def construct(self):
glass = self.get_continuous_glass()
self.play(ApplyMethod(glass.fade, 0.8))
self.freeze_background()
paths = self.get_paths()
for path in paths:
if path.get_height() > self.total_glass_height:
path.stretch(0.7, 1)
path.shift(self.top - path.get_top())
path.rgbas[:, 2] = 0
loop = paths.pop(1) ##Bad!
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
photon_run = self.photon_run_along_path(
loop, rate_func=lambda t: smooth(1.2 * t, 2), run_time=4.1)
text = self.get_text().to_edge(UP, buff=0.2)
self.play(ShowCreation(loop))
self.dither()
self.play(photon_run)
self.remove(photon_run.mobject)
randy = self.slide(randy, loop)
self.add(randy)
self.dither()
self.remove(randy)
self.play(ShimmerIn(text))
for path in paths:
self.play(
Transform(loop,
path,
path_func=path_along_arc(np.pi / 2),
run_time=2))
def construct(self):
self.knob = Circle(color = BLUE_D)
self.knob.add_line(UP, DOWN)
self.knob.to_corner(UP+RIGHT)
self.knob.shift(0.5*DOWN)
self.last_angle = np.pi/2
arrow = Vector(ORIGIN, RIGHT)
arrow.next_to(self.knob, LEFT)
words = TextMobject("Turn this knob over time to define the curve")
words.next_to(arrow, LEFT)
self.path = self.get_path()
self.path.shift(1.5*DOWN)
self.path.show()
self.path.highlight(BLACK)
randy = Randolph()
randy.scale(RANDY_SCALE_VAL)
randy.shift(-randy.get_bottom())
self.play(ShimmerIn(words))
self.play(ShowCreation(arrow))
self.play(ShowCreation(self.knob))
self.dither()
self.add(self.path)
self.slide(randy, self.path)
self.dither()
def construct(self):
self.knob = Circle(color=BLUE_D)
self.knob.add_line(UP, DOWN)
self.knob.to_corner(UP + RIGHT)
self.knob.shift(0.5 * DOWN)
self.last_angle = np.pi / 2
arrow = Vector(ORIGIN, RIGHT)
arrow.next_to(self.knob, LEFT)
words = TextMobject("Turn this knob over time to define the curve")
words.next_to(arrow, LEFT)
self.path = self.get_path()
self.path.shift(1.5 * DOWN)
self.path.show()
self.path.highlight(BLACK)
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
self.play(ShimmerIn(words))
self.play(ShowCreation(arrow))
self.play(ShowCreation(self.knob))
self.dither()
self.add(self.path)
self.slide(randy, self.path)
self.dither()
def construct(self):
self.add_cycloid_end_points()
start = self.point_a.get_center()
end = self.point_b.get_center()
angle = 2 * np.pi / 3
path = Arc(angle, radius=3)
path.gradient_highlight(RED_D, WHITE)
radius = Line(ORIGIN, path.points[0])
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
randy_copy = randy.copy()
words = TextMobject(
"Circular paths are good, \\\\ but still not the best")
words.shift(UP)
self.play(
ShowCreation(path),
ApplyMethod(radius.rotate, angle, path_func=path_along_arc(angle)))
self.play(FadeOut(radius))
self.play(ApplyMethod(path.position_endpoints_on,
start,
end,
path_func=path_along_arc(-angle)),
run_time=3)
self.adjust_mobject_to_index(randy_copy, 1, path.points)
self.play(FadeIn(randy_copy))
self.remove(randy_copy)
self.slide(randy, path)
self.play(ShimmerIn(words))
self.dither()
def construct(self):
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
self.add_cycloid_end_points()
self.add(self.cycloid)
self.slide(randy, self.cycloid)
self.play(self.photon_run_along_path(self.cycloid))
self.wait()
def construct(self):
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
self.add_cycloid_end_points()
self.add(self.cycloid)
self.slide(randy, self.cycloid)
self.play(self.photon_run_along_path(self.cycloid))
self.dither()
def construct(self, with_words):
CycloidScene.construct(self)
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
central_randy = randy.copy()
start_randy = self.adjust_mobject_to_index(
randy.copy(), 1, self.cycloid.points
)
if with_words:
words1 = TextMobject("Trajectory due to gravity")
arrow = TexMobject("\\leftrightarrow")
words2 = TextMobject("Trajectory due \\emph{constantly} rotating wheel")
words1.next_to(arrow, LEFT)
words2.next_to(arrow, RIGHT)
words = Mobject(words1, arrow, words2)
words.scale_to_fit_width(2*SPACE_WIDTH-1)
words.to_edge(UP, buff = 0.2)
words.to_edge(LEFT)
self.play(ShowCreation(self.cycloid.copy()))
self.slide(randy, self.cycloid)
self.add(self.slider)
self.wait()
self.grow_parts()
self.draw_cycloid()
self.wait()
self.play(Transform(self.slider, start_randy))
self.wait()
self.roll_back()
self.wait()
if with_words:
self.play(*map(ShimmerIn, [words1, arrow, words2]))
self.wait()
self.remove(self.circle)
start_time = len(self.frames)*self.frame_duration
self.remove(self.slider)
self.slide(central_randy, self.cycloid)
end_time = len(self.frames)*self.frame_duration
self.play_over_time_range(
start_time,
end_time,
RollAlongVector(
self.circle,
self.cycloid.points[-1]-self.cycloid.points[0],
run_time = end_time-start_time,
rate_func = None
)
)
self.add(self.circle, self.slider)
self.wait()
def construct(self, with_words):
CycloidScene.construct(self)
randy = Randolph()
randy.scale(RANDY_SCALE_VAL)
randy.shift(-randy.get_bottom())
central_randy = randy.copy()
start_randy = self.adjust_mobject_to_index(
randy.copy(), 1, self.cycloid.points
)
if with_words:
words1 = TextMobject("Trajectory due to gravity")
arrow = TexMobject("\\leftrightarrow")
words2 = TextMobject("Trajectory due \\emph{constantly} rotating wheel")
words1.next_to(arrow, LEFT)
words2.next_to(arrow, RIGHT)
words = Mobject(words1, arrow, words2)
words.scale_to_fit_width(2*SPACE_WIDTH-1)
words.to_edge(UP, buff = 0.2)
words.to_edge(LEFT)
self.play(ShowCreation(self.cycloid.copy()))
self.slide(randy, self.cycloid)
self.add(self.slider)
self.dither()
self.grow_parts()
self.draw_cycloid()
self.dither()
self.play(Transform(self.slider, start_randy))
self.dither()
self.roll_back()
self.dither()
if with_words:
self.play(*map(ShimmerIn, [words1, arrow, words2]))
self.dither()
self.remove(self.circle)
start_time = len(self.frames)*self.frame_duration
self.remove(self.slider)
self.slide(central_randy, self.cycloid)
end_time = len(self.frames)*self.frame_duration
self.play_over_time_range(
start_time,
end_time,
RollAlongVector(
self.circle,
self.cycloid.points[-1]-self.cycloid.points[0],
run_time = end_time-start_time,
rate_func = None
)
)
self.add(self.circle, self.slider)
self.dither()
def construct(self):
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
self.add_cycloid_end_points()
arrow = Arrow(ORIGIN, 2 * RIGHT)
arrows = Mobject(
*
[arrow.copy().shift(vect) for vect in 3 * LEFT, ORIGIN, 3 * RIGHT])
arrows.shift(2 * SPACE_WIDTH * RIGHT)
self.add(arrows)
self.add(self.cycloid)
self.slide(randy, self.cycloid)
everything = Mobject(*self.mobjects)
self.play(
ApplyMethod(everything.shift,
4 * SPACE_WIDTH * LEFT,
run_time=2,
rate_func=rush_into))
def construct(self):
randy = Randolph()
randy.scale(RANDY_SCALE_VAL)
randy.shift(-randy.get_bottom())
self.add_cycloid_end_points()
arrow = Arrow(ORIGIN, 2*RIGHT)
arrows = Mobject(*[
arrow.copy().shift(vect)
for vect in 3*LEFT, ORIGIN, 3*RIGHT
])
arrows.shift(2*SPACE_WIDTH*RIGHT)
self.add(arrows)
self.add(self.cycloid)
self.slide(randy, self.cycloid)
everything = Mobject(*self.mobjects)
self.play(ApplyMethod(
everything.shift, 4*SPACE_WIDTH*LEFT,
run_time = 2,
rate_func = rush_into
))
def construct(self):
randy = Randolph()
randy.scale(RANDY_SCALE_VAL)
randy.shift(-randy.get_bottom())
self.add_cycloid_end_points()
points = self.cycloid.points
ceiling = points[0, 1]
n = len(points)
broken_points = [
points[k*n/self.num_pieces:(k+1)*n/self.num_pieces]
for k in range(self.num_pieces)
]
words = TextMobject("""
What determines the speed\\\\
at each point?
""")
words.to_edge(UP)
self.add(self.cycloid)
sliders, vectors = [], []
for points in broken_points:
path = Mobject().add_points(points)
vect = points[-1] - points[-2]
magnitude = np.sqrt(ceiling - points[-1, 1])
vect = magnitude*vect/np.linalg.norm(vect)
slider = self.slide(randy, path, ceiling = ceiling)
vector = Vector(slider.get_center(), vect)
self.add(slider, vector)
sliders.append(slider)
vectors.append(vector)
self.dither()
self.play(ShimmerIn(words))
self.dither(3)
slider = sliders.pop(1)
vector = vectors.pop(1)
faders = sliders+vectors+[words]
self.play(*map(FadeOut, faders))
self.remove(*faders)
self.show_geometry(slider, vector)
def construct(self):
randy = Randolph()
randy.shift(-randy.get_bottom())
self.slider = randy.copy()
randy.scale(RANDY_SCALE_VAL)
paths = self.get_paths()
point_a = Dot(paths[0].points[0])
point_b = Dot(paths[0].points[-1])
A = TexMobject("A").next_to(point_a, LEFT)
B = TexMobject("B").next_to(point_b, RIGHT)
for point, tex in [(point_a, A), (point_b, B)]:
self.play(ShowCreation(point))
self.play(ShimmerIn(tex))
self.dither()
curr_path = None
for path in paths:
new_slider = self.adjust_mobject_to_index(
randy.copy(), 1, path.points
)
if curr_path is None:
curr_path = path
self.play(ShowCreation(curr_path))
else:
self.play(Transform(curr_path, path))
self.play(Transform(self.slider, new_slider))
self.dither()
self.remove(self.slider)
self.slide(randy, curr_path)
self.clear()
self.add(point_a, point_b, A, B, curr_path)
text = self.get_text()
text.to_edge(UP)
self.play(ShimmerIn(text))
for path in paths:
self.play(Transform(
curr_path, path,
path_func = path_along_arc(np.pi/2),
run_time = 3
))
def construct(self):
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
self.add_cycloid_end_points()
points = self.cycloid.points
ceiling = points[0, 1]
n = len(points)
broken_points = [
points[k * n / self.num_pieces:(k + 1) * n / self.num_pieces]
for k in range(self.num_pieces)
]
words = TextMobject("""
What determines the speed\\\\
at each point?
""")
words.to_edge(UP)
self.add(self.cycloid)
sliders, vectors = [], []
for points in broken_points:
path = Mobject().add_points(points)
vect = points[-1] - points[-2]
magnitude = np.sqrt(ceiling - points[-1, 1])
vect = magnitude * vect / np.linalg.norm(vect)
slider = self.slide(randy, path, ceiling=ceiling)
vector = Vector(slider.get_center(), vect)
self.add(slider, vector)
sliders.append(slider)
vectors.append(vector)
self.dither()
self.play(ShimmerIn(words))
self.dither(3)
slider = sliders.pop(1)
vector = vectors.pop(1)
faders = sliders + vectors + [words]
self.play(*map(FadeOut, faders))
self.remove(*faders)
self.show_geometry(slider, vector)
def construct(self):
randy = Randolph()
randy.shift(-randy.get_bottom())
self.slider = randy.copy()
randy.scale(RANDY_SCALE_FACTOR)
paths = self.get_paths()
point_a = Dot(paths[0].points[0])
point_b = Dot(paths[0].points[-1])
A = TexMobject("A").next_to(point_a, LEFT)
B = TexMobject("B").next_to(point_b, RIGHT)
for point, tex in [(point_a, A), (point_b, B)]:
self.play(ShowCreation(point))
self.play(ShimmerIn(tex))
self.wait()
curr_path = None
for path in paths:
new_slider = self.adjust_mobject_to_index(
randy.copy(), 1, path.points
)
if curr_path is None:
curr_path = path
self.play(ShowCreation(curr_path))
else:
self.play(Transform(curr_path, path))
self.play(Transform(self.slider, new_slider))
self.wait()
self.remove(self.slider)
self.slide(randy, curr_path)
self.clear()
self.add(point_a, point_b, A, B, curr_path)
text = self.get_text()
text.to_edge(UP)
self.play(ShimmerIn(text))
for path in paths:
self.play(Transform(
curr_path, path,
path_func = path_along_arc(np.pi/2),
run_time = 3
))
def construct(self):
self.add_cycloid_end_points()
start = self.point_a.get_center()
end = self.point_b.get_center()
angle = 2*np.pi/3
path = Arc(angle, radius = 3)
path.gradient_highlight(RED_D, WHITE)
radius = Line(ORIGIN, path.points[0])
randy = Randolph()
randy.scale(RANDY_SCALE_VAL)
randy.shift(-randy.get_bottom())
randy_copy = randy.copy()
words = TextMobject("Circular paths are good, \\\\ but still not the best")
words.shift(UP)
self.play(
ShowCreation(path),
ApplyMethod(
radius.rotate,
angle,
path_func = path_along_arc(angle)
)
)
self.play(FadeOut(radius))
self.play(
ApplyMethod(
path.position_endpoints_on, start, end,
path_func = path_along_arc(-angle)
),
run_time = 3
)
self.adjust_mobject_to_index(randy_copy, 1, path.points)
self.play(FadeIn(randy_copy))
self.remove(randy_copy)
self.slide(randy, path)
self.play(ShimmerIn(words))
self.dither()
def construct(self):
glass = self.get_continuous_glass()
self.play(ApplyMethod(glass.fade, 0.8))
self.freeze_background()
paths = self.get_paths()
for path in paths:
if path.get_height() > self.total_glass_height:
path.stretch(0.7, 1)
path.shift(self.top - path.get_top())
path.rgbs[:,2] = 0
loop = paths.pop(1) ##Bad!
randy = Randolph()
randy.scale(RANDY_SCALE_VAL)
randy.shift(-randy.get_bottom())
photon_run = self.photon_run_along_path(
loop,
rate_func = lambda t : smooth(1.2*t, 2),
run_time = 4.1
)
text = self.get_text().to_edge(UP, buff = 0.2)
self.play(ShowCreation(loop))
self.dither()
self.play(photon_run)
self.remove(photon_run.mobject)
randy = self.slide(randy, loop)
self.add(randy)
self.dither()
self.remove(randy)
self.play(ShimmerIn(text))
for path in paths:
self.play(Transform(
loop, path,
path_func = path_along_arc(np.pi/2),
run_time = 2
))
def construct(self):
randy = Randolph()
randy.scale(RANDY_SCALE_VAL)
randy.shift(-randy.get_bottom())
self.add_cycloid_end_points()
self.slide(randy, self.cycloid, roll = True)
def construct(self):
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
self.add_cycloid_end_points()
self.slide(randy, self.cycloid, roll=True)