mirror of
https://github.com/3b1b/manim.git
synced 2025-08-01 08:54:38 +08:00
Factor out holomorphic project into two separate videos
This commit is contained in:
Grant Sanderson
@ -1,419 +0,0 @@
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from big_ol_pile_of_manim_imports import *
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# Helper functions
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def get_flow_start_points(x_min=-8, x_max=8,
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y_min=-5, y_max=5,
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delta_x=0.5, delta_y=0.5,
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n_repeats=1,
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noise_factor=0.01
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):
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return np.array([
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x * RIGHT + y * UP + noise_factor * np.random.random(3)
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for n in xrange(n_repeats)
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for x in np.arange(x_min, x_max + delta_x, delta_x)
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for y in np.arange(y_min, y_max + delta_y, delta_y)
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])
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def joukowsky_map(z):
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return z + fdiv(1, 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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return (w + u * np.sqrt(w**2 - 4)) / 2
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def derivative(func, dt=1e-7):
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return lambda z: (func(z + dt) - func(z)) / dt
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def cylinder_flow_vector_field(point, R=1, U=1):
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z = R3_to_complex(point)
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return complex_to_R3(1.0 / derivative(joukowsky_map)(z))
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# Continual animations
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class VectorFieldFlow(ContinualAnimation):
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CONFIG = {
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"mode": None,
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}
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def __init__(self, mobject, func, **kwargs):
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"""
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Func should take in a vector in R3, and output a vector in R3
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"""
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self.func = func
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ContinualAnimation.__init__(self, mobject, **kwargs)
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def update_mobject(self, dt):
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self.apply_nudge(dt)
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def apply_nudge(self):
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self.mobject.shift(self.func(self.mobject.get_center()) * dt)
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class VectorFieldSubmobjectFlow(VectorFieldFlow):
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def apply_nudge(self, dt):
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for submob in self.mobject:
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submob.shift(self.func(submob.get_center()) * dt)
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class VectorFieldPointFlow(VectorFieldFlow):
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def apply_nudge(self, dt):
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self.mobject.apply_function(
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lambda p: p + self.func(p) * dt
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)
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class StreamLines(VGroup):
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CONFIG = {
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"start_points_generator": get_flow_start_points,
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"dt": 0.05,
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"virtual_time": 20,
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"n_anchors_per_line": 30,
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"stroke_width": 1,
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"stroke_color": WHITE,
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}
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def __init__(self, func, **kwargs):
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VGroup.__init__(self, **kwargs)
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self.func = func
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dt = self.dt
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start_points = self.start_points_generator()
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for point in start_points:
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points = [point]
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for t in np.arange(0, self.virtual_time, dt):
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last_point = points[-1]
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points.append(last_point + dt * func(last_point))
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line = VMobject()
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line.set_points_smoothly(
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points[::(len(points) / self.n_anchors_per_line)]
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)
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self.add(line)
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self.set_stroke(self.stroke_color, self.stroke_width)
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class StreamLineAnimation(ContinualAnimation):
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CONFIG = {
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"lag_range": 4,
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"line_anim_class": ShowPassingFlash,
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"line_anim_config": {
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"run_time": 4,
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"rate_func": None,
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"time_width": 0.4,
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},
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}
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def __init__(self, stream_lines, **kwargs):
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digest_config(self, kwargs)
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self.stream_lines = stream_lines
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for line in stream_lines:
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line.anim = self.line_anim_class(line, **self.line_anim_config)
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line.time = -self.lag_range * random.random()
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ContinualAnimation.__init__(self, stream_lines, **kwargs)
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def update_mobject(self, dt):
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stream_lines = self.stream_lines
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for line in stream_lines:
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line.time += dt
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adjusted_time = max(line.time, 0) % line.anim.run_time
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line.anim.update(adjusted_time / line.anim.run_time)
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# Scenes
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class TestVectorField(Scene):
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CONFIG = {
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"func": cylinder_flow_vector_field,
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}
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def construct(self):
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plane = ComplexPlane()
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self.add(plane)
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circle = Circle(stroke_color=YELLOW)
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circle.set_fill(BLACK, 1)
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self.add_foreground_mobject(circle)
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lines = StreamLines(
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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=-2, y_max=2,
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delta_x=0.5, delta_y=0.2,
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n_repeats=4,
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noise_factor=0.2,
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),
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)
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self.add(lines)
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return
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stream_line_animation = StreamLineAnimation(lines)
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self.add(stream_line_animation)
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self.wait(8)
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self.play(VFadeOut(lines))
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self.remove(stream_line_animation)
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self.wait()
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# dots = VGroup(*[
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# Dot().move_to(start_point)
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# for start_point in get_flow_start_points()
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# ])
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# dots.set_color_by_gradient(YELLOW, RED)
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# self.add(dots)
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# self.add(VectorFieldSubmobjectFlow(dots, self.func))
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# self.wait(5)
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class ComplexAnalysisOverlay(Scene):
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def construct(self):
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words = TextMobject("Complex analysis")
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words.scale(1.25)
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words.to_edge(UP)
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words.add_background_rectangle()
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self.add(words)
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self.wait()
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class CompelxAnalyticFluidFlow(ComplexTransformationScene, MovingCameraScene):
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CONFIG = {
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"num_anchors_to_add_per_line": 200,
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"plane_config": {"y_radius": 8}
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}
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def setup(self):
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MovingCameraScene.setup(self)
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ComplexTransformationScene.setup(self)
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def construct(self):
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self.camera.frame.shift(2 * UP)
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self.camera.frame.scale(0.5, about_point=ORIGIN)
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plane = NumberPlane(
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x_radius=15,
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y_radius=25,
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y_unit_size=0.5,
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secondary_line_ratio=0,
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)
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plane.next_to(ORIGIN, UP, buff=0.001)
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horizontal_lines = VGroup(*filter(
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lambda l: np.abs(l.get_center()[0]) < 0.1,
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list(plane.main_lines) + [plane.axes[0]]
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))
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plane.set_stroke(MAROON_B, width=2)
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horizontal_lines.set_stroke(BLUE, width=2)
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for line in horizontal_lines:
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# To lag the paths of the droplets
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line.scale(1 + random.random())
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self.prepare_for_transformation(plane)
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self.add_transformable_mobjects(plane)
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self.background.set_stroke(width=2)
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for label in self.background.coordinate_labels:
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label.set_stroke(width=0)
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label.scale(0.75, about_edge=UR)
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words = TextMobject("Flow near \\\\", "a wall")
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words.scale(0.75)
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words.add_background_rectangle_to_submobjects()
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words.next_to(0.75 * UP, LEFT, MED_LARGE_BUFF)
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equation = TexMobject("z \\rightarrow z^{1/2}")
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equation.scale(0.75)
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equation.add_background_rectangle()
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equation.next_to(words, UP)
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self.apply_complex_function(
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lambda x: x**(1. / 2),
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added_anims=[Write(equation)]
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)
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self.play(Write(words, run_time=1))
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dots = VGroup()
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num_dots_per_line = 50
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for x in range(num_dots_per_line):
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for line in horizontal_lines:
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dot = Dot(radius=0.025)
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opacity = 1.0 - x / float(num_dots_per_line)
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dot.set_fill(opacity=opacity)
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dot.path = line
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dots.add(dot)
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dots.set_color_by_gradient(BLUE_B, BLUE_D)
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self.play(LaggedStart(
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MoveAlongPath, dots,
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lambda d: (d, d.path),
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run_time=3,
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lag_ratio=0.9
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))
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class AnalyzeZSquared(ComplexTransformationScene, ZoomedScene):
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CONFIG = {
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"num_anchors_to_add_per_line": 20,
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"complex_homotopy": lambda z, t: z**(1.0 + t),
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"zoom_factor": 0.05,
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}
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def setup(self):
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ComplexTransformationScene.setup(self)
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ZoomedScene.setup(self)
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def construct(self):
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self.edit_background_plane()
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self.add_title()
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# self.add_transforming_planes()
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# self.preview_some_numbers()
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self.zoom_in_to_one_plus_half_i()
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self.write_derivative()
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def add_title(self):
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title = TexMobject("z \\rightarrow z^2")
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title.add_background_rectangle()
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title.scale(1.5)
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title.to_corner(UL, buff=MED_SMALL_BUFF)
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self.add_foreground_mobject(title)
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def edit_background_plane(self):
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self.background.main_lines.set_stroke(GREY, 2)
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self.background.secondary_lines.set_stroke(DARK_GREY, 1)
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self.add_foreground_mobject(self.background.coordinate_labels)
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def add_transforming_planes(self):
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self.plane = self.get_plane()
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self.add_transformable_mobjects(self.plane)
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def preview_some_numbers(self):
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dots = VGroup(*[
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Dot().move_to(self.background.number_to_point(z))
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for z in [
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1, 2, complex(0, 1),
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-1, complex(2, 0.5), complex(-1, -1), complex(3, 0.5),
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]
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])
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dots.set_color_by_gradient(RED, YELLOW)
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d_angle = 30 * DEGREES
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dot_groups = VGroup()
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for dot in dots:
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point = dot.get_center()
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z = self.background.point_to_number(point)
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z_out = self.complex_homotopy(z, 1)
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out_point = self.background.number_to_point(z_out)
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path_arc = angle_of_vector(point)
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if abs(z - 1) < 0.01:
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# One is special
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arrow = Arc(
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start_angle=(-90 * DEGREES + d_angle),
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angle=(360 * DEGREES - 2 * d_angle),
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radius=0.25
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)
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arrow.add_tip(tip_length=0.15)
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arrow.pointwise_become_partial(arrow, 0, 0.9)
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arrow.next_to(dot, UP, buff=0)
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else:
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arrow = Arrow(
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point, out_point,
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use_rectangular_stem=False,
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path_arc=path_arc,
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buff=SMALL_BUFF,
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)
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arrow.match_color(dot)
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out_dot = dot.copy()
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# out_dot.set_fill(opacity=0.5)
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out_dot.set_stroke(BLUE, 1)
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out_dot.move_to(out_point)
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dot.path_arc = path_arc
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dot.out_dot = out_dot
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dot_group = VGroup(dot, arrow, out_dot)
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dot_groups.add(dot_group)
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dot_copy = dot.copy()
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dot.save_state()
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dot.scale(3)
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dot.fade(1)
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dot_group.anim = Succession(
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ApplyMethod(dot.restore),
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AnimationGroup(
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ShowCreation(arrow),
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ReplacementTransform(
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dot_copy, out_dot,
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path_arc=path_arc
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)
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)
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)
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for dot_group in dot_groups[:3]:
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self.play(dot_group.anim)
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self.wait()
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self.play(*[dg.anim for dg in dot_groups[3:]])
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self.apply_complex_homotopy(
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self.complex_homotopy,
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added_anims=[Animation(dot_groups)]
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)
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self.wait()
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self.play(FadeOut(dot_groups))
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self.wait()
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self.play(FadeOut(self.plane))
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self.transformable_mobjects.remove(self.plane)
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def zoom_in_to_one_plus_half_i(self):
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z = complex(1, 0.5)
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point = self.background.number_to_point(z)
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point_mob = VectorizedPoint(point)
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frame = self.zoomed_camera.frame
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frame.move_to(point)
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tiny_plane = NumberPlane(
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x_radius=2, y_radius=2,
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color=GREEN,
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secondary_color=GREEN_E
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)
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tiny_plane.replace(frame)
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plane = self.get_plane()
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words = TextMobject("What does this look like")
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words.add_background_rectangle()
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words.next_to(self.zoomed_display, LEFT, aligned_edge=UP)
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arrow = Arrow(words.get_bottom(), self.zoomed_display.get_left())
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VGroup(words, arrow).set_color(YELLOW)
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self.play(FadeIn(plane))
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self.activate_zooming(animate=True)
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self.play(ShowCreation(tiny_plane))
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self.wait()
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self.add_transformable_mobjects(plane, tiny_plane, point_mob)
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self.add_foreground_mobjects(words, arrow)
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self.apply_complex_homotopy(
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self.complex_homotopy,
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added_anims=[
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Write(words),
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GrowArrow(arrow),
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MaintainPositionRelativeTo(frame, point_mob)
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]
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)
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self.wait(2)
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def write_derivative(self):
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pass
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# Helpers
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def get_plane(self):
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top_plane = NumberPlane(
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y_radius=FRAME_HEIGHT / 2,
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)
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self.prepare_for_transformation(top_plane)
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bottom_plane = top_plane.copy()
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tiny_tiny_buff = 0.001
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top_plane.next_to(ORIGIN, UP, buff=tiny_tiny_buff)
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bottom_plane.next_to(ORIGIN, DOWN, buff=tiny_tiny_buff)
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return VGroup(top_plane, bottom_plane)
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Block a user