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https://github.com/3b1b/manim.git
synced 2025-07-30 13:34:19 +08:00
Fixes to multilayered scnes
This commit is contained in:
Grant Sanderson
@ -47,20 +47,15 @@ class Cycloid(ParametricFunction):
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class LoopTheLoop(ParametricFunction):
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CONFIG = {
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"color" : YELLOW_D,
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"density" : 20*DEFAULT_POINT_DENSITY_1D
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"density" : 10*DEFAULT_POINT_DENSITY_1D
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}
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def __init__(self, **kwargs):
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digest_config(self, kwargs)
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pre_func = lambda t : [
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t**3 - 1.5*t,
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t**2 + 0.6*(t**2 - 4)*(t**2 - 1),
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0
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]
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ParametricFunction.__init__(
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self,
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lambda t : pre_func(4*t-2),
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**kwargs
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)
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def func(t):
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t = (6*np.pi/2)*(t-0.5)
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return (t/2-np.sin(t))*RIGHT + \
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(np.cos(t)+(t**2)/10)*UP
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ParametricFunction.__init__(self, func, **kwargs)
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class SlideWordDownCycloid(Animation):
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@ -24,17 +24,6 @@ from brachistochrone.light import PhotonScene
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from brachistochrone.curves import *
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#Two to many
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#race light in each
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#n layers
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#v_1, v_2, v_3
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#proportional to sqrt y_1, y_2, y_3
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#limiting process
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#show sliding object and light
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#which path is fastest
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#instantaneously obey snell's law
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class MultilayeredScene(Scene):
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CONFIG = {
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"n_layers" : 5,
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@ -293,7 +282,7 @@ class ShowLightAndSlidingObject(MultilayeredScene, TryManyPaths, PhotonScene):
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}
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def construct(self):
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glass = self.get_continuous_glass()
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self.play(ApplyMethod(glass.fade, 0.3))
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self.play(ApplyMethod(glass.fade, 0.8))
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self.freeze_background()
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paths = self.get_paths()
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@ -301,14 +290,14 @@ class ShowLightAndSlidingObject(MultilayeredScene, TryManyPaths, PhotonScene):
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if path.get_height() > self.total_glass_height:
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path.stretch(0.7, 1)
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path.shift(self.top - path.get_top())
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path.rgbs[:2] = 0
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path.rgbs[:,2] = 0
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loop = paths.pop(1) ##Bad!
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randy = Randolph()
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randy.scale(RANDY_SCALE_VAL)
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randy.shift(-randy.get_bottom())
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photon_run = self.photon_run_along_path(
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loop,
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rate_func = lambda t : smooth(t, 3),
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rate_func = lambda t : smooth(1.2*t, 2),
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run_time = 4.1
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)
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text = self.get_text().to_edge(UP, buff = 0.2)
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@ -330,66 +319,106 @@ class ShowLightAndSlidingObject(MultilayeredScene, TryManyPaths, PhotonScene):
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))
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class ContinuouslyObeyingSnellsLaw(MultilayeredScene, ZoomedScene):
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class ContinuouslyObeyingSnellsLaw(MultilayeredScene):
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CONFIG = {
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"arc_radius" : 0.1,
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"arc_radius" : 0.5,
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"RectClass" : FilledRectangle
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}
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def construct(self):
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glass = self.get_continuous_glass()
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self.add(glass)
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self.freeze_background()
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line = Line(
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UP, DOWN,
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density = self.zoom_factor*DEFAULT_POINT_DENSITY_1D
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)
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theta = TexMobject("\\theta")
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theta.scale(0.5/self.zoom_factor)
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equation = TexMobject([
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"\\dfrac{\\sin(\\theta)}",
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"{\\sqrt{y}}",
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" = \\text{constant}"
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])
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equation.next_to(Point(self.top), DOWN)
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equation.shift(LEFT)
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cycloid = Cycloid(end_theta = np.pi)
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cycloid = Cycloid()
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cycloid.highlight(YELLOW)
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chopped_cycloid = cycloid.copy()
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n = cycloid.get_num_points()
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chopped_cycloid.filter_out(lambda p : p[1] > 1 and p[0] < 0)
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chopped_cycloid.reverse_points()
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for mob in equation.split():
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self.play(GrowFromCenter(mob), run_time = 0.5)
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self.play(ShowCreation(cycloid))
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self.activate_zooming()
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little_square = self.get_zoomed_camera_mobject()
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self.snells_law_at_every_point(cycloid, chopped_cycloid)
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self.show_equation(chopped_cycloid)
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self.add(line)
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indices = np.arange(
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0, cycloid.get_num_points()-1, 10
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def snells_law_at_every_point(self, cycloid, chopped_cycloid):
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square = Square(side_length = 0.2, color = WHITE)
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words = TextMobject("Snell's law at every point")
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words.next_to(square)
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words.shift(0.3*UP)
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combo = Mobject(square, words)
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combo.get_center = lambda : square.get_center()
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self.play(MoveAlongPath(
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combo, cycloid,
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run_time = 3
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))
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self.play(MoveAlongPath(
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combo, chopped_cycloid,
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run_time = 2
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))
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dot = Dot(combo.get_center())
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self.play(Transform(combo.ingest_sub_mobjects(), dot))
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self.dither()
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def get_marks(self, point1, point2):
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vert_line = Line(2*DOWN, 2*UP)
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tangent_line = vert_line.copy()
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theta = TexMobject("\\theta")
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theta.scale(0.5)
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angle = angle_of_vector(point1 - point2)
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tangent_line.rotate(
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angle - tangent_line.get_angle()
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)
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for index in indices:
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point = cycloid.points[index]
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next_point = cycloid.points[index+1]
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angle = angle_of_vector(point - next_point)-np.pi/2
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for mob in little_square, line:
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mob.shift(point - mob.get_center())
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arc = Arc(angle, start_angle = np.pi/2)
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angle_from_vert = angle - np.pi/2
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for mob in vert_line, tangent_line:
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mob.shift(point1 - mob.get_center())
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arc = Arc(angle_from_vert, start_angle = np.pi/2)
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arc.scale(self.arc_radius)
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arc.shift(point)
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color = Color()
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height = (self.top-self.point)[1]
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color.set_rgb([height/self.total_glass_height]*3)
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for mob in arc, theta, line:
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mob.highlight(color)
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if angle > np.pi/15:
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arc.shift(point1)
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self.add(arc)
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if angle > np.pi/6:
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vect_angle = angle/2 + np.pi/2
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vect_angle = angle_from_vert/2 + np.pi/2
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vect = rotate_vector(RIGHT, vect_angle)
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theta.center()
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theta.shift(point)
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theta.shift(point1)
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theta.shift(1.5*self.arc_radius*vect)
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self.add(theta)
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self.dither(self.frame_duration)
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self.remove(arc)
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return arc, theta, vert_line, tangent_line
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def show_equation(self, chopped_cycloid):
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point1, point2 = chopped_cycloid.points[-2:]
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arc, theta, vert_line, tangent_line = self.get_marks(
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point1, point2
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)
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sin, sqrt_y = TexMobject([
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"\\sin(\\theta)",
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"\\over \\sqrt{y}",
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]).split()
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equation = Mobject(sin, sqrt_y)
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equation.next_to(Point(self.top), DOWN)
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equation.shift(LEFT)
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const = TexMobject(" = \\text{constant}")
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const.next_to(equation)
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ceil_point = np.array(point)
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ceil_point[1] = self.top[1]
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brace = Brace(
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Mobject(Point(point), Point(ceil_point)),
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RIGHT
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)
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y_mob = TexMobject("y").next_to(brace)
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self.play(GrowFromCenter(sin))
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self.play(ShowCreation(vert_line))
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self.play(ShowCreation(tangent_line))
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self.play(ShowCreation(arc), GrowFromCenter(theta))
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self.dither()
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self.play(
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GrowFromCenter(sqrt_y),
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GrowFromCenter(brace),
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GrowFromCenter(y_mob)
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)
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self.dither()
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self.play(ShimmerIn(const))
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self.dither()
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@ -20,7 +20,7 @@ LOW_QUALITY_CAMERA_CONFIG = {
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DEFAULT_POINT_DENSITY_2D = 25
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DEFAULT_POINT_DENSITY_1D = 200
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DEFAULT_POINT_DENSITY_1D = 250
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DEFAULT_POINT_THICKNESS = 3
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