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https://github.com/3b1b/manim.git
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More finishing touches to chapter 7
This commit is contained in:
Grant Sanderson
273
eola/chapter7.py
273
eola/chapter7.py
@ -21,7 +21,6 @@ from eola.matrix import *
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from eola.two_d_space import *
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from eola.footnote2 import TwoDTo1DTransformWithDots
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from ka_playgrounds.circuits import Resistor, Source, LongResistor
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V_COLOR = YELLOW
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W_COLOR = MAROON_B
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@ -584,13 +583,15 @@ class SymmetricVAndW(VectorScene):
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self.remove(vect_copy)
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self.add(vect.proj)
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self.dither()
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self.play(*map(FadeOut,[
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v.proj, v.proj_line, w.proj, w.proj_line
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]))
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self.show_doubling(v, w)
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def show_doubling(self, v, w):
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scalar = 2
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new_v = v.copy().scale(scalar)
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new_v.label = VMobject(TexMobject("c"), v.label.copy())
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new_v.label = VMobject(TexMobject("2"), v.label.copy())
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new_v.label.arrange_submobjects(aligned_edge = DOWN)
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new_v.label.next_to(new_v.get_end(), DOWN+RIGHT)
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new_v.proj = v.proj.copy().scale(scalar)
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@ -602,9 +603,9 @@ class SymmetricVAndW(VectorScene):
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v_tex, w_tex = ["\\vec{\\textbf{%s}}"%c for c in "v", "w"]
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equation = TexMobject(
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"(", "c", v_tex, ")", "\\cdot", w_tex,
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"(", "2", v_tex, ")", "\\cdot", w_tex,
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"=",
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"c(", v_tex, "\\cdot", w_tex, ")"
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"2(", v_tex, "\\cdot", w_tex, ")"
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)
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equation.highlight_by_tex(v_tex, V_COLOR)
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equation.highlight_by_tex(w_tex, W_COLOR)
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@ -616,23 +617,26 @@ class SymmetricVAndW(VectorScene):
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v.save_state()
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v.proj.save_state()
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v.proj_line.save_state()
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self.play(Transform(*[
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Group(mob, mob.proj, mob.proj_line, mob.label)
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Group(mob, mob.label)
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for mob in v, new_v
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]), run_time = 2)
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last_mob = self.get_mobjects_from_last_animation()[0]
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last_mob = self.get_mobjects_from_last_animation()[0]
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self.remove(last_mob)
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self.add(*last_mob)
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self.add(*last_mob)
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Transform(
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Group(v.proj, v.proj_line),
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Group(new_v.proj, new_v.proj_line)
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).update(1)##Hacky
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self.play(Write(words))
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self.dither()
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two_v_parts = equation[1:3]
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equation.remove(*two_v_parts)
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for v_part, projector, stable in zip([v, v.proj], [w, v], [v, w]):
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self.play(*map(FadeOut, [
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stable.proj, stable.proj_line
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]))
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for full_v, projector, stable in zip([False, True], [w, v], [v, w]):
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self.play(
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Transform(projector.copy(), projector.proj),
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ShowCreation(projector.proj_line)
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@ -646,26 +650,32 @@ class SymmetricVAndW(VectorScene):
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Transform(new_v.label.copy(), VMobject(*two_v_parts))
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)
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self.dither()
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v_parts = [v]
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if full_v:
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v_parts += [v.proj, v.proj_line]
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self.play(
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v_part.restore,
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*[v_part.restore for v_part in v_parts],
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rate_func = there_and_back,
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run_time = 2
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)
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self.dither()
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self.play(*map(FadeOut, [
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projector.proj, projector.proj_line
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]))
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class LurkingQuestion(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("That's the standard intro")
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self.dither()
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self.student_says(
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"""
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Wait, why are the
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two views connected?
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""",
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student_index = 2,
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pi_creature_target_mode = "raise_left_hand",
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width = 6,
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)
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# self.teacher_says("That's the standard intro")
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# self.dither()
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# self.student_says(
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# """
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# Wait, why are the
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# two views connected?
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# """,
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# student_index = 2,
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# pi_creature_target_mode = "raise_left_hand",
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# width = 6,
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# )
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self.change_student_modes(
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"raise_right_hand", "confused", "raise_left_hand"
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)
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@ -675,7 +685,7 @@ class LurkingQuestion(TeacherStudentsScene):
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answer comes from""",
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"duality"
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)
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answer.highlight_by_tex("duality", PINK)
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answer[-1].gradient_highlight(BLUE, YELLOW)
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self.teacher_says(answer)
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self.random_blink(2)
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self.teacher_thinks("")
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@ -767,6 +777,64 @@ class Symbolic2To1DTransform(Scene):
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self.play(Write(special_words))
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self.dither()
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class RecommendChapter3(Scene):
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def construct(self):
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title = TextMobject("""
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Definite watch Chapter 3
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if you haven't already
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""")
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title.to_edge(UP)
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rect = Rectangle(width = 16, height = 9, color = BLUE)
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rect.scale_to_fit_height(6)
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rect.next_to(title, DOWN)
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self.add(title)
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self.play(ShowCreation(rect))
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self.dither()
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class OkayToIgnoreFormalProperties(Scene):
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def construct(self):
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title = TextMobject("Formal linearity properties")
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title.to_edge(UP)
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h_line = Line(LEFT, RIGHT).scale(SPACE_WIDTH)
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h_line.next_to(title, DOWN)
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v_tex, w_tex = ["\\vec{\\textbf{%s}}"%s for s in "v", "w"]
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additivity = TexMobject(
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"L(", v_tex, "+", w_tex, ") = ",
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"L(", v_tex, ") + L(", w_tex, ")",
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)
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scaling = TexMobject(
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"L(", "c", v_tex, ") =", "c", "L(", v_tex, ")",
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)
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for tex_mob in additivity, scaling:
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tex_mob.highlight_by_tex(v_tex, V_COLOR)
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tex_mob.highlight_by_tex(w_tex, W_COLOR)
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tex_mob.highlight_by_tex("c", GREEN)
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additivity.next_to(h_line, DOWN, buff = MED_BUFF)
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scaling.next_to(additivity, DOWN, buff = MED_BUFF)
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words = TextMobject("We'll ignore these")
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words.highlight(RED)
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arrow = Arrow(DOWN, UP, color = RED)
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arrow.next_to(scaling, DOWN)
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words.next_to(arrow, DOWN)
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randy = Randolph().to_corner(DOWN+LEFT)
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morty = Mortimer().to_corner(DOWN+RIGHT)
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self.add(randy, morty, title)
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self.play(ShowCreation(h_line))
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for tex_mob in additivity, scaling:
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self.play(Write(tex_mob, run_time = 2))
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self.play(
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FadeIn(words),
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ShowCreation(arrow),
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)
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self.play(
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randy.look, LEFT,
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morty.look, RIGHT,
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)
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self.dither()
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class FormalVsVisual(Scene):
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def construct(self):
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title = TextMobject("Linearity")
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@ -937,6 +1005,48 @@ class ScalingPropertyPart2(ScalingProperty):
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class ThisTwoDTo1DTransformWithDots(TwoDTo1DTransformWithDots):
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pass
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class NonLinearFailsDotTest(TwoDTo1DTransformWithDots):
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def construct(self):
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line = NumberLine()
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self.add(line, *self.get_mobjects())
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offset = LEFT+DOWN
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vect = 2*RIGHT+UP
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dots = VMobject(*[
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Dot(offset + a*vect, radius = 0.075)
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for a in np.linspace(-2, 3, 18)
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])
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dots.submobject_gradient_highlight(YELLOW_B, YELLOW_C)
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func = lambda p : (p[0]**2 - p[1]**2)*RIGHT
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new_dots = VMobject(*[
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Dot(
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func(dot.get_center()),
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color = dot.get_color(),
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radius = dot.radius
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)
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for dot in dots
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])
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words = TextMobject(
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"Line of dots", "do not", "remain evenly spaced"
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)
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words.highlight_by_tex("do not", RED)
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words.next_to(line, UP, buff = MED_BUFF)
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array_tex = matrix_to_tex_string(["x", "y"])
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equation = TexMobject(
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"f", "\\left(%s \\right)"%array_tex, " = x^2 - y^2"
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)
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for part in equation:
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part.add_to_back(BackgroundRectangle(part))
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equation.to_corner(UP+LEFT)
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self.add_foreground_mobject(equation)
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self.play(Write(dots))
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self.apply_nonlinear_transformation(
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func,
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added_anims = [Transform(dots, new_dots)]
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)
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self.play(Write(words))
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self.dither()
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class AlwaysfollowIHatJHat(TeacherStudentsScene):
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def construct(self):
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i_tex, j_tex = ["$\\hat{\\%smath}$"%c for c in "i", "j"]
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@ -1242,6 +1352,69 @@ class WhatAboutTheGeometricView(TeacherStudentsScene):
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self.change_student_modes("pondering", "raise_right_hand", "pondering")
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self.random_blink(2)
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class SomeKindOfConnection(Scene):
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CONFIG = {
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"v_coords" : [2, 3]
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}
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def construct(self):
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width = SPACE_WIDTH-1
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plane = NumberPlane(x_radius = 4, y_radius = 6)
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squish_plane = plane.copy()
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i_hat = Vector([1, 0], color = X_COLOR)
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j_hat = Vector([0, 1], color = Y_COLOR)
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vect = Vector(self.v_coords, color = YELLOW)
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plane.add(vect, i_hat, j_hat)
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plane.scale_to_fit_width(SPACE_WIDTH)
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plane.to_edge(LEFT, buff = 0)
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plane.remove(vect, i_hat, j_hat)
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squish_plane.apply_function(
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lambda p : np.dot(p, [4, 1, 0])*RIGHT
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)
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squish_plane.add(Vector(self.v_coords[1]*RIGHT, color = Y_COLOR))
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squish_plane.add(Vector(self.v_coords[0]*RIGHT, color = X_COLOR))
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squish_plane.scale(width/(2*SPACE_WIDTH))
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plane.add(j_hat, i_hat)
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number_line = NumberLine().stretch_to_fit_width(width)
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number_line.to_edge(RIGHT)
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squish_plane.move_to(number_line)
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numbers = number_line.get_numbers(*range(-6, 8, 2))
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v_line = Line(UP, DOWN).scale(SPACE_HEIGHT)
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v_line.highlight(GREY)
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v_line.set_stroke(width = 10)
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matrix = Matrix([self.v_coords])
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matrix.highlight_columns(X_COLOR, Y_COLOR)
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matrix.next_to(number_line, UP, buff = LARGE_BUFF)
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v_coords = Matrix(self.v_coords)
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v_coords.highlight_columns(YELLOW)
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v_coords.scale(0.75)
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v_coords.next_to(vect.get_end(), RIGHT)
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for array in matrix, v_coords:
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array.add_to_back(BackgroundRectangle(array))
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self.play(*map(ShowCreation, [
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plane, number_line, v_line
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])+[
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Write(numbers, run_time = 2)
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])
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self.play(Write(matrix, run_time = 1))
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mover = plane.copy()
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interim = plane.copy().scale(0.8).move_to(number_line)
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for target in interim, squish_plane:
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self.play(
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Transform(mover, target),
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Animation(plane),
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run_time = 1,
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)
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self.dither()
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self.play(ShowCreation(vect))
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self.play(Transform(matrix.copy(), v_coords))
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self.dither()
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class AnExampleWillClarify(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("An example will clarify...")
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@ -1269,33 +1442,32 @@ class ProjectOntoUnitVectorNumberline(VectorScene):
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plane.fade()
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u_hat = Vector([1, 0], color = self.u_hat_color)
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u_brace = Brace(u_hat)
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u_brace = Brace(u_hat, UP)
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u_hat.rotate(self.tilt_angle)
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u_hat.label = TexMobject("\\hat{\\textbf{u}}")
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u_hat.label.highlight(u_hat.get_color())
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u_hat.label.next_to(u_hat.get_end(), UP+LEFT)
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one = TexMobject("1")
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u_brace.put_at_tip(one)
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u_brace.add(one)
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u_brace.rotate(u_hat.get_angle())
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one = TexMobject("1").add_background_rectangle()
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one.next_to(u_brace.get_center(), DOWN+RIGHT, buff = MED_BUFF/2)
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one.rotate_in_place(-u_hat.get_angle())
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number_line = NumberLine(x_min = -9, x_max = 9)
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numbers = number_line.get_numbers()
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Group(number_line, numbers).rotate(u_hat.get_angle())
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if self.animate_setup:
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self.play(ShowCreation(u_hat))
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self.play(Write(u_hat.label))
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self.play(
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GrowFromCenter(u_brace),
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Write(one)
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)
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self.dither()
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self.play(
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ShowCreation(number_line),
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Write(numbers),
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Animation(u_hat),
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*map(FadeOut, [u_brace, one]),
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run_time = 3
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)
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self.dither()
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self.play(ShowCreation(u_hat))
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self.play(FadeIn(u_brace))
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self.play(FadeOut(u_brace))
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self.play(Write(u_hat.label))
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self.dither()
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else:
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self.add(number_line, numbers, u_hat)
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@ -1514,7 +1686,7 @@ class ProjectBasisVectors(ProjectOntoUnitVectorNumberline):
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i_label = TexMobject(i_tex[1:-1])
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j_label = TexMobject(j_tex[1:-1])
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u_label = TexMobject("\\vec{\\textbf{u}}")
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u_label = TexMobject("\\hat{\\textbf{u}}")
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trips = zip(
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(i_label, j_label, u_label),
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(i_hat, j_hat, self.u_hat),
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@ -1964,6 +2136,31 @@ class IsntThisBeautiful(TeacherStudentsScene):
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self.teacher_says(duality_words)
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self.random_blink()
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class RememberGraphDuality(Scene):
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def construct(self):
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words = TextMobject("""
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\\centering
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Some of you may remember an
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early video I did on graph duality
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""")
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words.to_edge(UP)
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self.play(Write(words, lag_factor = 4))
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self.dither()
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class LooseDualityDescription(Scene):
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def construct(self):
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duality = TextMobject("Duality")
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duality.gradient_highlight(BLUE, YELLOW)
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arrow = TexMobject("\\Leftrightarrow")
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words = TextMobject("Natural-but-surprising", "correspondence")
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words[1].gradient_highlight(BLUE, YELLOW)
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Group(duality, arrow, words).arrange_submobjects(buff = MED_BUFF)
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self.add(duality)
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self.play(Write(arrow))
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self.play(Write(words))
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self.dither()
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class DualOfAVector(ScaleUpUHat):
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pass #Exact copy
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