes(*["thinking"]*3)
|
||||
self.dither(3)
|
||||
|
||||
class Chapter2PatreonThanks(PatreonThanks):
|
||||
CONFIG = {
|
||||
"specific_patrons" : [
|
||||
"Meshal Alshammari",
|
||||
"Ali Yahya",
|
||||
"CrypticSwarm ",
|
||||
"Yu Jun",
|
||||
"Shelby Doolittle",
|
||||
"Dave Nicponski",
|
||||
"Damion Kistler",
|
||||
"Juan Benet",
|
||||
"Othman Alikhan",
|
||||
"Markus Persson",
|
||||
"Dan Buchoff",
|
||||
"Derek Dai",
|
||||
"Joseph Cox",
|
||||
"Luc Ritchie",
|
||||
"Mark Govea",
|
||||
"Guido Gambardella",
|
||||
"Vecht",
|
||||
"Jonathan Eppele",
|
||||
"Shimin Kuang",
|
||||
"Rish Kundalia",
|
||||
"Achille Brighton",
|
||||
"Kirk Werklund",
|
||||
"Ripta Pasay",
|
||||
"Felipe Diniz",
|
||||
]
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user