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A few curl animations

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This commit is contained in:
Grant Sanderson 2016-01-12 11:51:54 -08:00
parent d5b4639659
commit 3346ea4815
1 changed files with 90 additions and 37 deletions
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127
fluid_flow.py
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@ -5,7 +5,8 @@ from region import region_from_polygon_vertices
from topics.geometry import Arrow, Dot, Circle
from topics.number_line import NumberPlane
from scene import Scene
from animation.simple_animations import ShowCreation, Rotating
from animation.simple_animations import \
ShowCreation, Rotating, PhaseFlow, ApplyToCenters
from animation.transform import Transform, ApplyMethod, FadeOut
from helpers import *
@ -82,19 +83,18 @@ class FluidFlow(Scene):
self.play(ShowCreation(self.arrows))
self.dither()
def add_paddle(self):
pass
def flow(self, **kwargs):
if not hasattr(self, "function"):
raise Exception("Must run use_function first")
self.play(*[
ApplyMethod(
dot.shift,
self.function(dot.get_center()),
**kwargs
)
for dot in self.dots.split()
])
self.play(ApplyToCenters(
PhaseFlow,
self.dots.split(),
function = self.function,
**kwargs
))
def label(self, text, time = 5):
mob = TextMobject(text)
@ -183,7 +183,7 @@ class OutwardFlow(FluidFlow):
""")
self.dither(3)
class ArticleExample(FluidFlow):
class DivergenceArticleExample(FluidFlow):
def construct(self):
def raw_function((x, y, z)):
return (2*x-y, y*y, 0)
@ -202,48 +202,42 @@ class ArticleExample(FluidFlow):
class IncompressibleFluid(FluidFlow):
DEFAULT_CONFIG = {
"points_width" : 2*SPACE_WIDTH,
"points_height" : 1.4*SPACE_HEIGHT
}
def construct(self):
self.use_function(
lambda (x, y, z) : (1, np.sin(x), 0)
lambda (x, y, z) : RIGHT+np.sin(x)*UP
)
self.add_plane()
self.add_arrows()
self.add_dots()
self.flow()
self.remove(self.arrows)
self.dither(3)
for x in range(8):
self.flow(
run_time = 1,
rate_func = None,
)
class ConstantInwardFlow(FluidFlow):
DEFAULT_CONFIG = {
"points_height" : 3*SPACE_HEIGHT,
"points_width" : 3*SPACE_WIDTH,
}
def construct(self):
self.use_function(
lambda p : -p/(2*np.linalg.norm(0.5*p)**0.5+0.01)
lambda p : -3*p/(np.linalg.norm(p)+0.1)
)
self.add_plane()
self.add_arrows()
self.add_dots()
for x in range(4):
dots = self.dots.split()
dot = dots[0].copy().center()
for x in np.arange(7.5, 9.5, 0.5):
for y in np.arange(-4, 4.5, 0.5):
dots.append(dot.copy().shift(
x*RIGHT + y*UP
))
dots.append(dot.copy().shift(
x*LEFT + y*UP
))
for x in np.arange(-9.5, 10, 0.5):
for y in np.arange(4.5, 6.5, 0.5):
dots.append(dot.copy().shift(
x*RIGHT + y*UP
))
dots.append(dot.copy().shift(
x*RIGHT + y*DOWN
))
self.dots = Mobject(*dots)
self.flow(rate_func = None)
self.flow(
run_time = 5,
rate_func = None,
)
@ -271,6 +265,9 @@ class ConstantOutwardFlow(FluidFlow):
class ConstantPositiveCurl(FluidFlow):
DEFAULT_CONFIG = {
"points_height" : SPACE_WIDTH,
}
def construct(self):
self.use_function(
lambda p : 0.5*(-p[1]*RIGHT+p[0]*UP)
@ -278,7 +275,63 @@ class ConstantPositiveCurl(FluidFlow):
self.add_plane()
self.add_arrows(true_length = True)
self.add_dots()
self.play(Rotating(self.dots, run_time = 10))
for x in range(10):
self.flow(
rate_func = None
)
class ComplexCurlExample(FluidFlow):
def construct(self):
self.use_function(
lambda (x, y, z) : np.cos(x+y)*RIGHT+np.sin(x*y)*UP
)
self.add_plane()
self.add_arrows(true_length = True)
self.add_dots()
for x in range(4):
self.flow(
run_time = 5,
rate_func = None,
)
class FourSwirls(FluidFlow):
DEFAULT_CONFIG = {
"points_height" :SPACE_WIDTH,
"points_width" : SPACE_WIDTH,
}
def construct(self):
circles = [
Circle().shift(3*vect)
for vect in compass_directions()
]
self.use_function(
lambda (x, y, z) : 0.5*(y**3-9*y)*RIGHT+(x**3-9*x)*UP
)
self.add_plane()
self.add_arrows()
Mobject(*circles).show()
for circle in circles:
self.play(ShowCreation(circle))
self.add_dots()
for x in range(4):
self.flow(
run_time = 5,
rate_func = None,
)