mirror of
https://github.com/3b1b/manim.git
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First few scens of eoc1 remake
This commit is contained in:
Grant Sanderson
parent
aa2b5b07cd
commit
ce93d88944
4 changed files with 603 additions and 31 deletions
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@ -75,7 +75,7 @@ class Write(ShowCreation):
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if "run_time" not in kwargs:
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self.establish_run_time(mobject)
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if "lag_factor" not in kwargs:
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if len(mobject.family_members_with_points()) < 2:
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if len(mobject.family_members_with_points()) < 3:
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min_lag_factor = 1
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else:
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min_lag_factor = 2
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622
eoc/chapter1.py
622
eoc/chapter1.py
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@ -32,16 +32,18 @@ class CircleScene(PiCreatureScene):
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"radius" : 1.5,
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"stroke_color" : WHITE,
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"fill_color" : BLUE_E,
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"fill_opacity" : 0.5,
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"fill_opacity" : 0.75,
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"radial_line_color" : MAROON_B,
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"outer_ring_color" : GREEN_E,
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"ring_colors" : [BLUE, GREEN],
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"dR" : 0.1,
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"dR_color" : YELLOW,
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"unwrapped_tip" : ORIGIN,
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"include_pi_creature" : False,
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"circle_corner" : UP+LEFT
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"circle_corner" : UP+LEFT,
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}
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def setup(self):
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PiCreatureScene.setup(self)
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self.circle = Circle(
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radius = self.radius,
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stroke_color = self.stroke_color,
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@ -57,19 +59,13 @@ class CircleScene(PiCreatureScene):
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self.radius_brace = Brace(self.radius_line, buff = SMALL_BUFF)
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self.radius_label = self.radius_brace.get_text("$R$", buff = SMALL_BUFF)
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self.add(
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self.circle, self.radius_line,
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self.radius_brace, self.radius_label
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self.radius_group = VGroup(
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self.radius_line, self.radius_brace, self.radius_label
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)
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self.add(self.circle, *self.radius_group)
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self.pi_creature = self.create_pi_creature()
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if self.include_pi_creature:
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self.add(self.pi_creature)
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else:
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self.pi_creature.set_fill(opacity = 0)
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def create_pi_creature(self):
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return Mortimer().to_corner(DOWN+RIGHT)
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if not self.include_pi_creature:
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self.remove(self.get_primary_pi_creature())
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def introduce_circle(self, added_anims = []):
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self.remove(self.circle)
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@ -150,6 +146,18 @@ class CircleScene(PiCreatureScene):
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ring.dR = dR
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return ring
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def get_rings(self, **kwargs):
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dR = kwargs.get("dR", self.dR)
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colors = kwargs.get("colors", self.ring_colors)
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radii = np.arange(0, self.radius, dR)
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colors = color_gradient(colors, len(radii))
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rings = VGroup(*[
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self.get_ring(radius, dR = dR, color = color)
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for radius, color in zip(radii, colors)
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])
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return rings
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def get_outer_ring(self):
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return self.get_ring(
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radius = self.radius, dR = self.dR,
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@ -197,12 +205,21 @@ class CircleScene(PiCreatureScene):
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)
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result.move_to(self.unwrapped_tip, aligned_edge = DOWN)
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result.shift(R_plus_dr*DOWN)
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result.to_edge(to_edge)
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if to_edge is not None:
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result.to_edge(to_edge)
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return result
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def create_pi_creature(self):
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self.pi_creature = Randolph(color = BLUE_C)
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self.pi_creature.to_corner(DOWN+LEFT)
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return self.pi_creature
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#############
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#revert_to_original_skipping_status
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class Chapter1OpeningQuote(OpeningQuote):
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CONFIG = {
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"quote" : [
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@ -218,20 +235,569 @@ class Chapter1OpeningQuote(OpeningQuote):
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"author" : "David Hilbert",
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}
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class Introduction(TeacherStudentsScene):
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def construct(self):
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self.show_series()
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self.show_many_facts()
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self.invent_calculus()
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def show_series(self):
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series = VideoSeries()
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series.to_edge(UP)
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this_video = series[0]
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this_video.highlight(YELLOW)
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this_video.save_state()
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this_video.set_fill(opacity = 0)
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this_video.center()
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this_video.scale_to_fit_height(2*SPACE_HEIGHT)
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self.this_video = this_video
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words = TextMobject(
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"Welcome to \\\\",
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"Essence of calculus"
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)
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words.highlight_by_tex("Essence of calculus", YELLOW)
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self.teacher.change_mode("happy")
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self.play(
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FadeIn(
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series,
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submobject_mode = "lagged_start",
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run_time = 2
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),
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Blink(self.get_teacher())
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)
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self.teacher_says(words, target_mode = "hooray")
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self.change_student_modes(
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*["hooray"]*3,
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look_at_arg = series[1].get_left(),
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added_anims = [
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ApplyMethod(this_video.restore, run_time = 3),
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]
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)
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self.play(
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ApplyWave(series, direction = DOWN, run_time = 2),
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Animation(self.teacher.bubble),
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Animation(self.teacher.bubble.content),
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)
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essence_words = words.get_part_by_tex("Essence").copy()
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self.play(
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FadeOut(self.teacher.bubble),
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FadeOut(self.teacher.bubble.content),
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essence_words.next_to, series, DOWN,
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*[
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ApplyMethod(pi.change_mode, "pondering")
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for pi in self.get_pi_creatures()
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]
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)
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self.dither(3)
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self.series = series
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self.essence_words = essence_words
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def show_many_facts(self):
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rules = list(it.starmap(TexMobject, [
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("{d(", "x", "^2)", "\\over \\,", "dx}", "=", "2", "x"),
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(
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"d(", "f", "g", ")", "=",
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"f", "dg", "+", "g", "df",
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),
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(
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"F(x)", "=", "\\int_0^x",
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"\\frac{dF}{dg}(t)\\,", "dt"
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),
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(
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"f(x)", "=", "\\sum_{n = 0}^\\infty",
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"f^{(n)}(a)", "\\frac{(x-a)^n}{n!}"
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),
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]))
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video_indices = [2, 3, 7, 10]
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tex_to_color = [
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("x", BLUE),
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("f", BLUE),
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("df", BLUE),
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("g", YELLOW),
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("dg", YELLOW),
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("f(x)", BLUE),
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( "f^{(n)}(a)", BLUE),
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]
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for rule in rules:
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for tex, color in tex_to_color:
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rule.highlight_by_tex(tex, color, substring = False)
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rule.next_to(self.teacher.get_corner(UP+LEFT), UP)
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rule.shift_onto_screen()
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student_index = 1
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student = self.get_students()[student_index]
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self.change_student_modes(
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"pondering", "sassy", "pondering",
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look_at_arg = self.teacher.eyes,
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added_anims = [
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self.teacher.change_mode, "plain"
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]
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)
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self.dither(2)
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self.play(
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Write(rules[0]),
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self.teacher.change_mode, "raise_right_hand",
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)
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self.dither()
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alt_rules_list = list(rules[1:]) + [VectorizedPoint(self.teacher.eyes.get_top())]
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for last_rule, rule, video_index in zip(rules, alt_rules_list, video_indices):
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video = self.series[video_index]
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self.play(
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last_rule.replace, video,
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FadeIn(rule),
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)
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self.play(Animation(rule))
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self.dither()
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self.play(
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self.teacher.change_mode, "happy",
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self.teacher.look_at, student.eyes
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)
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def invent_calculus(self):
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student = self.get_students()[1]
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creatures = self.get_pi_creatures()
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creatures.remove(student)
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creature_copies = creatures.copy()
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self.remove(creatures)
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self.add(creature_copies)
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calculus = VGroup(*self.essence_words[-len("calculus"):])
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calculus.generate_target()
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invent = TextMobject("Invent")
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invent_calculus = VGroup(invent, calculus.target)
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invent_calculus.arrange_submobjects(RIGHT, buff = MED_SMALL_BUFF)
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invent_calculus.next_to(student, UP, 1.5*LARGE_BUFF)
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invent_calculus.shift(RIGHT)
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arrow = Arrow(invent_calculus, student)
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fader = Rectangle(
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width = 2*SPACE_WIDTH,
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height = 2*SPACE_HEIGHT,
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stroke_width = 0,
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fill_color = BLACK,
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fill_opacity = 0.5,
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)
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self.play(
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FadeIn(fader),
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Animation(student),
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Animation(calculus)
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)
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self.play(
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Write(invent),
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MoveToTarget(calculus),
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student.change_mode, "erm",
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student.look_at, calculus
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)
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self.play(ShowCreation(arrow))
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self.dither(2)
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class PreviewFrame(Scene):
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def construct(self):
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frame = Rectangle(height = 9, width = 16, color = WHITE)
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frame.scale_to_fit_height(1.5*SPACE_HEIGHT)
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colors = iter(color_gradient([BLUE, YELLOW], 3))
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titles = [
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TextMobject("Chapter %d:"%d, s).to_edge(UP).highlight(colors.next())
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for d, s in [
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(3, "Derivative formulas through geometry"),
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(4, "Chain rule, product rule, etc."),
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(7, "Limits"),
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]
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]
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title = titles[0]
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frame.next_to(title, DOWN)
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self.add(frame, title)
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self.dither(3)
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for next_title in titles[1:]:
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self.play(Transform(title, next_title))
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self.dither(3)
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class ProductRuleDiagram(Scene):
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def construct(self):
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df = 0.4
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dg = 0.2
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rect_kwargs = {
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"stroke_width" : 0,
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"fill_color" : BLUE,
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"fill_opacity" : 0.6,
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}
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rect = Rectangle(width = 4, height = 3, **rect_kwargs)
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rect.shift(DOWN)
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df_rect = Rectangle(
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height = rect.get_height(),
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width = df,
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**rect_kwargs
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)
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dg_rect = Rectangle(
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height = dg,
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width = rect.get_width(),
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**rect_kwargs
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)
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corner_rect = Rectangle(
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height = dg,
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width = df,
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**rect_kwargs
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)
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d_rects = VGroup(df_rect, dg_rect, corner_rect)
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for d_rect, direction in zip(d_rects, [RIGHT, DOWN, RIGHT+DOWN]):
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d_rect.next_to(rect, direction, buff = 0)
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d_rect.set_fill(YELLOW, 0.75)
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corner_pairs = [
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(DOWN+RIGHT, UP+RIGHT),
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(DOWN+RIGHT, DOWN+LEFT),
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(DOWN+RIGHT, DOWN+RIGHT),
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]
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for d_rect, corner_pair in zip(d_rects, corner_pairs):
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line = Line(*[
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rect.get_corner(corner)
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for corner in corner_pair
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])
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d_rect.line = d_rect.copy().replace(line, stretch = True)
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d_rect.line.highlight(d_rect.get_color())
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f_brace = Brace(rect, UP)
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g_brace = Brace(rect, LEFT)
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df_brace = Brace(df_rect, UP)
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dg_brace = Brace(dg_rect, LEFT)
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f_label = f_brace.get_text("$f$")
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g_label = g_brace.get_text("$g$")
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df_label = df_brace.get_text("$df$")
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dg_label = dg_brace.get_text("$dg$")
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VGroup(f_label, df_label).highlight(GREEN)
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VGroup(g_label, dg_label).highlight(RED)
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f_label.generate_target()
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g_label.generate_target()
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fg_group = VGroup(f_label.target, g_label.target)
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fg_group.generate_target()
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fg_group.target.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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fg_group.target.move_to(rect.get_center())
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for mob in df_brace, df_label, dg_brace, dg_label:
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mob.save_state()
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mob.scale(0.01, about_point = rect.get_corner(
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mob.get_center() - rect.get_center()
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))
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self.add(rect)
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self.play(
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GrowFromCenter(f_brace),
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GrowFromCenter(g_brace),
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Write(f_label),
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Write(g_label),
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)
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self.play(MoveToTarget(fg_group))
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self.play(*[
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mob.restore
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for mob in df_brace, df_label, dg_brace, dg_label
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] + [
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ReplacementTransform(d_rect.line, d_rect)
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for d_rect in d_rects
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])
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self.dither()
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self.play(
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d_rects.space_out_submobjects, 1.2,
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MaintainPositionRelativeTo(
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VGroup(df_brace, df_label),
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df_rect
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),
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MaintainPositionRelativeTo(
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VGroup(dg_brace, dg_label),
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dg_rect
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),
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)
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self.dither()
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deriv = TexMobject(
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"d(", "fg", ")", "=",
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"f", "\\cdot", "dg", "+", "g", "\\cdot", "df"
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)
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deriv.to_edge(UP)
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alpha_iter = iter(np.linspace(0, 0.5, 5))
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self.play(*[
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ApplyMethod(
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mob.copy().move_to,
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deriv.get_part_by_tex(tex, substring = False),
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rate_func = squish_rate_func(smooth, alpha, alpha+0.5)
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)
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for mob, tex in [
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(fg_group, "fg"),
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(f_label, "f"),
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(dg_label, "dg"),
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(g_label, "g"),
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(df_label, "df"),
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]
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for alpha in [alpha_iter.next()]
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]+[
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Write(VGroup(*it.chain(*[
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deriv.get_parts_by_tex(tex, substring = False)
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for tex in "d(", ")", "=", "\\cdot", "+"
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])))
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], run_time = 3)
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self.dither()
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class IntroduceCircle(CircleScene):
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CONFIG = {
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"include_pi_creature" : True,
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"unwrapped_tip" : 2*RIGHT
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}
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def construct(self):
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self.force_skipping()
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self.introduce_area()
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self.question_area()
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self.show_calculus_symbols()
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def introduce_area(self):
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area = TexMobject("\\text{Area}", "=", "\\pi", "R", "^2")
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area.next_to(self.pi_creature.get_corner(UP+RIGHT), UP+RIGHT)
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self.remove(self.circle, self.radius_group)
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self.play(
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self.pi_creature.change_mode, "pondering",
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self.pi_creature.look_at, self.circle
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)
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self.introduce_circle()
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self.dither()
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R_copy = self.radius_label.copy()
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self.play(
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self.pi_creature.change_mode, "raise_right_hand",
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self.pi_creature.look_at, area,
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Transform(R_copy, area.get_part_by_tex("R"))
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)
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self.play(Write(area))
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self.remove(R_copy)
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self.dither()
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self.area = area
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def question_area(self):
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q_marks = TexMobject("???")
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q_marks.next_to(self.pi_creature, UP)
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rings = VGroup(*reversed(self.get_rings()))
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unwrapped_rings = VGroup(*[
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self.get_unwrapped(ring, to_edge = None)
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for ring in rings
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])
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unwrapped_rings.arrange_submobjects(UP, buff = SMALL_BUFF)
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unwrapped_rings.move_to(self.unwrapped_tip, UP)
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ring_anim_kwargs = {
|
||||
"run_time" : 3,
|
||||
"submobject_mode" : "lagged_start"
|
||||
}
|
||||
|
||||
self.play(
|
||||
Animation(self.area),
|
||||
Write(q_marks),
|
||||
self.pi_creature.change_mode, "confused",
|
||||
self.pi_creature.look_at, self.area,
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
FadeIn(rings, **ring_anim_kwargs),
|
||||
Animation(self.radius_group),
|
||||
FadeOut(q_marks),
|
||||
self.pi_creature.change_mode, "thinking"
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
rings.rotate, np.pi/2,
|
||||
rings.move_to, unwrapped_rings.get_top(),
|
||||
Animation(self.radius_group),
|
||||
path_arc = np.pi/2,
|
||||
**ring_anim_kwargs
|
||||
)
|
||||
self.play(
|
||||
Transform(rings, unwrapped_rings, **ring_anim_kwargs),
|
||||
)
|
||||
self.dither()
|
||||
|
||||
def show_calculus_symbols(self):
|
||||
ftc = TexMobject(
|
||||
"\\int_0^R", "\\frac{dA}{dr}", "\\,dr",
|
||||
"=", "A(R)"
|
||||
)
|
||||
ftc.shift(2*UP)
|
||||
|
||||
self.play(
|
||||
ReplacementTransform(
|
||||
self.area.get_part_by_tex("R").copy(),
|
||||
ftc.get_part_by_tex("int")
|
||||
),
|
||||
self.pi_creature.change_mode, "plain"
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
ReplacementTransform(
|
||||
self.area.get_part_by_tex("Area").copy(),
|
||||
ftc.get_part_by_tex("frac")
|
||||
),
|
||||
ReplacementTransform(
|
||||
self.area.get_part_by_tex("R").copy(),
|
||||
ftc.get_part_by_tex("\\,dr")
|
||||
)
|
||||
)
|
||||
self.dither()
|
||||
self.play(Write(VGroup(*ftc[-2:])))
|
||||
self.dither(2)
|
||||
|
||||
class ApproximateOneRing(CircleScene):
|
||||
CONFIG = {
|
||||
"num_lines" : 24,
|
||||
"ring_index_proportion" : 0.75,
|
||||
"ring_shift_val" : 6*RIGHT,
|
||||
"ring_colors" : [BLUE, GREEN_E],
|
||||
}
|
||||
def construct(self):
|
||||
self.force_skipping()
|
||||
|
||||
self.write_radius_three()
|
||||
self.try_to_understand_area()
|
||||
self.slice_into_rings()
|
||||
self.isolate_one_ring()
|
||||
self.straighten_ring_out()
|
||||
self.ask_about_precise_shape()
|
||||
self.approximate_as_rectangle()
|
||||
|
||||
def write_radius_three(self):
|
||||
three = TexMobject("3")
|
||||
three.move_to(self.radius_label)
|
||||
|
||||
self.look_at(self.circle)
|
||||
self.play(Transform(
|
||||
self.radius_label, three,
|
||||
path_arc = np.pi
|
||||
))
|
||||
self.dither()
|
||||
|
||||
def try_to_understand_area(self):
|
||||
line_sets = [
|
||||
VGroup(*[
|
||||
Line(
|
||||
self.circle.point_from_proportion(alpha),
|
||||
self.circle.point_from_proportion(func(alpha)),
|
||||
)
|
||||
for alpha in np.linspace(0, 1, self.num_lines)
|
||||
])
|
||||
for func in [
|
||||
lambda alpha : 1-alpha,
|
||||
lambda alpha : (0.5-alpha)%1,
|
||||
lambda alpha : (alpha + 0.4)%1,
|
||||
lambda alpha : (alpha + 0.5)%1,
|
||||
]
|
||||
]
|
||||
for lines in line_sets:
|
||||
lines.set_stroke(BLACK, 2)
|
||||
lines = line_sets[0]
|
||||
|
||||
self.play(
|
||||
ShowCreation(
|
||||
lines,
|
||||
run_time = 2,
|
||||
submobject_mode = "lagged_start"
|
||||
),
|
||||
Animation(self.radius_group),
|
||||
self.pi_creature.change_mode, "maybe"
|
||||
)
|
||||
self.dither(2)
|
||||
for new_lines in line_sets[1:]:
|
||||
self.play(
|
||||
Transform(lines, new_lines),
|
||||
Animation(self.radius_group)
|
||||
)
|
||||
self.dither()
|
||||
self.dither()
|
||||
self.play(FadeOut(lines), Animation(self.radius_group))
|
||||
|
||||
def slice_into_rings(self):
|
||||
rings = self.get_rings()
|
||||
rings.set_stroke(BLACK, 1)
|
||||
|
||||
self.play(
|
||||
FadeIn(
|
||||
rings,
|
||||
submobject_mode = "lagged_start",
|
||||
run_time = 3
|
||||
),
|
||||
Animation(self.radius_group),
|
||||
self.pi_creature.change_mode, "pondering",
|
||||
self.pi_creature.look_at, self.circle
|
||||
)
|
||||
self.dither(2)
|
||||
group = VGroup(self.circle, rings, self.radius_group)
|
||||
for x in range(2):
|
||||
self.play(
|
||||
ApplyMethod(
|
||||
group.rotate_in_place, np.pi,
|
||||
path_arc = np.pi,
|
||||
rate_func = there_and_back,
|
||||
),
|
||||
self.pi_creature.change_mode, "happy"
|
||||
)
|
||||
self.dither(2)
|
||||
|
||||
self.rings = rings
|
||||
|
||||
def isolate_one_ring(self):
|
||||
index = int(self.ring_index_proportion*len(self.rings))
|
||||
ring = self.rings[index]
|
||||
|
||||
radius = Line(ORIGIN, ring.R*RIGHT, color = WHITE)
|
||||
radius.rotate(np.pi/4)
|
||||
r_label = TexMobject("r")
|
||||
r_label.next_to(radius.get_center(), UP+LEFT, SMALL_BUFF)
|
||||
area_q = TextMobject("Area?")
|
||||
area_q.highlight(YELLOW)
|
||||
|
||||
|
||||
self.revert_to_original_skipping_status()
|
||||
self.play(ring.shift, self.ring_shift_val)
|
||||
|
||||
VGroup(radius, r_label).shift(ring.get_center())
|
||||
area_q.next_to(ring, DOWN)
|
||||
|
||||
self.play(ShowCreation(radius))
|
||||
self.play(Write(r_label))
|
||||
self.dither()
|
||||
self.play(Write(area_q))
|
||||
self.dither()
|
||||
self.play(
|
||||
Indicate(
|
||||
self.rings,
|
||||
scale_factor = 1.01,
|
||||
submobject_mode = "lagged_start",
|
||||
run_time = 3,
|
||||
),
|
||||
Animation(self.radius_group)
|
||||
)
|
||||
self.dither()
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
def straighten_ring_out(self):
|
||||
pass
|
||||
|
||||
def ask_about_precise_shape(self):
|
||||
pass
|
||||
|
||||
def approximate_as_rectangle(self):
|
||||
pass
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -208,7 +208,13 @@ class VMobject(Mobject):
|
|||
|
||||
def append_vectorized_mobject(self, vectorized_mobject):
|
||||
new_points = list(vectorized_mobject.points)
|
||||
self.add_control_points(2*[new_points[0]] + new_points)
|
||||
if len(new_points) == 0:
|
||||
return
|
||||
if self.get_num_points() == 0:
|
||||
self.start_at(new_points[0])
|
||||
self.add_control_points(new_points[1:])
|
||||
else:
|
||||
self.add_control_points(2*[new_points[0]] + new_points)
|
||||
return self
|
||||
|
||||
def get_subpath_mobjects(self):
|
||||
|
|
|
|||
|
|
@ -543,7 +543,7 @@ class PiCreatureScene(Scene):
|
|||
if pi_creatures is None:
|
||||
pi_creatures = self.get_pi_creatures()
|
||||
self.play(*it.chain(*[
|
||||
[pi.look_at, self.get_teacher().eyes]
|
||||
[pi.look_at, thing_to_look_at]
|
||||
for pi in pi_creatures
|
||||
]))
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue