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MonomialTerm
This commit is contained in:
Grant Sanderson
parent
973063f9b7
commit
b968f13faa
1 changed files with 198 additions and 2 deletions
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@ -2139,9 +2139,205 @@ class BackToEquationSolving(AltTeacherStudentsScene):
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])
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self.wait(3)
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class SearchSpacePerimeterVsArea(Scene):
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class SearchSpacePerimeterVsArea(EquationSolver2d):
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CONFIG = {
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"func" : plane_func_by_wind_spec(
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(-3, -1.3, 2), (0.1, 0.2, 1), (2.8, -2, 1)
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),
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"num_iterations" : 15,
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"display_in_parallel" : False,
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"use_fancy_lines" : True,
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}
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def construct(self):
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pass
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self.force_skipping()
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EquationSolver2d.construct(self)
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self.revert_to_original_skipping_status()
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all_parts = VGroup(*self.get_mobjects())
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path_parts = VGroup()
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non_path_parts = VGroup()
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for part in all_parts:
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if part.get_background_image_file() is not None:
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path_parts.add(part)
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else:
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non_path_parts.add(part)
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path_parts.save_state()
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path_parts.generate_target()
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for path_target in path_parts.target:
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if isinstance(path_target, Line):
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path_target.rotate(-path_target.get_angle())
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path_parts.target.arrange_submobjects(DOWN, buff = MED_SMALL_BUFF)
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alt_path_parts = path_parts.copy()
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size = lambda m : m.get_height() + m.get_width()
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alt_path_parts.submobjects.sort(
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lambda m1, m2 : -cmp(size(m1), size(m2))
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)
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full_rect = SurroundingRectangle(
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path_parts,
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stroke_width = 0,
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fill_color = WHITE,
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fill_opacity = 1,
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background_image_file = path_parts[0].background_image_file
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)
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full_rect.save_state()
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full_rect.stretch(0, 1, about_edge = UP)
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self.play(
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FadeOut(non_path_parts),
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path_parts.set_stroke, {"width" : 1},
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)
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self.remove(all_parts)
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for x in range(2):
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alt_path_parts.save_state()
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self.play(LaggedStart(
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FadeIn, alt_path_parts,
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rate_func = there_and_back,
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lag_ratio = 0.3,
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run_time = 3,
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remover = True
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))
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alt_path_parts.restore()
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self.play(
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full_rect.restore,
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run_time = 2,
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)
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self.wait()
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self.play(FadeOut(full_rect))
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self.wait()
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class MonomialTerm(PathContainingZero):
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CONFIG = {
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"non_renormalized_func" : plane_func_from_complex_func(lambda z : z**5),
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"func_label" : "x^5",
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"loop_radius" : 1.1,
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"label_buff" : 0.3,
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}
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def construct(self):
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self.setup_planes()
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self.relabel_planes()
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self.add_function_label()
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self.show_winding()
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def relabel_planes(self):
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for plane in self.input_plane, self.output_plane:
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for mob in plane:
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if isinstance(mob, TexMobject):
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plane.remove(mob)
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if hasattr(plane, "numbers_to_show"):
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_range = plane.numbers_to_show
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else:
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_range = range(-2, 3)
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for x in _range:
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if x == 0:
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continue
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label = TexMobject(str(x))
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label.scale(0.5)
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point = plane.coords_to_point(x, 0)
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label.next_to(point, DOWN, MED_SMALL_BUFF)
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plane.add(label)
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tick = Line(SMALL_BUFF*DOWN, SMALL_BUFF*UP)
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tick.move_to(point)
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plane.add(tick)
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for y in _range:
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if y == 0:
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continue
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label = TexMobject("%di"%y)
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label.scale(0.5)
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point = plane.coords_to_point(0, y)
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label.next_to(point, LEFT, MED_SMALL_BUFF)
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plane.add(label)
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tick = Line(SMALL_BUFF*LEFT, SMALL_BUFF*RIGHT)
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tick.move_to(point)
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plane.add(tick)
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def add_function_label(self):
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label = TexMobject("f(x) = %s"%self.func_label)
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label.add_background_rectangle(opacity = 1)
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arrow = Arrow(
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2*LEFT, 2*RIGHT, path_arc = -TAU/3,
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use_rectangular_stem = False
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)
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arrow.pointwise_become_partial(arrow, 0, 0.95)
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label.next_to(arrow, UP)
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VGroup(arrow, label).to_edge(UP)
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self.add(label, arrow)
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def show_winding(self):
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loop = Arc(color = WHITE, angle = 1.02*TAU, num_anchors = 42)
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loop.scale(self.loop_radius)
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loop.match_background_image_file(self.input_coloring)
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loop.move_to(self.input_plane.coords_to_point(0, 0))
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out_loop = loop.copy()
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out_loop.apply_function(self.point_function)
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out_loop.match_background_image_file(self.output_coloring)
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get_in_point = lambda : loop.points[-1]
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get_out_point = lambda : out_loop.points[-1]
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in_origin = self.input_plane.coords_to_point(0, 0)
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out_origin = self.output_plane.coords_to_point(0, 0)
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dot = Dot()
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update_dot = UpdateFromFunc(dot, lambda d : d.move_to(get_in_point()))
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out_dot = Dot()
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update_out_dot = UpdateFromFunc(out_dot, lambda d : d.move_to(get_out_point()))
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buff = self.label_buff
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def generate_label_update(label, point_func, origin):
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return UpdateFromFunc(
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label, lambda m : m.move_to(
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(1+buff)*point_func() - buff*origin,
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)
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)
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x = TexMobject("x")
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fx = TexMobject(self.func_label)
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update_x = generate_label_update(x, get_in_point, in_origin)
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update_fx = generate_label_update(fx, get_out_point, out_origin)
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morty = self.pi_creature
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kwargs = {
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"run_time" : 15,
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"rate_func" : None,
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}
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self.play(
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ShowCreation(loop, **kwargs),
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ShowCreation(out_loop, **kwargs),
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update_dot,
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update_out_dot,
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update_x,
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update_fx,
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Succession(
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morty.change, "pondering",
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Blink(morty),
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Animation(morty, run_time = 4),
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Blink(morty),
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Animation(morty, run_time = 4),
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Blink(morty),
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)
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)
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###
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def func(self, coords):
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return self.non_renormalized_func(coords)
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class PolynomialTerms(MonomialTerm):
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CONFIG = {
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"non_renormalized_func" : plane_func_from_complex_func(lambda z : z**5 - z - 1),
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"func_label" : "x^5 - x - 1",
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"loop_radius" : 2.0,
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"label_buff" : 0.3,
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}
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def relabel_planes(self):
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self.output_plane.x_radius = 50
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self.output_plane.y_radius = 50
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self.output_plane.numbers_to_show = range(-45, 50, 10)
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MonomialTerm.relabel_planes(self)
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class EndingCredits(Scene):
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def construct(self):
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