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All animations for divergence article

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This commit is contained in:
Grant Sanderson 2016-01-09 20:07:44 -08:00
parent 454502b403
commit f29b2aa383
1 changed files with 87 additions and 11 deletions
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98
divergence.py
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@ -18,6 +18,8 @@ class DivergenceFlow(Scene):
"dot_color" : RED, "dot_color" : RED,
"text_color" : WHITE, "text_color" : WHITE,
"arrow_color" : GREEN, "arrow_color" : GREEN,
"points_height" : SPACE_HEIGHT,
"points_width" : SPACE_WIDTH,
} }
def use_function(self, function): def use_function(self, function):
# def normalized_func(point): # def normalized_func(point):
@ -32,7 +34,7 @@ class DivergenceFlow(Scene):
def get_points(self, spacing): def get_points(self, spacing):
x_radius, y_radius = [ x_radius, y_radius = [
val-val%spacing val-val%spacing
for val in SPACE_WIDTH, SPACE_HEIGHT for val in self.points_width, self.points_height
] ]
return map(np.array, it.product( return map(np.array, it.product(
np.arange(-x_radius, x_radius+spacing, spacing), np.arange(-x_radius, x_radius+spacing, spacing),
@ -75,18 +77,18 @@ class DivergenceFlow(Scene):
self.dither() self.dither()
def flow(self): def flow(self, **kwargs):
if not hasattr(self, "function"): if not hasattr(self, "function"):
raise Exception("Must run use_function first") raise Exception("Must run use_function first")
points = self.get_points(self.dot_spacing)
end_dots = Mobject(*[
Dot(point+self.function(point))
for point in points
])
end_dots.highlight(self.dot_color)
self.play(Transform(self.dots, end_dots)) self.play(*[
self.dither() ApplyMethod(
dot.shift,
self.function(dot.get_center()),
**kwargs
)
for dot in self.dots.split()
])
def label(self, text, time = 5): def label(self, text, time = 5):
mob = TextMobject(text) mob = TextMobject(text)
@ -178,7 +180,7 @@ class OutwardFlow(DivergenceFlow):
class ArticleExample(DivergenceFlow): class ArticleExample(DivergenceFlow):
def construct(self): def construct(self):
def raw_function((x, y, z)): def raw_function((x, y, z)):
return (2*x-y, x*x, 0) return (2*x-y, y*y, 0)
def normalized_function(p): def normalized_function(p):
result = raw_function(p) result = raw_function(p)
return result/(np.linalg.norm(result)+0.01) return result/(np.linalg.norm(result)+0.01)
@ -192,3 +194,77 @@ class ArticleExample(DivergenceFlow):
self.dither() self.dither()
class IncompressibleFluid(DivergenceFlow):
def construct(self):
self.use_function(
lambda (x, y, z) : (1, np.sin(x), 0)
)
self.add_plane()
self.add_arrows()
self.add_dots()
self.flow()
self.remove(self.arrows)
self.dither()
class ConstantInwardFlow(DivergenceFlow):
def construct(self):
self.use_function(
lambda p : -p/(2*np.linalg.norm(0.5*p)**0.5+0.01)
)
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)
class ConstantOutwardFlow(DivergenceFlow):
def construct(self):
self.use_function(
lambda p : p/(2*np.linalg.norm(0.5*p)**0.5+0.01)
)
self.add_plane()
self.add_arrows()
self.add_dots()
for x in range(4):
self.flow(rate_func = None)
dot = self.dots.split()[0].copy()
dot.center()
new_dots = [
dot.copy().shift(0.5*vect)
for vect in [
UP, DOWN, LEFT, RIGHT,
UP+RIGHT, UP+LEFT, DOWN+RIGHT, DOWN+LEFT
]
]
self.dots.add(*new_dots)