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
|
from manimlib.imports import *
import numpy as np
def function(coordinate):
x,y = coordinate[:2]
return np.array([
x,
y,
0,
])
def x_dir(coordinate):
x,y = coordinate[:2]
return np.array([
x,
0,
0
])
def y_dir(coordinate):
x,y = coordinate[:2]
return np.array([
0,
y,
0,
])
class PartialDerivatives(MovingCameraScene):
def setup(self):
MovingCameraScene.setup(self)
def construct(self):
dot = Dot().move_to(np.array([2.5,2,0]))
self.camera_frame.save_state()
self.play(
self.camera_frame.set_width,dot.get_width()*35,
self.camera_frame.move_to,dot)
dx = TexMobject(r"\frac{\partial f}{\partial x}").move_to(np.array([4,2.5, 0])).set_color(["#00635D", BLUE_E]).scale(0.5)
x_aros = VectorField(x_dir, x_min = 0.5, x_max = 3, y_min = 0.5, y_max =3).set_color(["#00635D", BLUE_E])
dy = TexMobject(r"\frac{\partial f}{\partial y}").move_to(np.array([4,1.5, 0])).set_color_by_gradient(["#BAAB68", WHITE]).scale(0.5)
y_aros = VectorField(y_dir, y_min = 0.5, y_max =3, x_min = 0.5, x_max = 3 ).set_color_by_gradient(["#BAAB68", WHITE])
partials = VGroup(x_aros, y_aros, dx, dy)
dxdy = VectorField(function, y_min = 0.5, y_max =3, x_min = 0.5, x_max = 3 ).set_color_by_gradient(["#BAAB68", "#00635D"])
field = VectorField(function, y_min = -3, y_max =3, x_min = -3, x_max = 3 ).set_color_by_gradient(["#BAAB68", "#00635D"])
vector = TexMobject(r"\nabla f =").set_color_by_gradient(["#BAAB68", "#00635D"]).move_to(np.array([4,2, 0])).scale(0.5)
threed = TexMobject(r"\textit{With respect to the function, the gradient is computed by...}").scale(0.3).move_to(dot.get_center())
self.play(Write(x_aros), Write(dx))
self.wait()
self.play(Write(y_aros), Write(dy))
self.wait()
self.play(Write(dxdy), Write(vector), ApplyMethod(dx.next_to,vector, RIGHT+0.3*UP), ApplyMethod(dy.next_to, vector, RIGHT+0.3*DOWN))
self.wait()
self.play(FadeOut(x_aros), FadeOut(dx), FadeOut(vector), FadeOut(dxdy), FadeOut(y_aros), FadeOut(dy), ShowCreation(threed))
self.wait(2)
self.play(Uncreate(threed))
|
