def snells_law_at_every_point(self, cycloid, chopped_cycloid):
square = Square(side_length = 0.2, color = WHITE)
words = TextMobject(["Snell's law ", "everywhere"])
snells, rest = words.split()
colon = TextMobject(":")
words.next_to(square)
words.shift(0.3*UP)
combo = Mobject(square, words)
combo.get_center = lambda : square.get_center()
new_snells = snells.copy().center().to_edge(UP, buff = 1.5)
colon.next_to(new_snells)
colon.shift(0.05*DOWN)
self.play(MoveAlongPath(
combo, cycloid,
run_time = 5
))
self.play(MoveAlongPath(
combo, chopped_cycloid,
run_time = 4
))
dot = Dot(combo.get_center())
self.play(Transform(square, dot))
self.play(
Transform(snells, new_snells),
Transform(rest, colon)
)
self.dither()
return colon
def __init__(self, direction = LEFT, index_of_tip = -1, center = ORIGIN):
self.direction = direction
self.content = Mobject()
self.index_of_tip = index_of_tip
self.center_offset = center - Mobject.get_center(self)
if direction[0] > 0:
self.rotate(np.pi, UP)
def __init__(self, direction=LEFT, index_of_tip=-1, center=ORIGIN):
self.direction = direction
self.content = Mobject()
self.index_of_tip = index_of_tip
self.center_offset = center - Mobject.get_center(self)
if direction[0] > 0:
self.rotate(np.pi, UP)
def show_equation(self):
equation = TexMobject([
"\\left(\\dfrac{1}{\\phantom{v_air}}\\right)", "\\sin(\\theta_1)",
"=", "\\left(\\dfrac{1}{\\phantom{v_water}}\\right)",
"\\sin(\\theta_2)"
])
equation.to_corner(UP + RIGHT)
frac1, sin1, equals, frac2, sin2 = equation.split()
v_air, v_water = [
TexMobject("v_{\\text{%s}}" % s, size="\\Large")
for s in "air", "water"
]
v_air.next_to(Point(frac1.get_center()), DOWN)
v_water.next_to(Point(frac2.get_center()), DOWN)
frac1.add(v_air)
frac2.add(v_water)
f1, f2 = [TexMobject("F_%d" % d, size="\\Large") for d in 1, 2]
f1.next_to(sin1, LEFT)
f2.next_to(equals, RIGHT)
sin2_start = sin2.copy().next_to(f2, RIGHT)
bar1 = TexMobject("\\dfrac{\\qquad}{\\qquad}")
bar2 = bar1.copy()
bar1.next_to(sin1, DOWN)
bar2.next_to(sin2, DOWN)
v_air_copy = v_air.copy().next_to(bar1, DOWN)
v_water_copy = v_water.copy().next_to(bar2, DOWN)
bars = Mobject(bar1, bar2)
new_eq = equals.copy().center().shift(bars.get_center())
snells = TextMobject("Snell's Law")
snells.highlight(YELLOW)
snells.shift(new_eq.get_center()[0] * RIGHT)
snells.shift(UP)
anims = []
for mob in f1, sin1, equals, f2, sin2_start:
anims.append(ShimmerIn(mob))
self.play(*anims)
self.wait()
for f, frac in (f1, frac1), (f2, frac2):
target = frac.copy().ingest_submobjects()
also = []
if f is f2:
also.append(Transform(sin2_start, sin2))
sin2 = sin2_start
self.play(Transform(f, target), *also)
self.remove(f)
self.add(frac)
self.wait()
self.play(FadeOut(frac1), FadeOut(frac2), Transform(v_air, v_air_copy),
Transform(v_water, v_water_copy), ShowCreation(bars),
Transform(equals, new_eq))
self.wait()
frac1 = Mobject(sin1, bar1, v_air)
frac2 = Mobject(sin2, bar2, v_water)
for frac, vect in (frac1, LEFT), (frac2, RIGHT):
self.play(ApplyMethod(frac.next_to, equals, vect))
self.wait()
self.play(ShimmerIn(snells))
self.wait()
def snells_law_at_every_point(self, cycloid, chopped_cycloid):
square = Square(side_length=0.2, color=WHITE)
words = TextMobject(["Snell's law ", "everywhere"])
snells, rest = words.split()
colon = TextMobject(":")
words.next_to(square)
words.shift(0.3 * UP)
combo = Mobject(square, words)
combo.get_center = lambda: square.get_center()
new_snells = snells.copy().center().to_edge(UP, buff=1.5)
colon.next_to(new_snells)
colon.shift(0.05 * DOWN)
self.play(MoveAlongPath(combo, cycloid, run_time=5))
self.play(MoveAlongPath(combo, chopped_cycloid, run_time=4))
dot = Dot(combo.get_center())
self.play(Transform(square, dot))
self.play(Transform(snells, new_snells), Transform(rest, colon))
self.dither()
return colon
def __init__(self, **kwargs):
Mobject.__init__(self, **kwargs)
self.center_offset = self.center_point - Mobject.get_center(self)
if self.direction[0] > 0:
self.rotate(np.pi, UP)
self.content = Mobject()
class PiCreature(Mobject):
DEFAULT_CONFIG = {
"color" : BLUE_E
}
PART_NAMES = [
'arm',
'body',
'left_eye',
'right_eye',
'left_leg',
'right_leg',
'mouth',
]
WHITE_PART_NAMES = ['left_eye', 'right_eye', 'mouth']
MOUTH_NAMES = ["smile", "frown", "straight_mouth"]
def __init__(self, **kwargs):
Mobject.__init__(self, **kwargs)
for part_name in self.PART_NAMES:
mob = ImageMobject(
part_name_to_directory(part_name),
should_center = False
)
if part_name not in self.WHITE_PART_NAMES:
mob.highlight(self.color)
setattr(self, part_name, mob)
self.eyes = Mobject(self.left_eye, self.right_eye)
self.legs = Mobject(self.left_leg, self.right_leg)
mouth_center = self.get_mouth_center()
self.mouth.center()
self.smile = self.mouth
self.frown = self.mouth.copy().rotate(np.pi, RIGHT)
self.straight_mouth = TexMobject("-").scale(0.7)
for mouth in self.smile, self.frown, self.straight_mouth:
mouth.sort_points(lambda p : p[0])
mouth.highlight(self.color) ##to blend into background
mouth.shift(mouth_center)
self.digest_mobject_attrs()
self.give_smile()
self.add(self.mouth)
self.scale(PI_CREATURE_SCALE_VAL)
def get_parts(self):
return [getattr(self, pn) for pn in self.PART_NAMES]
def get_white_parts(self):
return [
getattr(self, pn)
for pn in self.WHITE_PART_NAMES+self.MOUTH_NAMES
]
def get_mouth_center(self):
result = self.body.get_center()
result[0] = self.eyes.get_center()[0]
return result
# left_center = self.left_eye.get_center()
# right_center = self.right_eye.get_center()
# l_to_r = right_center-left_center
# eyes_to_mouth = rotate_vector(l_to_r, -np.pi/2, OUT)
# eyes_to_mouth /= np.linalg.norm(eyes_to_mouth)
# return left_center/2 + right_center/2 + \
# PI_CREATURE_MOUTH_TO_EYES_DISTANCE*eyes_to_mouth
def highlight(self, color, condition = None):
for part in set(self.get_parts()).difference(self.get_white_parts()):
part.highlight(color, condition)
return self
def move_to(self, destination):
self.shift(destination-self.get_bottom())
return self
def change_mouth_to(self, mouth_name):
#TODO, This is poorly implemented
self.mouth = getattr(self, mouth_name)
self.sub_mobjects = list_update(
self.sub_mobjects,
self.get_parts()
)
self.mouth.highlight(WHITE)
return self
def give_smile(self):
return self.change_mouth_to("smile")
def give_frown(self):
return self.change_mouth_to("frown")
def give_straight_face(self):
return self.change_mouth_to("straight_mouth")
def get_eye_center(self):
return self.eyes.get_center()
def make_mean(self):
eye_x, eye_y = self.get_eye_center()[:2]
def should_delete((x, y, z)):
return y - eye_y > 0.3*abs(x - eye_x)
self.eyes.highlight("black", should_delete)
self.give_straight_face()
return self
def make_sad(self):
eye_x, eye_y = self.get_eye_center()[:2]
eye_y += 0.15
def should_delete((x, y, z)):
return y - eye_y > -0.3*abs(x - eye_x)
self.eyey.highlight("black", should_delete)
self.give_frown()
return self
def get_step_intermediate(self, pi_creature):
vect = pi_creature.get_center() - self.get_center()
result = self.copy().shift(vect / 2.0)
left_forward = vect[0] > 0
if self.right_leg.get_center()[0] < self.left_leg.get_center()[0]:
#For Mortimer's case
left_forward = not left_forward
if left_forward:
result.left_leg.wag(vect/2.0, DOWN)
result.right_leg.wag(-vect/2.0, DOWN)
else:
result.right_leg.wag(vect/2.0, DOWN)
result.left_leg.wag(-vect/2.0, DOWN)
return result
def blink(self):
bottom = self.eyes.get_bottom()
self.eyes.apply_function(
lambda (x, y, z) : (x, bottom[1], z)
)
return self
def shift_eyes(self):
for eye in self.left_eye, self.right_eye:
eye.rotate_in_place(np.pi, UP)
return self
def to_symbol(self):
Mobject.__init__(
self,
*list(set(self.get_parts()).difference(self.get_white_parts()))
)
def __init__(self, **kwargs):
Mobject.__init__(self, **kwargs)
self.center_offset = self.center_point - Mobject.get_center(self)
if self.direction[0] > 0:
self.rotate(np.pi, UP)
self.content = Mobject()
class PiCreature(Mobject):
DEFAULT_CONFIG = {"color": BLUE_E}
PART_NAMES = [
'arm',
'body',
'left_eye',
'right_eye',
'left_leg',
'right_leg',
'mouth',
]
WHITE_PART_NAMES = ['left_eye', 'right_eye', 'mouth']
MOUTH_NAMES = ["smile", "frown", "straight_mouth"]
def __init__(self, **kwargs):
Mobject.__init__(self, **kwargs)
for part_name in self.PART_NAMES:
mob = ImageMobject(part_name_to_directory(part_name),
should_center=False)
if part_name not in self.WHITE_PART_NAMES:
mob.highlight(self.color)
setattr(self, part_name, mob)
self.eyes = Mobject(self.left_eye, self.right_eye)
self.legs = Mobject(self.left_leg, self.right_leg)
mouth_center = self.get_mouth_center()
self.mouth.center()
self.smile = self.mouth
self.frown = self.mouth.copy().rotate(np.pi, RIGHT)
self.straight_mouth = TexMobject("-").scale(0.7)
for mouth in self.smile, self.frown, self.straight_mouth:
mouth.sort_points(lambda p: p[0])
mouth.highlight(self.color) ##to blend into background
mouth.shift(mouth_center)
self.digest_mobject_attrs()
self.give_smile()
self.add(self.mouth)
self.scale(PI_CREATURE_SCALE_VAL)
def get_parts(self):
return [getattr(self, pn) for pn in self.PART_NAMES]
def get_white_parts(self):
return [
getattr(self, pn)
for pn in self.WHITE_PART_NAMES + self.MOUTH_NAMES
]
def get_mouth_center(self):
result = self.body.get_center()
result[0] = self.eyes.get_center()[0]
return result
# left_center = self.left_eye.get_center()
# right_center = self.right_eye.get_center()
# l_to_r = right_center-left_center
# eyes_to_mouth = rotate_vector(l_to_r, -np.pi/2, OUT)
# eyes_to_mouth /= np.linalg.norm(eyes_to_mouth)
# return left_center/2 + right_center/2 + \
# PI_CREATURE_MOUTH_TO_EYES_DISTANCE*eyes_to_mouth
def highlight(self, color, condition=None):
for part in set(self.get_parts()).difference(self.get_white_parts()):
part.highlight(color, condition)
return self
def move_to(self, destination):
self.shift(destination - self.get_bottom())
return self
def change_mouth_to(self, mouth_name):
#TODO, This is poorly implemented
self.mouth = getattr(self, mouth_name)
self.sub_mobjects = list_update(self.sub_mobjects, self.get_parts())
self.mouth.highlight(WHITE)
return self
def give_smile(self):
return self.change_mouth_to("smile")
def give_frown(self):
return self.change_mouth_to("frown")
def give_straight_face(self):
return self.change_mouth_to("straight_mouth")
def get_eye_center(self):
return self.eyes.get_center()
def make_mean(self):
eye_x, eye_y = self.get_eye_center()[:2]
def should_delete((x, y, z)):
return y - eye_y > 0.3 * abs(x - eye_x)
self.eyes.highlight("black", should_delete)
self.give_straight_face()
return self
def make_sad(self):
eye_x, eye_y = self.get_eye_center()[:2]
eye_y += 0.15
def should_delete((x, y, z)):
return y - eye_y > -0.3 * abs(x - eye_x)
self.eyey.highlight("black", should_delete)
self.give_frown()
return self
def get_step_intermediate(self, pi_creature):
vect = pi_creature.get_center() - self.get_center()
result = self.copy().shift(vect / 2.0)
left_forward = vect[0] > 0
if self.right_leg.get_center()[0] < self.left_leg.get_center()[0]:
#For Mortimer's case
left_forward = not left_forward
if left_forward:
result.left_leg.wag(vect / 2.0, DOWN)
result.right_leg.wag(-vect / 2.0, DOWN)
else:
result.right_leg.wag(vect / 2.0, DOWN)
result.left_leg.wag(-vect / 2.0, DOWN)
return result
def blink(self):
bottom = self.eyes.get_bottom()
self.eyes.apply_function(lambda (x, y, z): (x, bottom[1], z))
return self
def shift_eyes(self):
for eye in self.left_eye, self.right_eye:
eye.rotate_in_place(np.pi, UP)
return self
def to_symbol(self):
Mobject.__init__(
self,
*list(set(self.get_parts()).difference(self.get_white_parts())))
def show_equation(self):
equation = TexMobject([
"\\left(\\dfrac{1}{\\phantom{v_air}}\\right)",
"\\sin(\\theta_1)",
"=",
"\\left(\\dfrac{1}{\\phantom{v_water}}\\right)",
"\\sin(\\theta_2)"
])
equation.to_corner(UP+RIGHT)
frac1, sin1, equals, frac2, sin2 = equation.split()
v_air, v_water = [
TexMobject("v_{\\text{%s}}"%s, size = "\\Large")
for s in "air", "water"
]
v_air.next_to(Point(frac1.get_center()), DOWN)
v_water.next_to(Point(frac2.get_center()), DOWN)
frac1.add(v_air)
frac2.add(v_water)
f1, f2 = [
TexMobject("F_%d"%d, size = "\\Large")
for d in 1, 2
]
f1.next_to(sin1, LEFT)
f2.next_to(equals, RIGHT)
sin2_start = sin2.copy().next_to(f2, RIGHT)
bar1 = TexMobject("\\dfrac{\\qquad}{\\qquad}")
bar2 = bar1.copy()
bar1.next_to(sin1, DOWN)
bar2.next_to(sin2, DOWN)
v_air_copy = v_air.copy().next_to(bar1, DOWN)
v_water_copy = v_water.copy().next_to(bar2, DOWN)
bars = Mobject(bar1, bar2)
new_eq = equals.copy().center().shift(bars.get_center())
snells = TextMobject("Snell's Law")
snells.highlight(YELLOW)
snells.shift(new_eq.get_center()[0]*RIGHT)
snells.shift(UP)
anims = []
for mob in f1, sin1, equals, f2, sin2_start:
anims.append(ShimmerIn(mob))
self.play(*anims)
self.dither()
for f, frac in (f1, frac1), (f2, frac2):
target = frac.copy().ingest_submobjects()
also = []
if f is f2:
also.append(Transform(sin2_start, sin2))
sin2 = sin2_start
self.play(Transform(f, target), *also)
self.remove(f)
self.add(frac)
self.dither()
self.play(
FadeOut(frac1),
FadeOut(frac2),
Transform(v_air, v_air_copy),
Transform(v_water, v_water_copy),
ShowCreation(bars),
Transform(equals, new_eq)
)
self.dither()
frac1 = Mobject(sin1, bar1, v_air)
frac2 = Mobject(sin2, bar2, v_water)
for frac, vect in (frac1, LEFT), (frac2, RIGHT):
self.play(ApplyMethod(
frac.next_to, equals, vect
))
self.dither()
self.play(ShimmerIn(snells))
self.dither()
