def __init__(self, **kwargs):
digest_config(self, kwargs)
def func(t):
t = (6*np.pi/2)*(t-0.5)
return (t/2-np.sin(t))*RIGHT + \
(np.cos(t)+(t**2)/10)*UP
ParametricFunction.__init__(self, func, **kwargs)
def graph_function(
self,
func,
color=BLUE,
animate=False,
is_main_graph=True,
):
def parameterized_function(alpha):
x = interpolate(self.x_min, self.x_max, alpha)
return self.coords_to_point(x, func(x))
graph = ParametricFunction(
parameterized_function,
color=color,
num_anchor_points=self.num_graph_anchor_points,
)
graph.underlying_function = func
if is_main_graph:
self.graph = graph
self.func = func
if animate:
self.play(ShowCreation(graph))
self.add(graph)
return graph
def construct(self):
t_axis = NumberLine()
theta_axis = NumberLine().rotate(np.pi / 2)
theta_mob = TexMobject("\\theta(t)")
t_mob = TexMobject("t")
theta_mob.next_to(theta_axis, RIGHT)
theta_mob.to_edge(UP)
t_mob.next_to(t_axis, UP)
t_mob.to_edge(RIGHT)
graph = ParametricFunction(
lambda t: 4 * t * RIGHT + 2 * smooth(t) * UP)
line = Line(graph.points[0], graph.points[-1], color=WHITE)
q_mark = TextMobject("?")
q_mark.next_to(Point(graph.get_center()), LEFT)
stars = Stars(color=BLACK)
stars.scale(0.1).shift(q_mark.get_center())
squiggle = ParametricFunction(lambda t: t * RIGHT + 0.2 * t * (5 - t) *
(np.sin(t)**2) * UP,
start=0,
end=5)
self.play(ShowCreation(t_axis), ShowCreation(theta_axis),
ShimmerIn(theta_mob), ShimmerIn(t_mob))
self.play(ShimmerIn(q_mark), ShowCreation(graph))
self.wait()
self.play(Transform(q_mark, stars), Transform(graph, line))
self.wait()
self.play(Transform(graph, squiggle))
self.wait()
def setup(self):
self.input_color = YELLOW_C
self.output_color = RED
def spiril(t):
theta = 2*np.pi*t
return t*np.cos(theta)*RIGHT+t*np.sin(theta)*UP
self.spiril1 = ParametricFunction(
lambda t : 1.5*RIGHT + DOWN + 2*spiril(t),
density = 5*DEFAULT_POINT_DENSITY_1D,
)
self.spiril2 = ParametricFunction(
lambda t : 5.5*RIGHT + UP - 2*spiril(1-t),
density = 5*DEFAULT_POINT_DENSITY_1D,
)
Mobject.align_data(self.spiril1, self.spiril2)
self.output = Mobject(self.spiril1, self.spiril2)
self.output.ingest_submobjects()
self.output.highlight(GREEN_A)
self.interval = UnitInterval()
self.interval.scale_to_fit_width(SPACE_WIDTH-1)
self.interval.to_edge(LEFT)
self.input_dot = Dot(color = self.input_color)
self.output_dot = self.input_dot.copy().highlight(self.output_color)
left, right = self.interval.get_left(), self.interval.get_right()
self.input_homotopy = lambda (x, y, z, t) : (x, y, t) + interpolate(left, right, t)
output_size = self.output.get_num_points()-1
output_points = self.output.points
self.output_homotopy = lambda (x, y, z, t) : (x, y, z) + output_points[int(t*output_size)]
def get_graph(
self, func,
color = None,
x_min = None,
x_max = None,
):
if color is None:
color = self.default_graph_colors_cycle.next()
if x_min is None:
x_min = self.x_min
if x_max is None:
x_max = self.x_max
def parameterized_function(alpha):
x = interpolate(x_min, x_max, alpha)
y = func(x)
if not np.isfinite(y):
y = self.y_max
return self.coords_to_point(x, y)
graph = ParametricFunction(
parameterized_function,
color = color,
num_anchor_points = self.num_graph_anchor_points,
)
graph.underlying_function = func
return graph
def __init__(self, **kwargs):
digest_config(self, kwargs)
def func(t):
t = (6*np.pi/2)*(t-0.5)
return (t/2-np.sin(t))*RIGHT + \
(np.cos(t)+(t**2)/10)*UP
ParametricFunction.__init__(self, func, **kwargs)
def get_graph(
self, func,
color = None,
x_min = None,
x_max = None,
):
if color is None:
color = self.default_graph_colors_cycle.next()
if x_min is None:
x_min = self.x_min
if x_max is None:
x_max = self.x_max
def parameterized_function(alpha):
x = interpolate(x_min, x_max, alpha)
y = func(x)
if not np.isfinite(y):
y = self.y_max
return self.coords_to_point(x, y)
graph = ParametricFunction(
parameterized_function,
color = color,
num_anchor_points = self.num_graph_anchor_points,
)
graph.underlying_function = func
return graph
def get_graph(self, function, num_graph_points=None, **kwargs):
kwargs["fill_opacity"] = kwargs.get("fill_opacity", 0)
kwargs["num_anchor_points"] = \
num_graph_points or self.default_num_graph_points
graph = ParametricFunction(
lambda t: self.coords_to_point(t, function(t)),
t_min=self.x_min,
t_max=self.x_max,
**kwargs)
graph.underlying_function = function
return graph
def construct(self):
point_a, point_b = 3 * LEFT, 3 * RIGHT
dots = []
for point, char in [(point_a, "A"), (point_b, "B")]:
dot = Dot(point)
letter = TexMobject(char)
letter.next_to(dot, UP + LEFT)
dot.add(letter)
dots.append(dot)
path = ParametricFunction(lambda t:
(t / 2 + np.cos(t)) * RIGHT + np.sin(t) * UP,
start=-2 * np.pi,
end=2 * np.pi)
path.scale(6 / (2 * np.pi))
path.shift(point_a - path.points[0])
path.highlight(RED)
line = Line(point_a, point_b)
words = TextMobject("Shortest path from $A$ to $B$")
words.to_edge(UP)
self.play(ShimmerIn(words), *map(GrowFromCenter, dots))
self.play(ShowCreation(path))
self.play(Transform(path, line, path_func=path_along_arc(np.pi)))
self.wait()
def construct(self):
point_a, point_b = 3*LEFT, 3*RIGHT
dots = []
for point, char in [(point_a, "A"), (point_b, "B")]:
dot = Dot(point)
letter = TexMobject(char)
letter.next_to(dot, UP+LEFT)
dot.add(letter)
dots.append(dot)
path = ParametricFunction(
lambda t : (t/2 + np.cos(t))*RIGHT + np.sin(t)*UP,
start = -2*np.pi,
end = 2*np.pi
)
path.scale(6/(2*np.pi))
path.shift(point_a - path.points[0])
path.highlight(RED)
line = Line(point_a, point_b)
words = TextMobject("Shortest path from $A$ to $B$")
words.to_edge(UP)
self.play(
ShimmerIn(words),
*map(GrowFromCenter, dots)
)
self.play(ShowCreation(path))
self.play(Transform(
path, line,
path_func = path_along_arc(np.pi)
))
self.dither()
def construct(self):
t_axis = NumberLine()
theta_axis = NumberLine().rotate(np.pi/2)
theta_mob = TexMobject("\\theta(t)")
t_mob = TexMobject("t")
theta_mob.next_to(theta_axis, RIGHT)
theta_mob.to_edge(UP)
t_mob.next_to(t_axis, UP)
t_mob.to_edge(RIGHT)
graph = ParametricFunction(
lambda t : 4*t*RIGHT + 2*smooth(t)*UP
)
line = Line(graph.points[0], graph.points[-1], color = WHITE)
q_mark = TextMobject("?")
q_mark.next_to(Point(graph.get_center()), LEFT)
stars = Stars(color = BLACK)
stars.scale(0.1).shift(q_mark.get_center())
squiggle = ParametricFunction(
lambda t : t*RIGHT + 0.2*t*(5-t)*(np.sin(t)**2)*UP,
start = 0,
end = 5
)
self.play(
ShowCreation(t_axis),
ShowCreation(theta_axis),
ShimmerIn(theta_mob),
ShimmerIn(t_mob)
)
self.play(
ShimmerIn(q_mark),
ShowCreation(graph)
)
self.dither()
self.play(
Transform(q_mark, stars),
Transform(graph, line)
)
self.dither()
self.play(Transform(graph, squiggle))
self.dither()
def graph_function(
self,
func,
color=BLUE,
animate=True,
is_main_graph=True,
):
def parameterized_graph(alpha):
x = interpolate(self.x_min, self.x_max, alpha)
return self.coords_to_point(x, func(x))
graph = ParametricFunction(parameterized_graph, color=color)
if is_main_graph:
self.graph = graph
self.func = func
if animate:
self.play(ShowCreation(graph))
self.add(graph)
return graph
def __init__(self, **kwargs):
digest_config(self, kwargs)
ParametricFunction.__init__(self, self.pos_func, **kwargs)
def get_path(self):
return ParametricFunction(lambda t: t * RIGHT +
(np.exp(-(t + 2)**2) - 0.2 * np.exp(t - 2)),
start=-4,
end=4)
def get_path(self):
return ParametricFunction(lambda t: t * RIGHT +
(-0.2 * t - np.sin(2 * np.pi * t / 6)) * UP,
start=-7,
end=10)
def __init__(self, **kwargs):
digest_config(self, kwargs)
ParametricFunction.__init__(self, self.pos_func, **kwargs)
