def generate_points(self):
self.cell_height = self.height / self.nrows
self.cell_width = self.width / self.nrows
self.bottom_left = (self.cell_width * self.nrows / 2.0)*LEFT + \
(self.cell_height * self.nrows / 2.0)*DOWN
num_to_num_mob = {}
self.coords_to_mobs = {}
self.coords = [
(n, k)
for n in range(self.nrows)
for k in range(n+1)
]
for n, k in self.coords:
num = choose(n, k)
center = self.coords_to_center(n, k)
num_mob = TexMobject(str(num))
scale_factor = min(
1,
self.portion_to_fill * self.cell_height / num_mob.get_height(),
self.portion_to_fill * self.cell_width / num_mob.get_width(),
)
num_mob.center().scale(scale_factor).shift(center)
if n not in self.coords_to_mobs:
self.coords_to_mobs[n] = {}
self.coords_to_mobs[n][k] = num_mob
self.add(*[
self.coords_to_mobs[n][k]
for n, k in self.coords
])
return self
def construct(self):
CycloidScene.construct(self)
equations = TexMobject(
["x(t) = Rt - R\\sin(t)", "y(t) = -R + R\\cos(t)"])
top, bottom = equations.split()
bottom.next_to(top, DOWN)
equations.center()
equations.to_edge(UP, buff=1.3)
self.play(ShimmerIn(equations))
self.grow_parts()
self.draw_cycloid(rate_func=None, run_time=5)
self.dither()
def generate_n_choose_k_mobs(self):
self.coords_to_n_choose_k = {}
for n, k in self.coords:
nck_mob = TexMobject(r"{%d \choose %d}" % (n, k))
scale_factor = min(
1,
self.portion_to_fill * self.cell_height / nck_mob.get_height(),
self.portion_to_fill * self.cell_width / nck_mob.get_width(),
)
center = self.coords_to_mobs[n][k].get_center()
nck_mob.center().scale(scale_factor).shift(center)
if n not in self.coords_to_n_choose_k:
self.coords_to_n_choose_k[n] = {}
self.coords_to_n_choose_k[n][k] = nck_mob
return self
def construct(self):
CycloidScene.construct(self)
equations = TexMobject([
"x(t) = Rt - R\\sin(t)",
"y(t) = -R + R\\cos(t)"
])
top, bottom = equations.split()
bottom.next_to(top, DOWN)
equations.center()
equations.to_edge(UP, buff = 1.3)
self.play(ShimmerIn(equations))
self.grow_parts()
self.draw_cycloid(rate_func = None, run_time = 5)
self.dither()
def generate_n_choose_k_mobs(self):
self.coords_to_n_choose_k = {}
for n, k in self.coords:
nck_mob = TexMobject(r"{%d \choose %d}"%(n, k))
scale_factor = min(
1,
self.portion_to_fill * self.cell_height / nck_mob.get_height(),
self.portion_to_fill * self.cell_width / nck_mob.get_width(),
)
center = self.coords_to_mobs[n][k].get_center()
nck_mob.center().scale(scale_factor).shift(center)
if n not in self.coords_to_n_choose_k:
self.coords_to_n_choose_k[n] = {}
self.coords_to_n_choose_k[n][k] = nck_mob
return self
def count_mobjects(self,
mobjects,
mode="highlight",
color="red",
display_numbers=True,
num_offset=DEFAULT_COUNT_NUM_OFFSET,
run_time=DEFAULT_COUNT_RUN_TIME):
"""
Note, leaves final number mobject as "number" attribute
mode can be "highlight", "show_creation" or "show", otherwise
a warning is given and nothing is animating during the count
"""
if len(mobjects) > 50: #TODO
raise Exception("I don't know if you should be counting \
too many mobjects...")
if len(mobjects) == 0:
raise Exception("Counting mobject list of length 0")
if mode not in ["highlight", "show_creation", "show"]:
raise Warning("Unknown mode")
frame_time = run_time / len(mobjects)
if mode == "highlight":
self.add(*mobjects)
for mob, num in zip(mobjects, it.count(1)):
if display_numbers:
num_mob = TexMobject(str(num))
num_mob.center().shift(num_offset)
self.add(num_mob)
if mode == "highlight":
original_color = mob.color
mob.highlight(color)
self.dither(frame_time)
mob.highlight(original_color)
if mode == "show_creation":
self.play(ShowCreation(mob, run_time=frame_time))
if mode == "show":
self.add(mob)
self.dither(frame_time)
if display_numbers:
self.remove(num_mob)
if display_numbers:
self.add(num_mob)
self.number = num_mob
return self
def get_marks(self, point1, point2):
vert_line = Line(2 * DOWN, 2 * UP)
tangent_line = vert_line.copy()
theta = TexMobject("\\theta")
theta.scale(0.5)
angle = angle_of_vector(point1 - point2)
tangent_line.rotate(angle - tangent_line.get_angle())
angle_from_vert = angle - np.pi / 2
for mob in vert_line, tangent_line:
mob.shift(point1 - mob.get_center())
arc = Arc(angle_from_vert, start_angle=np.pi / 2)
arc.scale(self.arc_radius)
arc.shift(point1)
vect_angle = angle_from_vert / 2 + np.pi / 2
vect = rotate_vector(RIGHT, vect_angle)
theta.center()
theta.shift(point1)
theta.shift(1.5 * self.arc_radius * vect)
return arc, theta, vert_line, tangent_line
def count_mobjects(
self, mobjects, mode = "highlight",
color = "red",
display_numbers = True,
num_offset = DEFAULT_COUNT_NUM_OFFSET,
run_time = DEFAULT_COUNT_RUN_TIME):
"""
Note, leaves final number mobject as "number" attribute
mode can be "highlight", "show_creation" or "show", otherwise
a warning is given and nothing is animating during the count
"""
if len(mobjects) > 50: #TODO
raise Exception("I don't know if you should be counting \
too many mobjects...")
if len(mobjects) == 0:
raise Exception("Counting mobject list of length 0")
if mode not in ["highlight", "show_creation", "show"]:
raise Warning("Unknown mode")
frame_time = run_time / len(mobjects)
if mode == "highlight":
self.add(*mobjects)
for mob, num in zip(mobjects, it.count(1)):
if display_numbers:
num_mob = TexMobject(str(num))
num_mob.center().shift(num_offset)
self.add(num_mob)
if mode == "highlight":
original_color = mob.color
mob.highlight(color)
self.dither(frame_time)
mob.highlight(original_color)
if mode == "show_creation":
self.play(ShowCreation(mob, run_time = frame_time))
if mode == "show":
self.add(mob)
self.dither(frame_time)
if display_numbers:
self.remove(num_mob)
if display_numbers:
self.add(num_mob)
self.number = num_mob
return self
class FlipThroughSymbols(Animation):
CONFIG = {
"start_center" : ORIGIN,
"end_center" : ORIGIN,
}
def __init__(self, tex_list, **kwargs):
mobject = TexMobject(self.curr_tex).shift(start_center)
Animation.__init__(self, mobject, **kwargs)
def update_mobject(self, alpha):
new_tex = self.tex_list[np.ceil(alpha*len(self.tex_list))-1]
if new_tex != self.curr_tex:
self.curr_tex = new_tex
self.mobject = TexMobject(new_tex).shift(self.start_center)
if not all(self.start_center == self.end_center):
self.mobject.center().shift(
(1-alpha)*self.start_center + alpha*self.end_center
)
def count_regions(self, regions,
mode = "one_at_a_time",
num_offset = DEFAULT_COUNT_NUM_OFFSET,
run_time = DEFAULT_COUNT_RUN_TIME,
**unused_kwargsn):
if mode not in ["one_at_a_time", "show_all"]:
raise Warning("Unknown mode")
frame_time = run_time / (len(regions))
for region, count in zip(regions, it.count(1)):
num_mob = TexMobject(str(count))
num_mob.center().shift(num_offset)
self.add(num_mob)
self.highlight_region(region)
self.dither(frame_time)
if mode == "one_at_a_time":
self.reset_background()
self.remove(num_mob)
self.add(num_mob)
self.number = num_mob
return self
def ask_continuous_question(self):
continuous = self.get_continuous_background()
line = Line(
UP, DOWN,
density = self.zoom_factor*DEFAULT_POINT_DENSITY_1D
)
theta = TexMobject("\\theta")
theta.scale(0.5/self.zoom_factor)
self.play(
ShowCreation(continuous),
Animation(self.equation)
)
self.remove(*self.layers)
self.play(ShowCreation(self.cycloid))
self.activate_zooming()
little_square = self.get_zoomed_camera_mobject()
self.add(line)
indices = np.arange(
0, self.cycloid.get_num_points()-1, 10
)
for index in indices:
point = self.cycloid.points[index]
next_point = self.cycloid.points[index+1]
angle = angle_of_vector(point - next_point)
for mob in little_square, line:
mob.shift(point - mob.get_center())
arc = Arc(angle-np.pi/2, start_angle = np.pi/2)
arc.scale(0.1)
arc.shift(point)
self.add(arc)
if angle > np.pi/2 + np.pi/6:
vect_angle = interpolate(np.pi/2, angle, 0.5)
vect = rotate_vector(RIGHT, vect_angle)
theta.center()
theta.shift(point)
theta.shift(0.15*vect)
self.add(theta)
self.wait(self.frame_duration)
self.remove(arc)
def ask_continuous_question(self):
continuous = self.get_continuous_background()
line = Line(
UP, DOWN,
density = self.zoom_factor*DEFAULT_POINT_DENSITY_1D
)
theta = TexMobject("\\theta")
theta.scale(0.5/self.zoom_factor)
self.play(
ShowCreation(continuous),
Animation(self.equation)
)
self.remove(*self.layers)
self.play(ShowCreation(self.cycloid))
self.activate_zooming()
little_square = self.get_zoomed_camera_mobject()
self.add(line)
indices = np.arange(
0, self.cycloid.get_num_points()-1, 10
)
for index in indices:
point = self.cycloid.points[index]
next_point = self.cycloid.points[index+1]
angle = angle_of_vector(point - next_point)
for mob in little_square, line:
mob.shift(point - mob.get_center())
arc = Arc(angle-np.pi/2, start_angle = np.pi/2)
arc.scale(0.1)
arc.shift(point)
self.add(arc)
if angle > np.pi/2 + np.pi/6:
vect_angle = interpolate(np.pi/2, angle, 0.5)
vect = rotate_vector(RIGHT, vect_angle)
theta.center()
theta.shift(point)
theta.shift(0.15*vect)
self.add(theta)
self.dither(self.frame_duration)
self.remove(arc)
def get_marks(self, point1, point2):
vert_line = Line(2*DOWN, 2*UP)
tangent_line = vert_line.copy()
theta = TexMobject("\\theta")
theta.scale(0.5)
angle = angle_of_vector(point1 - point2)
tangent_line.rotate(
angle - tangent_line.get_angle()
)
angle_from_vert = angle - np.pi/2
for mob in vert_line, tangent_line:
mob.shift(point1 - mob.get_center())
arc = Arc(angle_from_vert, start_angle = np.pi/2)
arc.scale(self.arc_radius)
arc.shift(point1)
vect_angle = angle_from_vert/2 + np.pi/2
vect = rotate_vector(RIGHT, vect_angle)
theta.center()
theta.shift(point1)
theta.shift(1.5*self.arc_radius*vect)
return arc, theta, vert_line, tangent_line
