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Opening scene of div_curl
This commit is contained in:
Grant Sanderson
parent
4c762aeb79
commit
09642c89b5
1 changed files with 189 additions and 13 deletions
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@ -1,7 +1,7 @@
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from big_ol_pile_of_manim_imports import *
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DEFAULT_SCALAR_FIELD_COLORS = [BLUE_E, GREEN, WHITE, ORANGE, RED]
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DEFAULT_SCALAR_FIELD_COLORS = [BLUE_E, WHITE, RED]
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# Helper functions
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@ -24,7 +24,7 @@ def joukowsky_map(z):
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def inverse_joukowsky_map(w):
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u = 1 if w.real <= 0 else -1
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u = 1 if w.real >= 0 else -1
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return (w + u * np.sqrt(w**2 - 4)) / 2
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@ -255,7 +255,8 @@ class TestVectorField(Scene):
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self.func,
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start_points_generator=lambda: get_flow_start_points(
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x_min=-8, x_max=-7, y_min=-4, y_max=4,
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delta_x=0.5, delta_y=0.1,
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delta_x=0.5,
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delta_y=0.1,
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n_repeats=1,
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noise_factor=0.1,
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),
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@ -284,11 +285,12 @@ class TestVectorField(Scene):
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class Introduction(Scene):
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CONFIG = {
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"production_quality_flow": True,
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}
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def construct(self):
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self.add_plane()
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self.add_title()
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self.show_numbers()
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self.show_contour_lines()
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self.show_flow()
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@ -300,15 +302,22 @@ class Introduction(Scene):
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self.plane.coordinate_labels.submobjects.pop(-1)
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self.add(self.plane)
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def show_numbers(self):
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def add_title(self):
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title = TextMobject("Complex Plane")
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title.scale(1.5)
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title.to_edge(UP, buff=MED_SMALL_BUFF)
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title.add_background_rectangle()
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self.title = title
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self.add(title)
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unit_circle = Circle(radius=self.plane.unit_size)
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unit_circle.set_color(YELLOW)
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def show_numbers(self):
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run_time = 5
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unit_circle = self.unit_circle = Circle(
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radius=self.plane.unit_size,
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fill_color=BLACK,
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fill_opacity=0,
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stroke_color=YELLOW
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)
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dot = Dot()
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dot_update = UpdateFromFunc(
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dot, lambda d: d.move_to(unit_circle.point_from_proportion(1))
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@ -328,11 +337,29 @@ class Introduction(Scene):
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exp_decimal_update = ChangeDecimalToValue(
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exp_decimal, TAU,
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position_update_func=lambda mob: mob.move_to(zero),
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run_time=4,
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run_time=run_time,
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)
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sample_numbers = [
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complex(-5, 2),
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complex(2, 2),
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complex(3, 1),
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complex(-5, -2),
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complex(-4, 1),
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]
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sample_labels = VGroup()
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for z in sample_numbers:
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sample_dot = Dot(self.plane.number_to_point(z))
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sample_label = DecimalNumber(
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z,
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num_decimal_places=0,
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include_background_rectangle=True,
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)
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sample_label.next_to(sample_dot, UR, SMALL_BUFF)
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sample_labels.add(VGroup(sample_dot, sample_label))
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self.play(
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ShowCreation(unit_circle, run_time=4),
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ShowCreation(unit_circle, run_time=run_time),
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VFadeIn(exp_tex),
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UpdateFromAlphaFunc(
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exp_decimal,
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@ -341,13 +368,162 @@ class Introduction(Scene):
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dot_update,
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exp_tex_update,
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exp_decimal_update,
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LaggedStart(
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FadeIn, sample_labels,
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remover=True,
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rate_func=there_and_back,
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run_time=run_time,
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)
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)
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self.play(
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FadeOut(exp_tex),
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FadeOut(exp_decimal),
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FadeOut(dot),
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unit_circle.set_fill, BLACK, {"opacity": 1},
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)
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self.wait()
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def show_contour_lines(self):
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pass
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warped_grid = self.warped_grid = self.get_warpable_grid()
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h_line = Line(3 * LEFT, 3 * RIGHT, color=WHITE) # Hack
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func_label = self.func_label = TexMobject("f(z) = z + 1 / z")
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func_label.add_background_rectangle()
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func_label.next_to(self.title, DOWN, MED_SMALL_BUFF)
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self.remove(self.plane)
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self.add_foreground_mobjects(self.unit_circle, self.title)
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self.play(
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warped_grid.apply_complex_function, inverse_joukowsky_map,
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Animation(h_line, remover=True)
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)
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self.play(Write(func_label))
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self.add_foreground_mobjects(func_label)
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self.wait()
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def show_flow(self):
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pass
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stream_lines = self.get_stream_lines()
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stream_lines_copy = stream_lines.copy()
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stream_lines_copy.set_stroke(YELLOW, 1)
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stream_lines_animation = self.get_stream_lines_animation(
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stream_lines
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)
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tiny_buff = 0.0001
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v_lines = VGroup(*[
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Line(
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UP, ORIGIN,
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path_arc=0,
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n_arc_anchors=20,
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).shift(x * RIGHT)
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for x in np.linspace(0, 1, 5)
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])
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v_lines.match_background_image_file(stream_lines)
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fast_lines, slow_lines = [
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VGroup(*[
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v_lines.copy().next_to(point, vect, tiny_buff)
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for point, vect in it.product(h_points, [UP, DOWN])
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])
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for h_points in [
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[0.5 * LEFT, 0.5 * RIGHT],
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[2 * LEFT, 2 * RIGHT],
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]
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]
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for lines in fast_lines, slow_lines:
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lines.apply_complex_function(inverse_joukowsky_map)
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self.add(stream_lines_animation)
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self.wait(7)
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self.play(
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ShowCreationThenDestruction(
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stream_lines_copy,
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submobject_mode="all_at_once",
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run_time=3,
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)
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)
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self.wait()
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self.play(ShowCreation(fast_lines))
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self.wait(2)
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self.play(ReplacementTransform(fast_lines, slow_lines))
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self.wait(3)
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self.play(
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FadeOut(slow_lines),
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VFadeOut(stream_lines_animation.mobject)
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)
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self.remove(stream_lines_animation)
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def apply_joukowsky_map(self):
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pass
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shift_val = 0.1 * LEFT + 0.2 * UP
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scale_factor = np.linalg.norm(RIGHT - shift_val)
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movers = VGroup(self.warped_grid, self.unit_circle)
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self.unit_circle.insert_n_anchor_points(50)
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stream_lines = self.get_stream_lines()
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stream_lines.scale(scale_factor)
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stream_lines.shift(shift_val)
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stream_lines.apply_complex_function(joukowsky_map)
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self.play(
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movers.scale, scale_factor,
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movers.shift, shift_val,
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)
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self.wait()
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self.play(
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movers.apply_complex_function, joukowsky_map,
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CircleThenFadeAround(self.func_label),
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run_time=2
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)
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self.add(self.get_stream_lines_animation(stream_lines))
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self.wait(20)
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# Helpers
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def get_warpable_grid(self):
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top_grid = NumberPlane()
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top_grid.prepare_for_nonlinear_transform()
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bottom_grid = top_grid.copy()
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tiny_buff = 0.0001
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top_grid.next_to(ORIGIN, UP, buff=tiny_buff)
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bottom_grid.next_to(ORIGIN, DOWN, buff=tiny_buff)
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result = VGroup(top_grid, bottom_grid)
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result.add(*[
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Line(
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ORIGIN, FRAME_WIDTH * RIGHT / 2,
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color=WHITE,
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path_arc=0,
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n_arc_anchors=100,
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).next_to(ORIGIN, vect, buff=2)
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for vect in LEFT, RIGHT
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])
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return result
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def get_stream_lines(self):
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func = cylinder_flow_vector_field
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if self.production_quality_flow:
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delta_x = 0.5
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delta_y = 0.1
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else:
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delta_x = 1
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# delta_y = 1
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delta_y = 0.1
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return StreamLines(
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func,
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start_points_generator=lambda: get_flow_start_points(
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x_min=-8, x_max=-7, y_min=-4, y_max=4,
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delta_x=delta_x,
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delta_y=delta_y,
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n_repeats=1,
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noise_factor=0.1,
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),
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stroke_width=2,
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)
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def get_stream_lines_animation(self, stream_lines):
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if self.production_quality_flow:
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line_anim_class = ShowPassingFlashWithThinningStrokeWidth
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else:
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line_anim_class = ShowPassingFlash
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return StreamLineAnimation(
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stream_lines,
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line_anim_class=line_anim_class,
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)
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