1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
|
from manimlib.imports import *
import numpy as np
def divergence(coordinate):
x,y = coordinate[:2]
return np.array([
np.sin(x),
np.cos(y),
0
])
def curl(coordinate):
x,y = coordinate[:2]
return np.array([
np.sin(y),
np.cos(x),
0
])
class fluid_flow(Scene):
def construct(self):
ball_a = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-6,-1,0])).fade(0.2).scale(1.2)
ball_b = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([0.1,3,0])).fade(0.2).scale(1.2)
ball_c = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-0.5,-1, 0])).fade(0.2).scale(1.2)
ball_d = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([4.5,-1.2,0])).fade(0.2).scale(1.2)
ball2 = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-0.5,0,0])).fade(0.2).scale(1.2)
ball3 = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-1.5,1.2,0])).fade(0.2).scale(1.2)
ball4 = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-1.5,-1.2,0])).fade(0.2).scale(1.2)
ball5 = Sphere(radius = 0.2, chekerboard_colors =["#F87666", "#F53A23", PURPLE_E]).set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).fade(0.2).move_to(np.array([-4.7,0,0]))
flow_one = StreamLines(
divergence,
virtual_time=3,
min_magnitude=0,
max_magnitude=1,
).set_color_by_gradient(["#003853", "#0478A1","#04AED9", WHITE])
flow_div =(AnimatedStreamLines(
flow_one,
line_anim_class=ShowPassingFlashWithThinningStrokeWidth
))
flow_two = StreamLines(
curl,
virtual_time=3,
min_magnitude=0,
max_magnitude=1,
).set_color_by_gradient(["#003853", "#0478A1","#04AED9", WHITE])
flow_curl =(AnimatedStreamLines(
flow_two,
line_anim_class=ShowPassingFlashWithThinningStrokeWidth
))
label_div = TexMobject(r"\textit{Fluid flows out from }", r"\textit{sources }", r"\textit{and into }", r"\textit{sinks}" ).move_to(np.array([0,3.5, 0])).set_stroke(width = 1.5).scale(0.7)
label_div[1].set_color("#F87666")
label_div[3].set_color("#F87666")
title_div = TexMobject(r"Divergence").set_stroke(width = 1.5).move_to(3*DOWN).set_color("#F87666").scale(1.2)
label_curl = TexMobject(r"\textit{Fluid also rotates }", r"\textit{clockwise }", r"\textit{and }", r"\textit{counter-clockwise}" ).move_to(np.array([0,3.5, 0])).set_stroke(width = 1.5).scale(0.7)
label_curl[1].set_color("#F87666")
label_curl[3].set_color("#F87666")
title_curl = TexMobject(r"Curl").set_stroke(width = 1.5).move_to(3*DOWN).set_color("#F87666").scale(1.2)
self.add(flow_div, label_div)
self.play(Write(title_div))
self.wait(5)
self.remove(flow_div)
self.wait()
self.add(flow_curl)
self.play(ReplacementTransform(label_div, label_curl), ReplacementTransform(title_div, title_curl))
self.wait(6)
|
