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Preliminary end to eoc4 animations
This commit is contained in:
Grant Sanderson
parent
aa9384c9b6
commit
77013e4142
3 changed files with 344 additions and 26 deletions
274
eoc/chapter4.py
274
eoc/chapter4.py
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@ -1676,9 +1676,10 @@ class GeneralizeChainRule(Scene):
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)
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general = TexMobject(
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"\\frac{d}{dx}", "g(", "h(x)", ")", "=",
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"{dg \\over ", " dh}(", "h(x)", ")", "{dh \\over", " dx}", "(x)"
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"{dg \\over ", " dh}", "(", "h(x)", ")", "{dh \\over", " dx}", "(x)"
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)
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example.to_edge(UP, buff = LARGE_BUFF)
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example.shift(RIGHT)
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general.next_to(example, DOWN, buff = 1.5*LARGE_BUFF)
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for mob in example, general:
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mob.highlight(SINE_COLOR)
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@ -1694,24 +1695,26 @@ class GeneralizeChainRule(Scene):
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general_outer = VGroup(*general[1:4])
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general_inner = general[2]
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d_general_outer = VGroup(*general[5:9])
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d_general_inner = general[7]
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d_general_d_inner = VGroup(*general[9:12])
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d_general_outer = VGroup(*general[5:10])
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d_general_inner = general[8]
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d_general_d_inner = VGroup(*general[10:13])
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example_outer_brace = Brace(example_outer)
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example_inner_brace = Brace(example_inner, buff = SMALL_BUFF)
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example_inner_brace = Brace(example_inner, UP, buff = SMALL_BUFF)
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d_example_outer_brace = Brace(d_example_outer)
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d_example_inner_brace = Brace(d_example_inner, buff = SMALL_BUFF)
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d_example_d_inner_brace = Brace(d_example_d_inner, UP, buff = SMALL_BUFF)
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general_outer_brace = Brace(general_outer)
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general_inner_brace = Brace(general_inner, buff = SMALL_BUFF)
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general_inner_brace = Brace(general_inner, UP, buff = SMALL_BUFF)
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d_general_outer_brace = Brace(d_general_outer)
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d_general_inner_brace = Brace(d_general_inner, buff = SMALL_BUFF)
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d_general_d_inner_brace = Brace(d_general_d_inner, UP, buff = SMALL_BUFF)
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for brace in example_outer_brace, general_outer_brace:
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brace.text = brace.get_text("Outer")
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for brace in example_inner_brace, general_inner_brace:
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brace.text = brace.get_text("Inner")
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for brace in d_example_outer_brace, d_general_outer_brace:
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brace.text = brace.get_text("d(Outer)")
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brace.text.shift(SMALL_BUFF*LEFT)
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@ -1720,12 +1723,16 @@ class GeneralizeChainRule(Scene):
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#d(out)d(in) for example
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self.add(example)
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outer_braces = VGroup(example_outer_brace, d_example_outer_brace)
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self.play(*map(GrowFromCenter, outer_braces))
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for brace in outer_braces:
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braces = VGroup(
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example_outer_brace,
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example_inner_brace,
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d_example_outer_brace
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)
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for brace in braces:
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self.play(GrowFromCenter(brace))
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self.play(Write(brace.text, run_time = 1))
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self.dither()
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self.dither()
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inner_braces = VGroup(example_inner_brace, d_example_inner_brace)
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self.play(*it.chain(*[
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[mob.scale_in_place, 1.2, mob.highlight, YELLOW]
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for mob in example_inner, d_example_inner
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@ -1750,12 +1757,247 @@ class GeneralizeChainRule(Scene):
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self.dither()
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#Generalize
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self.play(*map(FadeIn, general[:5]))
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self.dither()
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self.play(
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Transform(example_outer_brace, general_outer_brace),
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Transform(example_outer_brace.text, general_outer_brace.text),
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Transform(example_inner_brace, general_inner_brace),
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Transform(example_inner_brace.text, general_inner_brace.text),
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)
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self.dither()
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self.play(
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Transform(d_example_outer_brace, d_general_outer_brace),
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Transform(d_example_outer_brace.text, d_general_outer_brace.text),
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)
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self.play(Write(d_general_outer))
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self.dither(2)
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self.play(
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Transform(d_example_d_inner_brace, d_general_d_inner_brace),
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Transform(d_example_d_inner_brace.text, d_general_d_inner_brace.text),
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)
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self.play(Write(d_general_d_inner))
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self.dither(2)
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#Name chain rule
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name = TextMobject("``Chain rule''")
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name.scale(1.2)
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name.highlight(YELLOW)
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name.to_corner(UP+LEFT)
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self.play(Write(name))
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self.dither()
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#Point out dh bottom
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morty = Mortimer().flip()
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morty.to_corner(DOWN+LEFT)
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d_general_outer_copy = d_general_outer.copy()
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morty.set_fill(opacity = 0)
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self.play(
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morty.set_fill, None, 1,
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morty.change_mode, "raise_left_hand",
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morty.look, UP+LEFT,
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d_general_outer_copy.next_to,
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morty.get_corner(UP+LEFT), UP, MED_LARGE_BUFF,
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d_general_outer_copy.shift_onto_screen
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)
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self.dither()
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circle = Circle(color = YELLOW)
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circle.replace(d_general_outer_copy[1])
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circle.scale_in_place(1.4)
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self.play(ShowCreation(circle))
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self.play(Blink(morty))
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self.dither()
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inner = d_general_outer_copy[3]
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self.play(
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morty.change_mode, "hooray",
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morty.look_at, inner,
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inner.shift, UP
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)
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self.play(inner.shift, DOWN)
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self.dither()
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self.play(morty.change_mode, "pondering")
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self.play(Blink(morty))
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self.dither()
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self.play(*map(FadeOut, [
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d_general_outer_copy, inner, circle
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]))
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#Show cancelation
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braces = [
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d_example_d_inner_brace,
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d_example_outer_brace,
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example_inner_brace,
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example_outer_brace,
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]
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texts = [brace.text for brace in braces]
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self.play(*map(FadeOut, braces+texts))
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to_collapse = VGroup(VGroup(*general[7:10]), general[12])
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dg_dh = VGroup(*general[5:7])
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dh_dx = VGroup(*general[10:12])
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to_collapse.generate_target()
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points = VGroup(*map(VectorizedPoint,
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[m.get_left() for m in to_collapse]
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))
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self.play(
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Transform(to_collapse, points),
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dh_dx.next_to, dg_dh,
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morty.look_at, dg_dh,
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)
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self.dither()
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for mob in list(dg_dh)+list(dh_dx):
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circle = Circle(color = YELLOW)
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circle.replace(mob)
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circle.scale_in_place(1.3)
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self.play(ShowCreation(circle))
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self.dither()
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self.play(FadeOut(circle))
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strikes = VGroup()
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for dh in dg_dh[1], dh_dx[0]:
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strike = TexMobject("/")
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strike.stretch(2, dim = 0)
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strike.rotate(-np.pi/12)
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strike.move_to(dh)
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strike.highlight(RED)
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strikes.add(strike)
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self.play(Write(strikes))
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self.play(morty.change_mode, "hooray")
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equals_dg_dx = TexMobject("= \\frac{dg}{dx}")
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equals_dg_dx.next_to(dh_dx)
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self.play(Write(equals_dg_dx))
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self.play(Blink(morty))
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self.dither()
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class WatchingVideo(PiCreatureScene):
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def construct(self):
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randy = self.get_primary_pi_creature()
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laptop = Laptop()
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laptop.next_to(randy.get_corner(UP+RIGHT), RIGHT)
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randy.look_at(laptop.screen)
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formulas = VGroup(*[
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TexMobject("\\frac{d}{dx}\\left( %s \\right)"%s)
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for s in [
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"e^x \\sin(x)",
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"\\sin(x) \\cdot \\frac{1}{\\cos(x)}",
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"\\cos(3x)^2",
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"e^x(x^2 + 3x + 2)",
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]
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])
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formulas.arrange_submobjects(
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DOWN,
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buff = MED_LARGE_BUFF,
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aligned_edge = LEFT
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)
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formulas.next_to(randy, LEFT, buff = MED_LARGE_BUFF)
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formulas.shift_onto_screen()
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self.add(randy, laptop)
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self.dither()
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self.play(randy.change_mode, "erm")
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self.play(Blink(randy))
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self.dither()
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self.play(randy.change_mode, "maybe")
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self.dither()
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self.play(Blink(randy))
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for formula in formulas:
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self.play(
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Write(formula, run_time = 2),
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randy.change_mode, "thinking"
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)
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self.dither()
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def create_pi_creatures(self):
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return [Randolph().shift(DOWN+RIGHT)]
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class NextVideo(TeacherStudentsScene):
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def construct(self):
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series = VideoSeries()
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series.to_edge(UP)
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next_video = series[4]
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pre_expression = TexMobject(
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"x", "^2", "+", "y", "^2", "=", "1"
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)
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d_expression = TexMobject(
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"2", "x", "\\,dx", "+", "2", "y", "\\,dy", "=", "0"
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)
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expression_to_d_expression_indices = [
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1, 0, 0, 2, 4, 3, 3, 5, 6
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]
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expression = VGroup()
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for i, j in enumerate(expression_to_d_expression_indices):
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submob = pre_expression[j].copy()
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if d_expression.expression_parts[i] == "2":
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two = TexMobject("2")
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two.replace(submob)
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expression.add(two)
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else:
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expression.add(submob)
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for mob in expression, d_expression:
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mob.scale(1.2)
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mob.next_to(
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self.get_teacher().get_corner(UP+LEFT), UP,
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buff = MED_LARGE_BUFF
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)
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mob.shift_onto_screen()
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self.add(series)
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self.play(
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next_video.shift, 0.5*DOWN,
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next_video.highlight, YELLOW,
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self.get_teacher().change_mode, "raise_right_hand"
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)
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self.dither()
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self.play(
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Write(expression),
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*[
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ApplyMethod(pi.change_mode, "pondering")
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for pi in self.get_students()
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]
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)
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self.dither()
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self.remove(expression)
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self.play(Transform(expression, d_expression, path_arc = np.pi/2))
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self.dither(3)
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class Chapter4Thanks(PatreonThanks):
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CONFIG = {
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"specific_patrons" : [
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"Ali Yahya",
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"Meshal Alshammari",
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"CrypticSwarm ",
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"Ankit Agarwal",
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"Yu Jun",
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"Shelby Doolittle",
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"Dave Nicponski",
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"Damion Kistler",
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"Juan Benet",
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"Othman Alikhan",
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"Justin Helps",
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"Markus Persson",
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"Dan Buchoff",
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"Derek Dai",
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"Joseph John Cox",
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"Luc Ritchie",
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"Nils Schneider",
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"Mathew Bramson",
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"Guido Gambardella",
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"Jerry Ling",
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"Mark Govea",
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"Vecht",
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"Shimin Kuang",
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"Rish Kundalia",
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"Achille Brighton",
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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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@ -8,9 +8,83 @@ from mobject.tex_mobject import TextMobject
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from animation import Animation
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from animation.simple_animations import Rotating
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from topics.geometry import Circle, Line
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from topics.geometry import Circle, Line, Rectangle, Square
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from topics.three_dimensions import Cube
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class Laptop(VGroup):
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CONFIG = {
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"width" : 3,
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"body_dimensions" : [4, 3, 0.05],
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"screen_thickness" : 0.01,
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"keyboard_width_to_body_width" : 0.9,
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"keyboard_height_to_body_height" : 0.5,
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"screen_width_to_screen_plate_width" : 0.9,
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"key_color_kwargs" : {
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"stroke_width" : 0,
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"fill_color" : BLACK,
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"fill_opacity" : 1,
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},
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"body_color" : LIGHT_GREY,
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"shaded_body_color" : GREY,
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"open_angle" : np.pi/4,
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}
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def generate_points(self):
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body = Cube(side_length = 1)
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for dim, scale_factor in enumerate(self.body_dimensions):
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body.stretch(scale_factor, dim = dim)
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body.scale_to_fit_width(self.width)
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body.set_fill(self.shaded_body_color, opacity = 1)
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body.sort_submobjects(lambda p : p[2])
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body[-1].set_fill(self.body_color)
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keyboard = VGroup(*[
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VGroup(*[
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Square(**self.key_color_kwargs)
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for x in range(12-y%2)
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]).arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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for y in range(4)
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]).arrange_submobjects(DOWN, buff = MED_SMALL_BUFF)
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keyboard.stretch_to_fit_width(
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self.keyboard_width_to_body_width*body.get_width(),
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)
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keyboard.stretch_to_fit_height(
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self.keyboard_height_to_body_height*body.get_height(),
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)
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keyboard.next_to(body, OUT, buff = 0.1*SMALL_BUFF)
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keyboard.shift(MED_SMALL_BUFF*UP)
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body.add(keyboard)
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screen_plate = body.copy()
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screen_plate.stretch(self.screen_thickness/self.body_dimensions[2], dim = 2)
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screen = Rectangle(
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stroke_width = 0,
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fill_color = BLACK,
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fill_opacity = 1,
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)
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screen.replace(screen_plate, stretch = True)
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screen.scale_in_place(self.screen_width_to_screen_plate_width)
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screen.next_to(screen_plate, OUT, buff = 0.1*SMALL_BUFF)
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screen_plate.add(screen)
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screen_plate.next_to(body, UP, buff = 0)
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screen_plate.rotate(
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self.open_angle, RIGHT,
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about_point = screen_plate.get_bottom()
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)
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self.screen_plate = screen_plate
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self.screen = screen
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axis = Line(
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body.get_corner(UP+LEFT+OUT),
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body.get_corner(UP+RIGHT+OUT),
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color = BLACK,
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stroke_width = 2
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)
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self.axis = axis
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self.add(body, screen_plate, axis)
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self.rotate(5*np.pi/12, LEFT)
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self.rotate(np.pi/6, DOWN)
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class PatreonLogo(SVGMobject):
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CONFIG = {
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"file_name" : "patreon_logo",
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@ -16,8 +16,11 @@ class ThreeDCamera(Camera):
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self.unit_sun_vect = self.sun_vect/np.linalg.norm(self.sun_vect)
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def display_multiple_vectorized_mobjects(self, vmobjects):
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def cmp_vmobs(vm1, vm2):
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return cmp(vm1.get_center()[2], vm2.get_center()[2])
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def cmp_vmobs(*vmobs):
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return cmp(*[
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vm.get_edge_center(IN)[2]
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for vm in vmobs
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])
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Camera.display_multiple_vectorized_mobjects(
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self,
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sorted(vmobjects, cmp = cmp_vmobs)
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@ -73,13 +76,12 @@ class Cube(VGroup):
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"side_length" : 2,
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}
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def generate_points(self):
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faces = [
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Square(side_length = self.side_length).shift(OUT).apply_function(
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lambda p : np.dot(p, z_to_vector(vect).T)
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)
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for vect in IN, OUT, LEFT, RIGHT, UP, DOWN
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]
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self.add(*faces)
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for vect in IN, OUT, LEFT, RIGHT, UP, DOWN:
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face = Square(side_length = self.side_length)
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face.shift(self.side_length*OUT/2.0)
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face.apply_function(lambda p : np.dot(p, z_to_vector(vect).T))
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self.add(face)
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