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Making divergence material more general for curl animations

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This commit is contained in:
Grant Sanderson 2016-01-11 15:54:52 -08:00
parent 78e855c495
commit 64ac1426b3
1 changed files with 34 additions and 20 deletions
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54
divergence.py → fluid_flow.py
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@ -5,19 +5,19 @@ 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
from animation.simple_animations import ShowCreation, Rotating
from animation.transform import Transform, ApplyMethod, FadeOut
from helpers import *
class DivergenceFlow(Scene):
class FluidFlow(Scene):
DEFAULT_CONFIG = {
"arrow_spacing" : 1,
"dot_spacing" : 0.5,
"dot_color" : RED,
"dot_color" : BLUE_B,
"text_color" : WHITE,
"arrow_color" : GREEN,
"arrow_color" : GREEN_A,
"points_height" : SPACE_HEIGHT,
"points_width" : SPACE_WIDTH,
}
@ -53,7 +53,7 @@ class DivergenceFlow(Scene):
self.play(ShowCreation(self.dots))
self.dither()
def add_arrows(self):
def add_arrows(self, true_length = False):
if not hasattr(self, "function"):
raise Exception("Must run use_function first")
points = self.get_points(self.arrow_spacing)
@ -68,10 +68,16 @@ class DivergenceFlow(Scene):
tip_length = 0.1,
buff = 0
)
self.arrows = Mobject(*[
prototype.copy().rotate(angle).shift(point)
for point, angle in zip(points, angles)
])
arrows = []
for point in points:
arrow = prototype.copy()
output = self.function(point)
if true_length:
arrow.scale(np.linalg.norm(output))
arrow.rotate(angle_of_vector(output))
arrow.shift(point)
arrows.append(arrow)
self.arrows = Mobject(*arrows)
self.play(ShowCreation(self.arrows))
self.dither()
@ -112,7 +118,7 @@ class DivergenceFlow(Scene):
class InwardFlow(DivergenceFlow):
class InwardFlow(FluidFlow):
def construct(self):
circle = Circle(color = YELLOW_C)
self.use_function(
@ -144,10 +150,10 @@ class InwardFlow(DivergenceFlow):
is negative at the origin:
$\\nabla \\cdot \\vec{\\textbf{v}}(0, 0) < 0$
""")
self.dither()
self.dither(3)
class OutwardFlow(DivergenceFlow):
class OutwardFlow(FluidFlow):
def construct(self):
circle = Circle(color = YELLOW_C, radius = 2)
self.use_function(
@ -175,9 +181,9 @@ class OutwardFlow(DivergenceFlow):
is positive at the origin:
$\\nabla \\cdot \\vec{\\textbf{v}}(0, 0) > 0$
""")
self.dither()
self.dither(3)
class ArticleExample(DivergenceFlow):
class ArticleExample(FluidFlow):
def construct(self):
def raw_function((x, y, z)):
return (2*x-y, y*y, 0)
@ -191,11 +197,11 @@ class ArticleExample(DivergenceFlow):
self.add_dots()
self.flow()
self.remove(self.arrows)
self.dither()
self.dither(3)
class IncompressibleFluid(DivergenceFlow):
class IncompressibleFluid(FluidFlow):
def construct(self):
self.use_function(
lambda (x, y, z) : (1, np.sin(x), 0)
@ -205,11 +211,11 @@ class IncompressibleFluid(DivergenceFlow):
self.add_dots()
self.flow()
self.remove(self.arrows)
self.dither()
self.dither(3)
class ConstantInwardFlow(DivergenceFlow):
class ConstantInwardFlow(FluidFlow):
def construct(self):
self.use_function(
lambda p : -p/(2*np.linalg.norm(0.5*p)**0.5+0.01)
@ -242,7 +248,7 @@ class ConstantInwardFlow(DivergenceFlow):
class ConstantOutwardFlow(DivergenceFlow):
class ConstantOutwardFlow(FluidFlow):
def construct(self):
self.use_function(
lambda p : p/(2*np.linalg.norm(0.5*p)**0.5+0.01)
@ -264,7 +270,15 @@ class ConstantOutwardFlow(DivergenceFlow):
self.dots.add(*new_dots)
class ConstantPositiveCurl(FluidFlow):
def construct(self):
self.use_function(
lambda p : 0.5*(-p[1]*RIGHT+p[0]*UP)
)
self.add_plane()
self.add_arrows(true_length = True)
self.add_dots()
self.play(Rotating(self.dots, run_time = 10))