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https://github.com/3b1b/manim.git
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Initial complex transformation material, and some reworking of the phi example of alt_cal
This commit is contained in:
Grant Sanderson
parent
e4c9636cf4
commit
24c387e7cb
2 changed files with 532 additions and 246 deletions
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@ -986,6 +986,11 @@ class MoreTopics(Scene):
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)
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self.wait()
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self.calculus = calculus
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self.lines = lines
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self.full_screen_rect = rect
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self.other_topics = others
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class TransformationalViewWrapper(Wrapper):
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CONFIG = {
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@ -1892,9 +1897,15 @@ class HowDoesThisSolveProblems(TeacherStudentsScene):
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class IntroduceContinuedFractionPuzzle(PiCreatureScene):
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CONFIG = {
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"remove_initial_rhs": True,
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}
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def construct(self):
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self.ask_question()
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self.plug_func_into_self()
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self.set_equal_to_x()
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# TODO, move this
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# self.plug_func_into_self()
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def create_pi_creatures(self):
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morty = Mortimer(height=2)
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@ -1902,6 +1913,7 @@ class IntroduceContinuedFractionPuzzle(PiCreatureScene):
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friend = PiCreature(color=GREEN, height=2)
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friend.to_edge(DOWN)
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friend.shift(0.5 * LEFT)
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group = VGroup(morty, friend)
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group.shift(2 * LEFT)
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@ -1910,7 +1922,8 @@ class IntroduceContinuedFractionPuzzle(PiCreatureScene):
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def ask_question(self):
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morty, friend = self.pi_creatures
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frac = get_phi_continued_fraction(5)
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frac = get_phi_continued_fraction(9)
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frac.scale(0.8)
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rhs = DecimalNumber(
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(1 - np.sqrt(5)) / 2.0,
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num_decimal_places=5,
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@ -1925,10 +1938,17 @@ class IntroduceContinuedFractionPuzzle(PiCreatureScene):
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group.to_corner(UR)
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self.play(
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FadeInFromDown(group),
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LaggedStart(
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Write, frac,
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run_time=15,
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lag_ratio=0.15,
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),
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FadeInFromDown(equals),
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FadeInFromDown(rhs),
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PiCreatureSays(
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friend, "Would this be valid? \\\\ If not, why not?",
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target_mode="confused",
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look_at_arg=frac,
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bubble_kwargs={
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"direction": RIGHT,
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"width": 4,
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@ -1937,50 +1957,344 @@ class IntroduceContinuedFractionPuzzle(PiCreatureScene):
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),
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morty.change, "pondering",
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)
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for x in range(3):
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self.play(LaggedStart(
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ApplyMethod, frac,
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lambda m: (m.set_color, YELLOW),
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rate_func=there_and_back,
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lag_ratio=0.2,
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run_time=2
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))
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self.wait()
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self.play(
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frac.scale, 0.5,
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frac.to_corner, UL,
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self.wait()
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anims = [
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RemovePiCreatureBubble(
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friend, target_mode="pondering",
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look_at_arg=frac
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),
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FadeOut(equals),
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rhs.scale, 0.5,
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rhs.to_corner, DL,
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)
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]
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if self.remove_initial_rhs:
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anims += [
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Animation(frac),
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FadeOut(equals),
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rhs.scale, 0.5,
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rhs.to_corner, DL,
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]
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self.play(*anims)
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self.neg_one_over_phi = rhs
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self.equals = equals
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self.frac = frac
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def plug_func_into_self(self):
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morty, friend = self.pi_creatures
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def set_equal_to_x(self):
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frac = self.frac
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morty, friend = self.get_pi_creatures()
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inner_frac = frac[4:]
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inner_frac_rect = SurroundingRectangle(
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inner_frac, stroke_width=2, buff=0.5 * SMALL_BUFF
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)
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inner_frac_group = VGroup(inner_frac, inner_frac_rect)
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equals = TexMobject("=")
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equals.next_to(frac[3], RIGHT)
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x, new_x = [TexMobject("x") for i in range(2)]
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xs = VGroup(x, new_x)
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xs.set_color(YELLOW)
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xs.scale(1.3)
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x.next_to(equals, RIGHT)
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new_x.next_to(frac[3], DOWN, 2 * SMALL_BUFF)
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fixed_point_words = VGroup(
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TextMobject("Fixed point of"),
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TexMobject(
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"f(x) = 1 + \\frac{1}{x}",
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tex_to_color_map={"x": YELLOW}
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)
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)
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fixed_point_words.arrange_submobjects(DOWN)
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self.play(Write(x), Write(equals))
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self.wait()
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self.play(ShowCreation(inner_frac_rect))
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self.wait()
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self.play(
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inner_frac_group.scale, 0.75,
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inner_frac_group.center,
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inner_frac_group.to_edge, LEFT,
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ReplacementTransform(
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x.copy(), new_x,
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path_arc=-90 * DEGREES
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)
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)
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self.wait()
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self.play(
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frac[3].stretch, 0.1, 0, {"about_edge": RIGHT},
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MaintainPositionRelativeTo(
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VGroup(frac[2], new_x), frac[3]
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),
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UpdateFromFunc(
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frac[:2], lambda m: m.next_to(frac[3], LEFT)
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)
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)
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self.wait()
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fixed_point_words.next_to(VGroup(frac[0], xs), DOWN, LARGE_BUFF)
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self.play(
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Write(fixed_point_words),
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morty.change, "hooray",
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friend.change, "happy"
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)
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self.wait(3)
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class GraphOnePlusOneOverX(GraphScene):
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CONFIG = {
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"x_min": -6,
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"x_max": 6,
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"x_axis_width": 12,
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"y_min": -4,
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"y_max": 5,
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"y_axis_height": 8,
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"y_axis_label": None,
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"graph_origin": 0.5 * DOWN,
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"num_graph_anchor_points": 100,
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"func_graph_color": GREEN,
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"identity_graph_color": BLUE,
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}
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def construct(self):
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self.add_title()
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self.setup_axes()
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self.draw_graphs()
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self.show_solutions()
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def add_title(self):
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title = self.title = TexMobject(
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"\\text{Solve: }", "1 + \\frac{1}{x}", "=", "x",
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)
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title.set_color_by_tex("x", self.identity_graph_color, substring=False)
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title.set_color_by_tex("frac", self.func_graph_color)
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title.to_corner(UL)
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self.add(title)
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def setup_axes(self):
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GraphScene.setup_axes(self)
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step = 2
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self.x_axis.add_numbers(*range(-6, 0, step) + range(step, 7, step))
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self.y_axis.label_direction = RIGHT
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self.y_axis.add_numbers(*range(-2, 0, step) + range(step, 4, step))
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def draw_graphs(self, animate=True):
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lower_func_graph, upper_func_graph = func_graph = VGroup(*[
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self.get_graph(
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lambda x: 1.0 + 1.0 / x,
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x_min=x_min,
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x_max=x_max,
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color=self.func_graph_color,
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)
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for x_min, x_max in (-10, -0.1), (0.1, 10)
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])
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func_graph.label = self.get_graph_label(
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upper_func_graph, "y = 1 + \\frac{1}{x}",
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x_val=6, direction=UP,
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)
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identity_graph = self.get_graph(
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lambda x: x, color=self.identity_graph_color
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)
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identity_graph.label = self.get_graph_label(
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identity_graph, "y = x",
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x_val=3, direction=UL, buff=SMALL_BUFF
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)
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if animate:
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for graph in func_graph, identity_graph:
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self.play(
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ShowCreation(graph),
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Write(graph.label),
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run_time=2
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)
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self.wait()
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else:
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self.add(
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func_graph, func_graph.label,
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identity_graph, identity_graph.label,
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)
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self.func_graph = func_graph
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self.identity_graph = identity_graph
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def show_solutions(self):
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phi = 0.5 * (1 + np.sqrt(5))
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phi_bro = 0.5 * (1 - np.sqrt(5))
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lines = VGroup()
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for n_terms in range(1, 5):
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lhs = get_nested_f(n_terms)
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for num in phi, phi_bro:
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line = DashedLine(
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self.coords_to_point(num, 0),
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self.coords_to_point(num, num),
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color=WHITE
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)
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line_copy = line.copy()
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line_copy.set_color(YELLOW)
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line.fade(0.5)
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line_anim = ShowCreationThenDestruction(
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line_copy,
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submobject_mode="lagged_start",
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run_time=2
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)
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line.continual_anim = CycleAnimation(line_anim)
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lines.add(line)
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phi_line, phi_bro_line = lines
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decimal_kwargs = {
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"num_decimal_places": 3,
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"show_ellipsis": True,
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"color": YELLOW,
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}
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arrow_kwargs = {
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"buff": SMALL_BUFF,
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"color": WHITE,
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"tip_length": 0.15,
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"rectangular_stem_width": 0.025,
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}
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phi_decimal = DecimalNumber(phi, **decimal_kwargs)
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phi_decimal.next_to(phi_line, DOWN, LARGE_BUFF)
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phi_arrow = Arrow(
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phi_decimal[:4].get_top(), phi_line.get_bottom(),
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**arrow_kwargs
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)
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phi_label = TexMobject("=", "\\varphi")
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phi_label.next_to(phi_decimal, RIGHT)
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phi_label.set_color_by_tex("\\varphi", YELLOW)
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phi_bro_decimal = DecimalNumber(phi_bro, **decimal_kwargs)
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phi_bro_decimal.next_to(phi_bro_line, UP, LARGE_BUFF)
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phi_bro_decimal.shift(0.5 * LEFT)
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phi_bro_arrow = Arrow(
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phi_bro_decimal[:6].get_bottom(), phi_bro_line.get_top(),
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**arrow_kwargs
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)
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brother_words = TextMobject(
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"$\\varphi$'s little brother",
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tex_to_color_map={"$\\varphi$": YELLOW},
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arg_separator=""
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)
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brother_words.next_to(
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phi_bro_decimal[-2], UP, buff=MED_SMALL_BUFF,
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aligned_edge=RIGHT
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)
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self.add(phi_line.continual_anim)
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self.play(ShowCreation(phi_line))
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self.play(
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Write(phi_decimal),
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GrowArrow(phi_arrow),
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)
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self.play(Write(phi_label))
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self.wait(3)
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self.add(phi_bro_line.continual_anim)
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self.play(ShowCreation(phi_bro_line))
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self.play(
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Write(phi_bro_decimal),
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GrowArrow(phi_bro_arrow),
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)
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self.wait(4)
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self.play(Write(brother_words))
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self.wait(8)
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class ThinkAboutWithRepeatedApplication(IntroduceContinuedFractionPuzzle):
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CONFIG = {
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"remove_initial_rhs": False,
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}
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def construct(self):
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self.force_skipping()
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self.ask_question()
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self.revert_to_original_skipping_status()
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self.obviously_not()
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self.plug_func_into_self()
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def obviously_not(self):
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morty, friend = self.get_pi_creatures()
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randy = Randolph()
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randy.match_height(morty)
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randy.to_corner(DL)
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frac = self.frac
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rhs = self.neg_one_over_phi
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plusses = frac[1::4]
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plus_rects = VGroup(*[
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SurroundingRectangle(plus, buff=0) for plus in plusses
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])
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plus_rects.set_color(PINK)
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self.play(FadeIn(randy))
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self.play(
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PiCreatureSays(
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randy, "Of course not!",
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bubble_kwargs={"width": 3, "height": 2},
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target_mode="angry",
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run_time=1,
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),
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morty.change, "guilty",
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friend.change, "hesitant"
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)
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self.wait()
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self.play(
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Animation(frac),
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RemovePiCreatureBubble(randy, target_mode="sassy"),
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morty.change, "confused",
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friend.change, "confused",
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)
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self.play(LaggedStart(
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ShowCreationThenDestruction, plus_rects,
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run_time=4,
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lag_ratio=0.35,
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))
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self.play(WiggleOutThenIn(rhs))
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self.wait(2)
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self.play(
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frac.scale, 0.7,
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frac.to_corner, UL,
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FadeOut(self.equals),
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rhs.scale, 0.5,
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rhs.center,
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rhs.to_edge, LEFT,
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FadeOut(randy),
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morty.change, "pondering",
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friend.change, "pondering",
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)
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def plug_func_into_self(self, value=1, value_str="1"):
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morty, friend = self.pi_creatures
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def func(x):
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return 1 + 1.0 / x
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lines = VGroup()
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value_labels = VGroup()
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for n_terms in range(5):
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lhs = get_nested_f(n_terms, arg="c")
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equals = TexMobject("=")
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rhs = get_nested_one_plus_one_over_x(n_terms)
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rhs = get_nested_one_plus_one_over_x(n_terms, bottom_term=value_str)
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equals.next_to(rhs[0], LEFT)
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lhs.next_to(equals, LEFT)
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lines.add(VGroup(lhs, equals, rhs))
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value_label = TexMobject("= %.3f" % value)
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value = func(value)
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value_labels.add(value_label)
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lines.arrange_submobjects(
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DOWN, buff=MED_LARGE_BUFF,
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# aligned_edge=RIGHT
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)
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VGroup(lines, value_labels).scale(0.8)
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lines.to_corner(UR)
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buff = MED_LARGE_BUFF + MED_SMALL_BUFF + value_labels.get_width()
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lines.to_edge(RIGHT, buff=buff)
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for line, value_label in zip(lines, value_labels):
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value_label.move_to(line[1]).to_edge(RIGHT)
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top_line = lines[0]
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colors = [WHITE] + color_gradient([YELLOW, RED], len(lines) - 1)
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colors = [WHITE] + color_gradient([YELLOW, RED, PINK], len(lines) - 1)
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for n in range(1, len(lines)):
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color = colors[n]
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lines[n][0].set_color(color)
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|
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@ -1988,10 +2302,19 @@ class IntroduceContinuedFractionPuzzle(PiCreatureScene):
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lines[n][2].set_color(color)
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lines[n][2][4:].match_style(lines[n - 1][2])
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self.play(FadeInFromDown(top_line))
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for n in range(1, 4):
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arrow = Vector(0.5 * DOWN, color=WHITE)
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arrow.next_to(value_labels[-1], DOWN)
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q_marks = TexMobject("???")
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q_marks.next_to(arrow, DOWN)
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self.play(
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FadeInFromDown(top_line),
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FadeInFromDown(value_labels[0])
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)
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for n in range(1, len(lines)):
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new_line = lines[n]
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last_line = lines[n - 1]
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value_label = value_labels[n]
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mover, target = [
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VGroup(
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line[0][0],
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|
|
@ -1999,9 +2322,11 @@ class IntroduceContinuedFractionPuzzle(PiCreatureScene):
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line[1],
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line[2][:4],
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)
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for line in top_line, new_line
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for line in lines[1], new_line
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]
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anims = [ReplacementTransform(mover.copy(), target, path_arc=30 * DEGREES)]
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anims = [ReplacementTransform(
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mover.copy().fade(1), target, path_arc=30 * DEGREES
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)]
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if n == 3:
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morty.generate_target()
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morty.target.change("horrified")
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|
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@ -2017,13 +2342,27 @@ class IntroduceContinuedFractionPuzzle(PiCreatureScene):
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last_line[2].copy(), new_line[2][4:]
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),
|
||||
)
|
||||
self.play(FadeIn(value_label))
|
||||
self.wait()
|
||||
self.play(friend.look_at, self.frac)
|
||||
self.wait(5)
|
||||
self.play(
|
||||
GrowArrow(arrow),
|
||||
Write(q_marks),
|
||||
friend.change, "confused"
|
||||
)
|
||||
self.wait(3)
|
||||
|
||||
|
||||
class NumericalPlay(ExternallyAnimatedScene):
|
||||
pass
|
||||
class RepeatedApplicationWithPhiBro(ThinkAboutWithRepeatedApplication):
|
||||
def construct(self):
|
||||
self.force_skipping()
|
||||
self.ask_question()
|
||||
self.obviously_not()
|
||||
self.revert_to_original_skipping_status()
|
||||
|
||||
self.plug_func_into_self(
|
||||
value=(1 - np.sqrt(5)) / 2,
|
||||
value_str="-1/\\varphi"
|
||||
)
|
||||
|
||||
|
||||
class ShowRepeatedApplication(Scene):
|
||||
|
|
@ -2152,7 +2491,6 @@ class ShowPhiAsFixedPoint(ShowRepeatedApplication):
|
|||
def construct(self):
|
||||
self.add_func_title()
|
||||
self.show_fixed_point_formulas()
|
||||
self.solve_infinite_fraction()
|
||||
|
||||
def show_fixed_point_formulas(self):
|
||||
var_formula = TexMobject(
|
||||
|
|
@ -2232,202 +2570,6 @@ class ShowPhiAsFixedPoint(ShowRepeatedApplication):
|
|||
)
|
||||
self.wait()
|
||||
|
||||
def solve_infinite_fraction(self):
|
||||
frac = get_phi_continued_fraction(n_terms=9)
|
||||
frac.to_edge(RIGHT, buff=LARGE_BUFF)
|
||||
|
||||
inner_frac = frac[4:]
|
||||
inner_frac_rect = SurroundingRectangle(
|
||||
inner_frac, stroke_width=2, buff=0.5 * SMALL_BUFF
|
||||
)
|
||||
inner_frac_group = VGroup(inner_frac, inner_frac_rect)
|
||||
|
||||
equals = TexMobject("=")
|
||||
equals.next_to(frac[0], LEFT)
|
||||
x = TexMobject("x")
|
||||
x.next_to(equals, LEFT)
|
||||
|
||||
new_x = TexMobject("x")
|
||||
new_x.next_to(frac[3], DOWN, 2 * SMALL_BUFF)
|
||||
|
||||
VGroup(x, new_x).set_color(YELLOW)
|
||||
|
||||
self.play(LaggedStart(GrowFromCenter, frac))
|
||||
self.play(Write(x), Write(equals))
|
||||
self.wait()
|
||||
self.play(ShowCreation(inner_frac_rect))
|
||||
self.wait()
|
||||
self.play(
|
||||
inner_frac_group.scale, 0.75,
|
||||
inner_frac_group.to_corner, DR,
|
||||
ReplacementTransform(
|
||||
x.copy(), new_x,
|
||||
path_arc=90 * DEGREES
|
||||
)
|
||||
)
|
||||
self.play(
|
||||
frac[3].stretch, 0.15, 0, {"about_edge": LEFT},
|
||||
MaintainPositionRelativeTo(
|
||||
VGroup(frac[2], new_x), frac[3]
|
||||
)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
class GraphOnePlusOneOverX(GraphScene):
|
||||
CONFIG = {
|
||||
"x_min": -6,
|
||||
"x_max": 6,
|
||||
"x_axis_width": 12,
|
||||
"y_min": -4,
|
||||
"y_max": 5,
|
||||
"y_axis_height": 8,
|
||||
"y_axis_label": None,
|
||||
"graph_origin": 0.5 * DOWN,
|
||||
"num_graph_anchor_points": 100,
|
||||
"func_graph_color": GREEN,
|
||||
"identity_graph_color": BLUE,
|
||||
}
|
||||
|
||||
def construct(self):
|
||||
self.add_title()
|
||||
self.setup_axes()
|
||||
self.draw_graphs()
|
||||
self.show_solutions()
|
||||
|
||||
def add_title(self):
|
||||
title = self.title = TexMobject(
|
||||
"\\text{Solve: }", "1 + \\frac{1}{x}", "=", "x",
|
||||
)
|
||||
title.set_color_by_tex("x", self.identity_graph_color, substring=False)
|
||||
title.set_color_by_tex("frac", self.func_graph_color)
|
||||
title.to_corner(UL)
|
||||
self.add(title)
|
||||
|
||||
def setup_axes(self):
|
||||
GraphScene.setup_axes(self)
|
||||
step = 2
|
||||
self.x_axis.add_numbers(*range(-6, 0, step) + range(step, 7, step))
|
||||
self.y_axis.label_direction = RIGHT
|
||||
self.y_axis.add_numbers(*range(-2, 0, step) + range(step, 4, step))
|
||||
|
||||
def draw_graphs(self, animate=True):
|
||||
lower_func_graph, upper_func_graph = func_graph = VGroup(*[
|
||||
self.get_graph(
|
||||
lambda x: 1.0 + 1.0 / x,
|
||||
x_min=x_min,
|
||||
x_max=x_max,
|
||||
color=self.func_graph_color,
|
||||
)
|
||||
for x_min, x_max in (-10, -0.1), (0.1, 10)
|
||||
])
|
||||
func_graph.label = self.get_graph_label(
|
||||
upper_func_graph, "y = 1 + \\frac{1}{x}",
|
||||
x_val=6, direction=UP,
|
||||
)
|
||||
|
||||
identity_graph = self.get_graph(
|
||||
lambda x: x, color=self.identity_graph_color
|
||||
)
|
||||
identity_graph.label = self.get_graph_label(
|
||||
identity_graph, "y = x",
|
||||
x_val=3, direction=UL, buff=SMALL_BUFF
|
||||
)
|
||||
|
||||
if animate:
|
||||
for graph in func_graph, identity_graph:
|
||||
self.play(
|
||||
ShowCreation(graph),
|
||||
Write(graph.label),
|
||||
run_time=2
|
||||
)
|
||||
self.wait()
|
||||
else:
|
||||
self.add(
|
||||
func_graph, func_graph.label,
|
||||
identity_graph, identity_graph.label,
|
||||
)
|
||||
|
||||
self.func_graph = func_graph
|
||||
self.identity_graph = identity_graph
|
||||
|
||||
def show_solutions(self):
|
||||
phi = 0.5 * (1 + np.sqrt(5))
|
||||
phi_bro = 0.5 * (1 - np.sqrt(5))
|
||||
|
||||
lines = VGroup()
|
||||
for num in phi, phi_bro:
|
||||
line = DashedLine(
|
||||
self.coords_to_point(num, 0),
|
||||
self.coords_to_point(num, num),
|
||||
color=WHITE
|
||||
)
|
||||
line_copy = line.copy()
|
||||
line.fade(0.5)
|
||||
line_anim = ShowCreationThenDestruction(
|
||||
line_copy,
|
||||
submobject_mode="lagged_start",
|
||||
run_time=2
|
||||
)
|
||||
line.continual_anim = CycleAnimation(line_anim)
|
||||
lines.add(line)
|
||||
|
||||
phi_line, phi_bro_line = lines
|
||||
|
||||
decimal_kwargs = {
|
||||
"num_decimal_places": 3,
|
||||
"show_ellipsis": True,
|
||||
"color": YELLOW,
|
||||
}
|
||||
arrow_kwargs = {
|
||||
"buff": SMALL_BUFF,
|
||||
"color": WHITE,
|
||||
"tip_length": 0.15,
|
||||
"rectangular_stem_width": 0.025,
|
||||
}
|
||||
|
||||
phi_decimal = DecimalNumber(phi, **decimal_kwargs)
|
||||
phi_decimal.next_to(phi_line, DOWN, LARGE_BUFF)
|
||||
phi_arrow = Arrow(
|
||||
phi_decimal[:4].get_top(), phi_line.get_bottom(),
|
||||
**arrow_kwargs
|
||||
)
|
||||
|
||||
phi_bro_decimal = DecimalNumber(phi_bro, **decimal_kwargs)
|
||||
phi_bro_decimal.next_to(phi_bro_line, UP, LARGE_BUFF)
|
||||
phi_bro_decimal.shift(0.5 * LEFT)
|
||||
phi_bro_arrow = Arrow(
|
||||
phi_bro_decimal[:6].get_bottom(), phi_bro_line.get_top(),
|
||||
**arrow_kwargs
|
||||
)
|
||||
|
||||
brother_words = TextMobject(
|
||||
"$\\varphi$'s little brother",
|
||||
tex_to_color_map={"$\\varphi$": YELLOW},
|
||||
arg_separator=""
|
||||
)
|
||||
brother_words.next_to(
|
||||
phi_bro_decimal[-2], UP, buff=MED_SMALL_BUFF,
|
||||
aligned_edge=RIGHT
|
||||
)
|
||||
|
||||
self.add(phi_line.continual_anim)
|
||||
self.play(ShowCreation(phi_line))
|
||||
self.play(
|
||||
Write(phi_decimal),
|
||||
GrowArrow(phi_arrow),
|
||||
)
|
||||
self.wait(4)
|
||||
self.add(phi_bro_line.continual_anim)
|
||||
self.play(ShowCreation(phi_bro_line))
|
||||
self.play(
|
||||
Write(phi_bro_decimal),
|
||||
GrowArrow(phi_bro_arrow),
|
||||
)
|
||||
self.wait(4)
|
||||
self.play(Write(brother_words))
|
||||
self.wait(8)
|
||||
|
||||
|
||||
class NumericalPlayFromOne(ExternallyAnimatedScene):
|
||||
pass
|
||||
|
|
@ -2744,23 +2886,17 @@ class AnalyzeFunctionWithTransformations(NumberlineTransformationScene):
|
|||
shift_vect[0] = 0
|
||||
lower_output_line = self.output_line.copy()
|
||||
upper_output_line = self.output_line.copy()
|
||||
lower_arrows = arrows.copy()
|
||||
upper_arrows = arrows.copy()
|
||||
lower_group = VGroup(lower_output_line, lower_arrows)
|
||||
lower_group.shift(-shift_vect)
|
||||
lower_group.fade(1)
|
||||
lower_output_line.shift(-shift_vect)
|
||||
lower_output_line.fade(1)
|
||||
|
||||
self.remove(self.output_line, *arrows)
|
||||
self.remove(self.output_line)
|
||||
self.play(
|
||||
ReplacementTransform(lower_arrows, arrows),
|
||||
ReplacementTransform(lower_output_line, self.output_line),
|
||||
upper_arrows.shift, shift_vect,
|
||||
upper_arrows.fade, 1,
|
||||
upper_output_line.shift, shift_vect,
|
||||
upper_output_line.fade, 1,
|
||||
sample_dots.shift, shift_vect,
|
||||
)
|
||||
self.remove(upper_output_line, upper_arrows)
|
||||
self.remove(upper_output_line)
|
||||
self.wait()
|
||||
self.play(FadeOut(sample_dots))
|
||||
|
||||
|
|
@ -3008,3 +3144,153 @@ class NotBetterThanGraphs(TeacherStudentsScene):
|
|||
self.get_student_changes("sad", "sassy", "hesitant")
|
||||
)
|
||||
self.wait(2)
|
||||
self.play(
|
||||
RemovePiCreatureBubble(self.students[1]),
|
||||
self.teacher.change, "raise_right_hand"
|
||||
)
|
||||
self.change_all_student_modes(
|
||||
"confused", look_at_arg=self.screen
|
||||
)
|
||||
self.wait(3)
|
||||
self.teacher_says(
|
||||
"You must flex those \\\\ conceptual muscles",
|
||||
added_anims=[self.get_student_changes(
|
||||
*3 * ["thinking"],
|
||||
look_at_arg=self.teacher.eyes
|
||||
)]
|
||||
)
|
||||
self.wait(3)
|
||||
|
||||
|
||||
class TopicsAfterSingleVariable(PiCreatureScene, MoreTopics):
|
||||
CONFIG = {
|
||||
"pi_creatures_start_on_screen": False,
|
||||
}
|
||||
|
||||
def construct(self):
|
||||
MoreTopics.construct(self)
|
||||
self.show_horror()
|
||||
self.zero_in_on_complex_analysis()
|
||||
|
||||
def create_pi_creatures(self):
|
||||
creatures = VGroup(*[
|
||||
PiCreature(color=color)
|
||||
for color in [BLUE_E, BLUE_C, BLUE_D]
|
||||
])
|
||||
creatures.arrange_submobjects(RIGHT, buff=LARGE_BUFF)
|
||||
creatures.scale(0.5)
|
||||
creatures.to_corner(DR)
|
||||
return creatures
|
||||
|
||||
def show_horror(self):
|
||||
creatures = self.get_pi_creatures()
|
||||
modes = ["horrified", "tired", "horrified"]
|
||||
for creature, mode in zip(creatures, modes):
|
||||
creature.generate_target()
|
||||
creature.target.change(mode, self.other_topics)
|
||||
creatures.fade(1)
|
||||
|
||||
self.play(LaggedStart(MoveToTarget, creatures))
|
||||
self.wait(2)
|
||||
|
||||
def zero_in_on_complex_analysis(self):
|
||||
creatures = self.get_pi_creatures()
|
||||
complex_analysis = self.other_topics[1]
|
||||
self.other_topics.remove(complex_analysis)
|
||||
|
||||
self.play(
|
||||
complex_analysis.scale, 1.25,
|
||||
complex_analysis.center,
|
||||
complex_analysis.to_edge, UP,
|
||||
LaggedStart(FadeOut, self.other_topics),
|
||||
LaggedStart(FadeOut, self.lines),
|
||||
FadeOut(self.calculus),
|
||||
*[
|
||||
ApplyMethod(creature.change, "pondering")
|
||||
for creature in creatures
|
||||
]
|
||||
)
|
||||
self.wait(4)
|
||||
|
||||
|
||||
class ComplexAnalysisOverlay(Scene):
|
||||
def construct(self):
|
||||
words = TextMobject("Complex analysis")
|
||||
words.scale(1.25)
|
||||
words.to_edge(UP)
|
||||
words.add_background_rectangle()
|
||||
self.add(words)
|
||||
self.wait()
|
||||
|
||||
|
||||
class CompelxAnalyticFluidFlow(ComplexTransformationScene, MovingCameraScene):
|
||||
CONFIG = {
|
||||
"num_anchors_to_add_per_line": 200,
|
||||
"plane_config": {"y_radius": 8}
|
||||
}
|
||||
|
||||
def setup(self):
|
||||
MovingCameraScene.setup(self)
|
||||
ComplexTransformationScene.setup(self)
|
||||
|
||||
def construct(self):
|
||||
self.camera.frame.shift(2 * UP)
|
||||
self.camera.frame.scale(0.5, about_point=ORIGIN)
|
||||
|
||||
plane = NumberPlane(
|
||||
x_radius=15,
|
||||
y_radius=25,
|
||||
y_unit_size=0.5,
|
||||
secondary_line_ratio=0,
|
||||
)
|
||||
plane.next_to(ORIGIN, UP, buff=0.001)
|
||||
horizontal_lines = VGroup(*filter(
|
||||
lambda l: np.abs(l.get_center()[0]) < 0.1,
|
||||
list(plane.main_lines) + [plane.axes[0]]
|
||||
))
|
||||
plane.set_stroke(MAROON_B, width=2)
|
||||
horizontal_lines.set_stroke(BLUE, width=2)
|
||||
for line in horizontal_lines:
|
||||
# To lag the paths of the droplets
|
||||
line.scale(1 + random.random())
|
||||
|
||||
self.prepare_for_transformation(plane)
|
||||
self.add_transformable_mobjects(plane)
|
||||
|
||||
self.background.set_stroke(width=2)
|
||||
for label in self.background.coordinate_labels:
|
||||
label.set_stroke(width=0)
|
||||
label.scale(0.75, about_edge=UR)
|
||||
|
||||
words = TextMobject("Flow near \\\\", "a wall")
|
||||
words.scale(0.75)
|
||||
words.add_background_rectangle_to_submobjects()
|
||||
words.next_to(0.75 * UP, LEFT, MED_LARGE_BUFF)
|
||||
equation = TexMobject("z \\rightarrow z^{1/2}")
|
||||
equation.scale(0.75)
|
||||
equation.add_background_rectangle()
|
||||
equation.next_to(words, UP)
|
||||
|
||||
self.apply_complex_function(
|
||||
lambda x: x**(1. / 2),
|
||||
added_anims=[Write(equation)]
|
||||
)
|
||||
self.play(Write(words, run_time=1))
|
||||
|
||||
dots = VGroup()
|
||||
num_dots_per_line = 50
|
||||
for x in range(num_dots_per_line):
|
||||
for line in horizontal_lines:
|
||||
dot = Dot(radius=0.025)
|
||||
opacity = 1.0 - x / float(num_dots_per_line)
|
||||
dot.set_fill(opacity=opacity)
|
||||
dot.path = line
|
||||
dots.add(dot)
|
||||
dots.set_color_by_gradient(BLUE_B, BLUE_D)
|
||||
|
||||
self.play(LaggedStart(
|
||||
MoveAlongPath, dots,
|
||||
lambda d: (d, d.path),
|
||||
run_time=3,
|
||||
lag_ratio=0.9
|
||||
))
|
||||
|
|
|
|||
|
|
@ -114,11 +114,11 @@ class ComplexTransformationScene(Scene):
|
|||
def get_transformer(self, **kwargs):
|
||||
transform_kwargs = dict(self.default_apply_complex_function_kwargs)
|
||||
transform_kwargs.update(kwargs)
|
||||
plane = self.plane
|
||||
self.prepare_for_transformation(plane)
|
||||
transformer = VGroup(
|
||||
plane, *self.transformable_mobjects
|
||||
)
|
||||
transformer = VGroup()
|
||||
if hasattr(self, "plane"):
|
||||
self.prepare_for_transformation(self.plane)
|
||||
transformer.add(self.plane)
|
||||
transformer.add(*self.transformable_mobjects)
|
||||
return transformer, transform_kwargs
|
||||
|
||||
def apply_complex_function(self, func, added_anims=[], **kwargs):
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue