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
77
78
79
80
81
82
83
84
85
86
87
88
|
from manimlib.imports import*
import math as m
#---- tangent to the trace with x constant
class firstScene(ThreeDScene):
def construct(self):
axes = ThreeDAxes().scale(1)
label_x= TextMobject("$x$").shift([5.8,-0.5,0])
label_y= TextMobject("$y$").shift([-0.5,-5.6,0]).rotate(-4.5)
#---- graph of f(x,y) = -x^2-y^2
surface = ParametricSurface(
lambda u, v: np.array([
u,
v,
-u**2-v**2
]),u_min=-1,u_max=1, v_min=-1,v_max=1,checkerboard_colors=[PURPLE_C,PURPLE_D,PURPLE_E,PURPLE_B]).scale(1.5).shift([0,0,2]).rotate(0.2)
#---- curve(trace) along y axis
curve = ParametricSurface(
lambda u, v: np.array([
u*0.4,
v,
-v**2
]),v_min =-1 , v_max =1 , u_min = -0.1, u_max = 0.1).scale(1.6).shift([0.02,0.1,2.3]).set_color("#800000").rotate(0.1)
d = Dot(color =YELLOW).shift([-0.05,-0.2,2.3]) #---- critical point
x_text = TextMobject("Tangent to the trace with $x$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL)
tangent_line = Line([-0.05,-1.5,2.3],[-0.05,1.5,2.3],color = '#228B22')
self.add(axes)
self.set_camera_orientation(phi = 40 * DEGREES, theta = 55 * DEGREES)
self.begin_ambient_camera_rotation(rate = 0.1)
self.add(label_x)
self.add(label_y)
self.play(Write(surface))
self.add_fixed_in_frame_mobjects(x_text)
self.add(curve)
self.wait(1)
self.play(Write(tangent_line),Write(d))
self.wait(1)
#---- tangent to the trace with y constant
class secondScene(ThreeDScene):
def construct(self):
axes = ThreeDAxes().scale(1)
label_x= TextMobject("$x$").shift([5.8,-0.5,0])
label_y= TextMobject("$y$").shift([-0.5,-5.6,0]).rotate(-4.5)
#---- graph of f(x,y) = -x^2-y^2
surface = ParametricSurface(
lambda u, v: np.array([
u,
v,
-u**2-v**2
]),u_min = -1, u_max = 1, v_min = -1, v_max = 1, checkerboard_colors = [PURPLE_B,PURPLE_C,PURPLE_D,PURPLE_E]).scale(1.5).shift([0,0,2]).rotate(0.2)
#---- curve(trace) along x axis
curve = ParametricSurface(
lambda u, v: np.array([
u,
v*0.4,
-u**2
]),v_min = -0.1, v_max = 0.1, u_min = -1, u_max = 1).scale(1.6).shift([0.07,0.1,2.3]).set_color("#800000")
d = Dot(color = YELLOW).shift([0,-0.2,2.3]) #---- critical point
tangent_line = Line(color = '#228B22').scale(1).shift([0,-0.2,2.3]).rotate(m.radians(190),LEFT)
y_text = TextMobject("Tangent to the trace with $y$ constant at critical point").shift(3*RIGHT+2*UP).scale(0.5).to_corner(UL)
self.add(axes)
self.set_camera_orientation(phi = 40 * DEGREES, theta = 55 * DEGREES)
self.add(label_x)
self.add(label_y)
self.begin_ambient_camera_rotation(rate = 0.1)
self.play(Write(surface))
self.add_fixed_in_frame_mobjects(y_text)
self.add(curve)
self.wait(1.5)
self.play(Write(tangent_line),Write(d))
self.wait(0.5)
|
