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lorentz.py
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from manimlib.imports import *
class Lorentz(LinearTransformationScene):
CONFIG = {
"camera_config": {
"frame_center": 3*UP
},
"show_basis_vectors": False,
"background_plane_kwargs": {
"y_max": 10
},
"include_foreground_plane": False,
"foreground_plane_kwargs": {
"y_min": -15,
"y_max": 15,
"x_min": -10,
"x_max": 10
}
}
def construct(self):
# Assets
lightlesshouse = ImageMobject ("lightless-house-centered.png")
rocket = ImageMobject("Rocket.png")
rocket.scale(0.5)
chad = ImageMobject("cool-rocket.png")
chad.scale(0.5)
photon = ImageMobject("photon.png")
photon.scale(0.2)
# Math
foreground_plane = NumberPlane(y_min=-15, y_max=15, x_min=-10, x_max=10)
your_beta = 1/3
chad_beta = 2/3
your_gamma = 1/math.sqrt(1 - (your_beta ** 2))
chad_gamma = 1/math.sqrt(1 - (chad_beta ** 2))
lighthouse_to_you = [[your_gamma, -1 * your_gamma * your_beta],
[-1 * your_gamma * your_beta, your_gamma]]
lighthouse_to_chad =[[chad_gamma, -1 * chad_gamma * chad_beta],
[-1 * chad_gamma * chad_beta, chad_gamma]]
# World Line Functions
def one_third(x):
return 3*x
def two_thirds(x):
return (3*x)/2
def light(x):
return x
# World Lines
stationary = Line(ORIGIN+DOWN, np.array([0, 8, 0]), stroke_color=RED)
your_world_line = FunctionGraph(one_third, x_min=-0.4, x_max=3, color=TEAL_B)
chad_world_line = FunctionGraph(two_thirds, x_min=-0.8, x_max=5.7, color=GREEN)
light_graph = FunctionGraph(light, x_min=-1.4, x_max=10, color=YELLOW)
#planet_breakthrough = Line(np.array([4, -1, 0]), np.array([4, 10, 0]), stroke_color=ORANGE)
assets = [lightlesshouse, rocket, chad, photon]
paths = [stationary, your_world_line, chad_world_line, light_graph]
# Slopes
your_run = Line(
ORIGIN, np.array([1, 0, 0]), color=MAROON, stroke_width=5
)
your_rise = Line(
np.array([1, 0, 0]), np.array([1, 3, 0]), color=MAROON, stroke_width=5
)
your_rise_label = TexMobject("3").next_to(your_rise, direction=RIGHT).add_background_rectangle()
your_run_label = TexMobject("1").next_to(your_run, direction=DOWN).add_background_rectangle()
chad_run = Line(
ORIGIN, np.array([2, 0, 0]), color=MAROON, stroke_width=5
)
chad_rise = Line(
np.array([2, 0, 0]), np.array([2, 3, 0]), color=MAROON, stroke_width=5
)
chad_rise_label = TexMobject("3").next_to(chad_rise, direction=RIGHT).add_background_rectangle()
chad_run_label = TexMobject("2").next_to(chad_run, direction=DOWN).add_background_rectangle()
light_run = Line(
ORIGIN, np.array([1, 0, 0]), color=MAROON, stroke_width=5
)
light_rise = Line(
np.array([1, 0, 0]), np.array([1, 1, 0]), color=MAROON, stroke_width=5
)
light_rise_label = TexMobject("1").next_to(light_rise, direction=RIGHT).add_background_rectangle()
light_run_label = TexMobject("1").next_to(light_run, direction=DOWN).add_background_rectangle()
slopes = ["skip", VGroup(your_rise, your_run, your_rise_label, your_run_label), VGroup(chad_rise, chad_run, chad_rise_label, chad_run_label), VGroup(light_rise, light_run, light_rise_label, light_run_label)]
# angles
lines = []
angles = VGroup()
# PLAY COMMANDS:
self.add_transformable_mobject(foreground_plane)
for asset, path, slope in zip(assets, paths, slopes):
asset.move_to(path.get_start())
line = Line(path.get_start(), asset.get_center())
def draw_line(obj):
obj.become(
Line(path.get_start(), asset.get_center(), color=path.get_color())
)
self.play(
FadeIn(asset)
)
self.add(line)
self.play(
MoveAlongPath(asset, path),
UpdateFromFunc(line, draw_line)
)
self.add(line)
if not slope == "skip":
self.play(
FadeIn(slope)
)
self.play(
FadeOut(slope)
)
lines.append(line)
self.remove(asset)
self.remove(line)
self.add_transformable_mobject(line)
self.wait()
angle = Arc(start_angle=lines[1].get_angle(), angle=lines[0].get_angle() - lines[1].get_angle(), radius=1)
self.play(
FadeIn(angle)
)
self.wait()
self.play(
FadeOut(angle)
)
self.apply_matrix(lighthouse_to_you, run_time=1)
angle = Arc(start_angle=lines[1].get_angle(), angle=lines[0].get_angle() - lines[1].get_angle(), radius=1)
self.play(
FadeOut(foreground_plane),
FadeIn(angle)
)
self.wait()
self.play(
WiggleOutThenIn(lines[1])
)
self.play(
Indicate(angle)
)
self.play(
WiggleOutThenIn(lines[3])
)
self.wait()
class RaceSimultaneity(Scene):
def construct(self):
# Assets
space = ImageMobject("space.png")
space.scale(10).shift(LEFT)
lighthouse = ImageMobject("lightless-house-centered.png")
lighthouse.move_to([0, -2, 0])
rocket = ImageMobject("Rocket.png")
rocket.scale(0.5)
rocket.move_to(np.array([-6, 2, 0]))
chad = ImageMobject("cool-rocket.png")
chad.scale(0.5)
chad.move_to(np.array([6, 2, 0]))
collision1 = ImageMobject("asteroid-collision.png")
collision1.scale(0.5)
collision1.move_to(lighthouse.get_center()+3*LEFT)
collision2 = ImageMobject("asteroid-collision.png")
collision2.scale(0.5)
collision2.move_to(lighthouse.get_center()+3*RIGHT)
# Paths
rocket_path = Line(
np.array([-6, 2, 0]), np.array([6, 2, 0]), color = BLUE
)
rocket_path2 = Line(
np.array([6, 2, 0]), np.array([-6, 2, 0]), color = BLUE
)
# PLAY COMMANDS
self.add(space)
self.add(lighthouse)
self.wait()
self.play(
FadeIn(collision1),
FadeIn(collision2)
)
self.play(
FadeOut(collision1),
FadeOut(collision2)
)
self.wait()
self.play(
FadeIn(rocket)
)
self.play(
MoveAlongPath(rocket, rocket_path),
AnimationGroup(
FadeIn(collision2),
FadeIn(collision1),
lag_ratio=0.4
),
run_time=3
)
self.play(
rocket.flip, UP
)
self.play(
MoveAlongPath(rocket, rocket_path2),
AnimationGroup(
FadeIn(collision1),
FadeIn(collision2),
lag_ratio=0.4
),
run_time=3
)
self.wait()
class Simultaneity(LinearTransformationScene):
CONFIG = {
"camera_config": {
"frame_center": 3*UP
},
"show_basis_vectors": False,
"background_plane_kwargs": {
"y_max": 10
},
"include_foreground_plane": False,
"foreground_plane_kwargs": {
"y_min": -15,
"y_max": 15,
"x_min": -10,
"x_max": 10
}
}
def construct(self):
your_beta = 1/3
chad_beta = 2/3
your_gamma = 1/math.sqrt(1 - (your_beta ** 2))
chad_gamma = 1/math.sqrt(1 - (chad_beta ** 2))
lighthouse_to_you = [[your_gamma, -1 * your_gamma * your_beta],
[-1 * your_gamma * your_beta, your_gamma]]
lighthouse_to_chad =[[chad_gamma, -1 * chad_gamma * chad_beta],
[-1 * chad_gamma * chad_beta, chad_gamma]]
def one_third(x):
return 3*x
def negative_one_third(x):
return -3*x
def two_thirds(x):
return (3*x)/2
def light(x):
return x
foreground_plane = NumberPlane(y_min=-15, y_max=15, x_min=-10, x_max=10)
stationary = Line(ORIGIN+DOWN, np.array([0, 10, 0]), stroke_color=RED)
your_world_line = FunctionGraph(one_third, x_min=-10, x_max=10, color=TEAL_B)
your_world_line2 = FunctionGraph(negative_one_third, x_min=-10, x_max=10, color=TEAL_B)
chad_world_line = FunctionGraph(two_thirds, x_min=-10, x_max=10, color=GREEN)
light_graph = FunctionGraph(light, x_min=-10, x_max=10, color=YELLOW)
planet_breakthrough = Line(np.array([4, -1, 0]), np.array([4, 10, 0]), stroke_color=ORANGE)
collision_one = Dot(np.array([-2, 0, 0]), color=LIGHT_BROWN)
collision_two = Dot(np.array([2, 0, 0]), color=LIGHT_BROWN)
time_main = Line(
collision_one.get_center()+LEFT,
[collision_one.get_center()[0]-1, collision_two.get_center()[1], 0],
color=MAROON, stroke_width=5
)
time_tips = VGroup(
Line(time_main.get_start()+0.3*LEFT, time_main.get_start()+0.3*RIGHT, color=MAROON, stroke_width=5),
Line(time_main.get_end()+0.3*LEFT, time_main.get_end()+0.3*RIGHT, color=MAROON, stroke_width=5)
)
time_main.add_updater(
lambda p: p.become(
Line(
collision_one.get_center()+0.8*LEFT,
[collision_one.get_center()[0]-0.8, collision_two.get_center()[1], 0],
color=MAROON, stroke_width=5
)
)
)
time_tips.add_updater(
lambda p: p.become(
VGroup(
Line(time_main.get_start()+0.3*LEFT, time_main.get_start()+0.3*RIGHT, color=MAROON, stroke_width=5),
Line(time_main.get_end()+0.3*LEFT, time_main.get_end()+0.3*RIGHT, color=MAROON, stroke_width=5)
)
)
)
time_label = TextMobject("Time Difference:")
time_number = DecimalNumber(collision_one.get_center()[1] - collision_two.get_center()[1], num_decimal_places=3, include_sign=False)
time_number.next_to(time_label, direction=DOWN).shift(LEFT)
time_number.add_updater(lambda p: p.set_value(abs(collision_one.get_center()[1] - collision_two.get_center()[1])))
time_unit = TextMobject("seconds")
time_unit.next_to(time_number, direction=RIGHT)
time_label_group = VGroup(time_label, time_number, time_unit)
time_label_group.add_background_rectangle()
time_label_group.add_updater(lambda p: p.next_to(time_main, direction=LEFT))
collision_label1 = TextMobject("Asteroid Collision").add_background_rectangle()
collision_label2 = TextMobject("Asteroid Collision").add_background_rectangle()
collision_label1.move_to([-3, 3, 0])
collision_label2.move_to([[4, 3, 0]])
first_collision = TextMobject("First Collision").add_background_rectangle()
first_collision.move_to(collision_label2)
second_collision = TextMobject("Second Collision").add_background_rectangle()
second_collision.move_to(collision_label1)
arrow1 = Arrow(collision_label1.get_edge_center(DOWN), collision_one.get_center()+0.1*UP)
arrow2 = Arrow(collision_label2.get_edge_center(DOWN), collision_two.get_center()+0.1*UP)
arrow1.add_updater(
lambda m: m.become(Arrow(collision_label1.get_edge_center(DOWN), collision_one.get_center()+0.2*UP))
)
arrow2.add_updater(
lambda m: m.become(Arrow(collision_label2.get_edge_center(DOWN), collision_two.get_center()+0.2*UP))
)
self.add_transformable_mobject(foreground_plane)
self.add_transformable_mobject(stationary)
self.add_transformable_mobject(your_world_line)
self.add_transformable_mobject(chad_world_line)
self.add_transformable_mobject(light_graph)
self.add_moving_mobject(collision_one)
self.add_moving_mobject(collision_two)
self.play(
Write(time_main),
Write(time_tips),
Write(time_label_group),
Write(collision_one),
Write(collision_two),
Write(arrow1),
Write(arrow2),
Write(collision_label1),
Write(collision_label2)
)
self.wait()
self.apply_matrix(lighthouse_to_you, run_time=1)
self.play(
FadeOut(foreground_plane),
ReplacementTransform(collision_label2, first_collision),
ReplacementTransform(collision_label1, second_collision),
)
self.wait()
self.play(
FadeIn(foreground_plane),
)
self.add(stationary)
self.apply_inverse(lighthouse_to_you, run_time=1)
self.wait()
self.play(
ReplacementTransform(your_world_line, your_world_line2)
)
self.remove(your_world_line2)
self.apply_inverse(lighthouse_to_you, run_time=1)
first_collision.generate_target()
second_collision.generate_target()
first_collision.target.move_to(collision_label1)
second_collision.target.move_to(collision_label2)
self.play(
FadeOut(foreground_plane),
MoveToTarget(first_collision),
MoveToTarget(second_collision)
)
self.wait()
class TimeDilation(LinearTransformationScene):
CONFIG = {
"camera_config": {
"frame_center": 3*UP
},
"show_basis_vectors": False,
"background_plane_kwargs": {
"y_max": 10
},
"include_foreground_plane": False
}
def construct(self):
your_beta = 1/3
chad_beta = 2/3
chad_new_beta = 3/7
your_gamma = 1/math.sqrt(1 - (your_beta ** 2))
chad_gamma = 1/math.sqrt(1 - (chad_beta ** 2))
chad_new_gamma = 1/math.sqrt(1 - (chad_new_beta ** 2))
lighthouse_to_you = [[your_gamma, -1 * your_gamma * your_beta],
[-1 * your_gamma * your_beta, your_gamma]]
lighthouse_to_chad = [[chad_gamma, -1 * chad_gamma * chad_beta],
[-1 * chad_gamma * chad_beta, chad_gamma]]
you_to_chad = [[chad_new_gamma, -1 * chad_new_gamma * chad_new_beta],
[-1 * chad_new_gamma * chad_new_beta, chad_new_gamma]]
def one_third(x):
return 3*x
def two_thirds(x):
return (3*x)/2
def light(x):
return x
foreground_plane = NumberPlane(y_min=-4, y_max=17, x_min=-10, x_max=12)
stationary = Line(ORIGIN+DOWN, np.array([0, 10, 0]), stroke_color=RED)
your_world_line = FunctionGraph(one_third, x_min=-10, x_max=10, color=TEAL_B)
chad_world_line = FunctionGraph(two_thirds, x_min=-10, x_max=10, color=GREEN)
light_graph = FunctionGraph(light, x_min=-10, x_max=15, color=YELLOW)
collision = Dot(np.array([4, 5, 0]), color=LIGHT_BROWN)
time = DashedLine(collision.get_center(), [0, collision.get_center()[1], 0], color=MAROON, stroke_width=5)
time.add_updater(
lambda p: p.become(
DashedLine(collision.get_center(), [0, collision.get_center()[1], 0], color=MAROON, stroke_width=5)
)
)
y_coord = DecimalNumber(5, num_decimal_places=3, include_sign=False)
y_coord.add_updater(lambda p: p.set_value(collision.get_center()[1]))
y_coord.add_updater(lambda p: p.next_to(collision, direction=UP).add_background_rectangle())
time_label = TextMobject("Time =").add_background_rectangle()
time_unit = TextMobject("seconds").add_background_rectangle()
time_label.add_updater(lambda p: p.next_to(y_coord, direction=LEFT))
time_unit.add_updater(lambda p: p.next_to(y_coord, direction=RIGHT))
self.add_transformable_mobject(foreground_plane)
self.add_transformable_mobject(stationary)
self.add_transformable_mobject(your_world_line)
self.add_transformable_mobject(chad_world_line)
self.add_transformable_mobject(light_graph)
self.add_moving_mobject(collision)
self.add(collision)
self.play(
Write(time),
Write(time_label),
Write(y_coord),
Write(time_unit)
)
self.wait()
self.apply_matrix(lighthouse_to_you, run_time=1)
self.play(
FadeOut(foreground_plane)
)
self.wait()
foreground_plane.apply_matrix(np.linalg.inv(lighthouse_to_you))
self.play(
FadeIn(foreground_plane)
)
self.apply_matrix(you_to_chad, run_time=1)
self.play(
FadeOut(foreground_plane)
)
self.wait()
class TimeDilation2(LinearTransformationScene):
CONFIG = {
"camera_config": {
"frame_center": 3*UP
},
"show_basis_vectors": False,
"background_plane_kwargs": {
"y_max": 10
},
"include_foreground_plane": False
}
def construct(self):
your_beta = 1/3
chad_beta = 2/3
chad_new_beta = 3/7
your_gamma = 1/math.sqrt(1 - (your_beta ** 2))
chad_gamma = 1/math.sqrt(1 - (chad_beta ** 2))
chad_new_gamma = 1/math.sqrt(1 - (chad_new_beta ** 2))
lighthouse_to_you = [[your_gamma, -1 * your_gamma * your_beta],
[-1 * your_gamma * your_beta, your_gamma]]
lighthouse_to_chad = [[chad_gamma, -1 * chad_gamma * chad_beta],
[-1 * chad_gamma * chad_beta, chad_gamma]]
you_to_chad = [[chad_new_gamma, -1 * chad_new_gamma * chad_new_beta],
[-1 * chad_new_gamma * chad_new_beta, chad_new_gamma]]
def one_third(x):
return 3*x
def two_thirds(x):
return (3*x)/2
def light(x):
return x
foreground_plane = NumberPlane(y_min=-4, y_max=17, x_min=-10, x_max=12)
stationary = Line(ORIGIN+DOWN, np.array([0, 10, 0]), stroke_color=RED)
your_world_line = FunctionGraph(one_third, x_min=-10, x_max=10, color=TEAL_B)
chad_world_line = FunctionGraph(two_thirds, x_min=-10, x_max=10, color=GREEN)
light_graph = FunctionGraph(light, x_min=-10, x_max=15, color=YELLOW)
# collision 1
collision = Dot(np.array([4, 5, 0]), color=LIGHT_BROWN)
y_coord = DecimalNumber(5, num_decimal_places=3, include_sign=False)
y_coord.add_updater(lambda p: p.set_value(collision.get_center()[1]))
# collision 2
collision2 = Dot(np.array([2, 3, 0]), color=LIGHT_BROWN)
y_coord2 = DecimalNumber(3, num_decimal_places=3, include_sign=False)
y_coord2.add_updater(lambda p: p.set_value(collision2.get_center()[1]))
# label
time_main = Line(
[(collision.get_center()[0] + collision2.get_center()[0])/2, collision.get_center()[1], 0],
[(collision.get_center()[0] + collision2.get_center()[0])/2, collision2.get_center()[1], 0],
color=MAROON, stroke_width=5
)
time_tips = VGroup(
Line(time_main.get_start()+0.3*LEFT, time_main.get_start()+0.3*RIGHT, color=MAROON, stroke_width=5),
Line(time_main.get_end()+0.3*LEFT, time_main.get_end()+0.3*RIGHT, color=MAROON, stroke_width=5)
)
time_main.add_updater(
lambda p: p.become(
Line(
[(collision.get_center()[0] + collision2.get_center()[0])/2, collision.get_center()[1], 0],
[(collision.get_center()[0] + collision2.get_center()[0])/2, collision2.get_center()[1], 0],
color=MAROON, stroke_width=5
)
)
)
time_tips.add_updater(
lambda p: p.become(
VGroup(
Line(time_main.get_start()+0.3*LEFT, time_main.get_start()+0.3*RIGHT, color=MAROON, stroke_width=5),
Line(time_main.get_end()+0.3*LEFT, time_main.get_end()+0.3*RIGHT, color=MAROON, stroke_width=5)
)
)
)
time_label = TextMobject("Time Difference:")
time_number = DecimalNumber(collision.get_center()[1] - collision2.get_center()[1], num_decimal_places=3, include_sign=False)
time_number.next_to(time_label, direction=DOWN).shift(LEFT)
time_number.add_updater(lambda p: p.set_value(collision.get_center()[1] - collision2.get_center()[1]))
time_unit = TextMobject("seconds")
time_unit.next_to(time_number, direction=RIGHT)
time_label_group = VGroup(time_label, time_number, time_unit)
time_label_group.add_background_rectangle()
time_label_group.add_updater(lambda p: p.next_to(time_main, direction=RIGHT))
self.add_transformable_mobject(foreground_plane)
self.add_transformable_mobject(stationary)
self.add_transformable_mobject(your_world_line)
self.add_transformable_mobject(chad_world_line)
self.add_transformable_mobject(light_graph)
self.add_moving_mobject(collision)
self.add_moving_mobject(collision2)
self.play(
Write(time_main),
Write(time_tips),
Write(time_label_group)
)
self.wait()
self.apply_matrix(lighthouse_to_you, run_time=1)
self.play(
FadeOut(foreground_plane)
)
self.wait()
foreground_plane.apply_matrix(np.linalg.inv(lighthouse_to_you))
self.play(
FadeIn(foreground_plane)
)
self.apply_matrix(you_to_chad, run_time=1)
self.play(
FadeOut(foreground_plane)
)
self.wait()
class RocketPath(Scene):
def construct(self):
rocket_path = Line(
np.array([-6, 0, 0]), ORIGIN, color=BLUE
)
space_path = Line(
ORIGIN, np.array([-20, 0, 0]), color=BLUE
)
rocket = ImageMobject("Rocket")
rocket.move_to(
np.array([-6, 0, 0])
)
space = ImageMobject("Space.png").scale(10)
# PLAY COMMANDS
self.add(space)
self.add(rocket)
self.wait()
self.play(
MoveAlongPath(rocket, rocket_path)
)
self.wait()
self.play(
MoveAlongPath(space, space_path)
)
self.wait()
class ConditionOne(Scene):
CONFIG = {
"camera_config": {
"frame_center": 3*UP
}
}
def construct(self):
plane = NumberPlane(y_min=-2, y_max=12)
# World Line Functions
def one_third(x):
return 3*x
def two_thirds(x):
return (3*x)/2
def light(x):
return x
# World Lines
stationary = Line(ORIGIN+DOWN, np.array([0, 8, 0]), stroke_color=RED)
your_world_line = FunctionGraph(one_third, x_min=-0.4, x_max=3, color=TEAL_B)
chad_world_line = FunctionGraph(two_thirds, x_min=-0.8, x_max=5.7, color=GREEN)
light_graph = FunctionGraph(light, x_min=-1.4, x_max=10, color=YELLOW)
# Observer
observer = TextMobject("Observer").move_to([-4, 6, 0]).scale(1.5).add_background_rectangle()
arrow = CurvedArrow(
observer.get_edge_center(direction=DOWN) + 0.1*DOWN, np.array([-0.1, 3.4, 0]), color=RED, buff=5
)
# PLAY COMMANDS
self.add(plane, stationary, your_world_line, chad_world_line, light_graph)
self.play(
Write(observer),
Write(arrow)
)
self.wait()
class ConditionTwo(Scene):
def construct(self):
# Paths
rocket_path = Line(
np.array([0, 2, 0]), np.array([6, 2, 0]), color=BLUE
)
lighthouse_path = Line(
np.array([0, -2, 0]), np.array([-6, -2, 0]), color=BLUE
)
space_path = Line(
ORIGIN, np.array([-6, 0, 0]), color=BLUE
)
# Assets
rocket = ImageMobject("Rocket")
rocket.move_to(
np.array([0, 2, 0])
)
lighthouse = ImageMobject("lightless-house-centered.png")
lighthouse.move_to(np.array([0, -2, 0]))
space = ImageMobject("Space.png").scale(10)
# UpdaterFunctions
your_speed = TexMobject("Speed = \\frac{1}{3}\ c").scale(0.8).next_to(rocket, direction=LEFT)
lighthouse_speed = TexMobject("Speed = \\frac{1}{3}\ c").scale(0.8).next_to(lighthouse, direction=RIGHT)
def rocket_text(obj):
obj.next_to(rocket, direction=LEFT)
def lighthouse_text(obj):
obj.next_to(lighthouse, direction=RIGHT)
your_speed.add_updater(rocket_text)
lighthouse_speed.add_updater(lighthouse_text)
# PLAY COMMANDS
self.add(space)
self.add(rocket)
self.add(your_speed)
self.add(lighthouse)
self.wait()
self.play(
MoveAlongPath(rocket, rocket_path)
)
self.wait()
self.play(
ReplacementTransform(your_speed, lighthouse_speed),
rocket.move_to, np.array([0, 2, 0]), run_time=0.5
)
self.play(
MoveAlongPath(space, space_path),
MoveAlongPath(lighthouse, lighthouse_path)
)
self.wait()
class ConditionTwoAngle(Scene):
CONFIG = {
"camera_config": {
"frame_center": 3*UP
}
}
def construct(self):
plane = NumberPlane(y_min=-2, y_max=12)
# World Line Functions
def one_third(x):
return 3*x
def negative_one_third(x):
return -3*x
# World Lines
stationary = Line(ORIGIN+DOWN, np.array([0, 8, 0]), stroke_color=RED)
stationary.generate_target()
stationary_target_graph = FunctionGraph(negative_one_third, x_min=-3, x_max=0.4, color=RED)
stationary.target = Line(stationary_target_graph.get_end(), stationary_target_graph.get_start(), color=RED)
your_world_line_graph = FunctionGraph(one_third, x_min=-0.4, x_max=3, color=TEAL_B)
your_world_line = Line(your_world_line_graph.get_start(), your_world_line_graph.get_end(), color=TEAL_B)
your_world_line.generate_target()
your_world_line.target = Line(ORIGIN+DOWN, np.array([0, 8, 0]), stroke_color=TEAL_B)
angle = Arc(start_angle=your_world_line.get_angle(), angle=stationary.get_angle() - your_world_line.get_angle(), radius=2, color=ORANGE)
angle.generate_target()
angle.target = Arc(start_angle=your_world_line.target.get_angle(), angle=stationary.target.get_angle() - your_world_line.target.get_angle(), radius=2, color=ORANGE)
# PLAY COMMANDS
self.add(plane, stationary, your_world_line, angle)
self.play(
Indicate(angle)
)
self.play(
MoveToTarget(stationary),
MoveToTarget(your_world_line),
MoveToTarget(angle)
)
self.play(
Indicate(angle)
)
self.wait()
class ConditionThree(Scene):
CONFIG = {
"camera_config": {
"frame_center": 3*UP
}
}
def construct(self):
# World Line Functions
def one_third(x):
return 3*x
def two_thirds(x):
return (3*x)/2
def light(x):
return x
def negative_light(x):
return -1*x
# World Lines
stationary = Line(ORIGIN+DOWN, np.array([0, 8, 0]), stroke_color=RED)
your_world_line = FunctionGraph(one_third, x_min=-0.4, x_max=3, color=TEAL_B)
chad_world_line = FunctionGraph(two_thirds, x_min=-0.8, x_max=5.7, color=GREEN)
light_graph = FunctionGraph(light, x_min=-10, x_max=10, color=YELLOW)
flipped_light_graph = FunctionGraph(negative_light, x_min=-10, x_max=10, color=YELLOW)
# slope
light_run = Line(
ORIGIN, np.array([1, 0, 0]), color=MAROON, stroke_width=5
)
light_rise = Line(
np.array([1, 0, 0]), np.array([1, 1, 0]), color=MAROON, stroke_width=5
)
light_rise_label = TexMobject("1").next_to(light_rise, direction=RIGHT).add_background_rectangle()
light_run_label = TexMobject("1").next_to(light_run, direction=DOWN).add_background_rectangle()
foreground_plane = NumberPlane(y_min=-4, y_max=17, x_min=-10, x_max=12)
# PLAY COMMANDS:
self.add(foreground_plane, stationary, your_world_line, chad_world_line, light_graph)
self.play(
WiggleOutThenIn(light_graph)
)
self.wait()
self.play(
*[FadeOut(i) for i in [stationary, your_world_line, chad_world_line]],
Write(light_run),
Write(light_rise),
Write(light_run_label),
Write(light_rise_label)
)
self.wait()
shifter = 1
self.play(Write(flipped_light_graph))
for i in range(5):
self.play(Write(light_graph.copy().shift(shifter*UP)))
self.play(Write(flipped_light_graph.copy().shift(shifter*UP)))
self.play(Write(light_graph.copy().shift(shifter*DOWN)))
self.play(Write(flipped_light_graph.copy().shift(shifter*DOWN)))
shifter += 1
self.wait()
class Race(Scene):
def construct(self):
# Assets
space = ImageMobject("space.png")
space.scale(10).shift(LEFT)
lighthouse_position = np.array([-4.6, -3, 0])
lighthouse = ImageMobject("space-lighthouse.png")
lighthouse.move_to(lighthouse_position)
lightlesshouse = ImageMobject ("space-lightless-house.png")
lightlesshouse.move_to(lighthouse_position)
rocket = ImageMobject("Rocket.png")
rocket.scale(0.5)
rocket.move_to(np.array([-6, 0, 0]))
chad = ImageMobject("cool-rocket.png")
chad.scale(0.5)
chad.move_to(np.array([-6, 3, 0]))
photon = ImageMobject("photon.png")
photon.move_to(np.array([-5, -2.35, 0]))
photon.scale(0.2)
# Labels
lighthouse_label = TextMobject("Interstellar Lighthouse").next_to(lighthouse, direction=RIGHT, buff = 1.5)
rocket_label = TextMobject("You").next_to(rocket, direction=RIGHT, buff = 3)
chad_label = TextMobject("Chad").next_to(chad, direction=RIGHT, buff = 2.8)
lighthouse_arrow = Arrow(lighthouse_label.get_left(), lighthouse.get_right() + LEFT, buff = SMALL_BUFF)
rocket_arrow = Arrow(rocket_label.get_left(), rocket.get_right(), buff = SMALL_BUFF)
chad_arrow = Arrow(chad_label.get_left(), chad.get_right(), buff = SMALL_BUFF)
labels = VGroup(lighthouse_label, rocket_label, chad_label, lighthouse_arrow, rocket_arrow, chad_arrow)
# Paths
chad_path = Line(
chad.get_center(), np.array([2, 3, 0]), color = BLUE
)
rocket_path = Line(
rocket.get_center(), np.array([-2, 0, 0]), color = BLUE
)
photon_path = Line(
photon.get_center(), np.array([7, -2.35, 0]), color = BLUE
)
line_up = Line(
chad.get_center() + RIGHT + UP, rocket.get_center() + RIGHT + 4*DOWN, color = RED
)
# Time
"""time = DecimalNumber(0, include_sign=False).to_edge(DOWN)
time.add_updater(lambda p: p.set_value((photon.get_center()[0]+5) * 5/12))
time_label = TextMobject("Time = ").next_to(time, direction=LEFT)
time_unit = TextMobject("seconds").next_to(time, direction=RIGHT)"""
# PLAY COMMANDS
self.add(space)
self.add(rocket)
self.add(chad)
self.add(lighthouse)
self.add(time, time_label, time_unit)
self.wait()
self.play(
Write(labels), run_time=0.8
)
"""self.play(
FadeIn(line_up)
)
self.play(
FadeOut(line_up)
)"""
self.wait(2)
self.play(
FadeOut(labels)
)
self.wait()
self.play(
MoveAlongPath(chad, chad_path),
MoveAlongPath(rocket, rocket_path),
MoveAlongPath(photon, photon_path),
run_time = 3
)
self.wait()
photon_label = TextMobject("Photon").next_to(photon, direction=LEFT, buff = 3)
photon_arrow = Arrow(photon_label.get_right(), photon.get_left(), buff = SMALL_BUFF)
# Speed Labels
your_speed = TexMobject("Speed = \\frac{1}{3}\ c").next_to(rocket, direction=LEFT)
chad_speed = TexMobject("Speed = \\frac{2}{3}\ c").next_to(chad, direction=LEFT)
photon_speed = TexMobject("Speed = c").next_to(photon, direction=LEFT)
c = TextMobject("*c = Speed of Light").scale(0.5).to_corner(DR, buff=0.4)
self.play(
Write(photon_label),
Write(photon_arrow),
)
self.wait()
self.play(
ReplacementTransform(photon_label, photon_speed),
FadeOut(photon_arrow),
FadeIn(your_speed),
FadeIn(chad_speed),
Write(c)
)
self.wait()
class RaceWithCollision(Scene):
def construct(self):
# Assets
space = ImageMobject("space.png")
space.scale(10).shift(LEFT)
lighthouse_position = np.array([-4.6, -3, 0])
lighthouse = ImageMobject("space-lighthouse.png")
lighthouse.move_to(lighthouse_position)
lightlesshouse = ImageMobject ("space-lightless-house.png")
lightlesshouse.move_to(lighthouse_position)
rocket = ImageMobject("Rocket.png")
rocket.scale(0.5)
rocket.move_to(np.array([-6, 0, 0]))
chad = ImageMobject("cool-rocket.png")
chad.scale(0.5)
chad.move_to(np.array([-6, 3, 0]))
photon = ImageMobject("photon.png")
photon.move_to(np.array([-5, -2.35, 0]))
photon.scale(0.2)
collision = ImageMobject("asteroid-collision.png")
collision.scale(0.3)
# Paths
chad_path = Line(
chad.get_center(), np.array([2, 3, 0]), color = BLUE