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
89
90
91
92
93
94
95
96
97
98
99
|
from manimlib.imports import *
class Helix(ThreeDScene):
def construct(self):
axes = ThreeDAxes() # creates a 3D Axis
helix1=ParametricFunction(
lambda u : np.array([
1.5*np.cos(u),
1.5*np.sin(u),
u/4
]),color=PURPLE,t_min=-TAU,t_max=TAU,
)
helix2=ParametricFunction(
lambda u : np.array([
2*np.cos(u),
2*np.sin(u),
u/2
]),color=GREEN_C,t_min=-TAU,t_max=TAU,
)
function = TexMobject("f(", "r", ",", "\\theta", ")", "=", "{ \\begin{bmatrix} r \\cos\\theta \\\ r \\sin \\theta \\\ h \\theta \\end{bmatrix}}" ).scale(0.6).to_corner(UL)
function.set_color_by_tex(r"\theta", BLUE_C)
function.set_color_by_tex(r"r", RED_C)
function.set_color_by_tex(r"\cos", GREEN_C)
function.set_color_by_tex(r"\sin", YELLOW_C)
function[0].set_color(ORANGE)
function[4].set_color(ORANGE)
slope_text = TextMobject(r"$\theta = $").move_to(3*UP+3*RIGHT)
number = DecimalNumber(0,unit=r" rad", color=RED_C).next_to(slope_text, RIGHT)
self.add_fixed_in_frame_mobjects(function,slope_text, number)
self.set_camera_orientation(phi=60*DEGREES, theta = 45*DEGREES)
self.add(axes)
axis = TextMobject(r"X",r"Y",r"Z")
axis[0].move_to(6*RIGHT)
axis[1].move_to(6*UP)
axis[2].move_to(np.array([0,0,3.7]))
self.add_fixed_orientation_mobjects(axis[2])
self.add_fixed_orientation_mobjects(axis[0])
self.add_fixed_orientation_mobjects(axis[1])
dot1 = Dot().rotate(PI/2).set_color(RED_C)
alpha1 = ValueTracker(0)
vector1 = self.get_vector(alpha1.get_value(),helix1)
dot1.add_updater(lambda m: m.move_to(vector1.get_end()))
number.add_updater(lambda m: m.set_value(alpha1.get_value()*4*np.pi))
number.add_updater(lambda m: self.add_fixed_in_frame_mobjects(m))
self.play(
ShowCreation(helix1),
GrowFromCenter(dot1),
GrowArrow(vector1)
)
vector1.add_updater(
lambda m: m.become(
self.get_vector(alpha1.get_value()%1,helix1)
)
)
self.add(vector1,dot1)
self.play(alpha1.increment_value, 1, run_time=10, rate_func=linear)
self.play(FadeOut(vector1), FadeOut(dot1), FadeOut(number))
self.move_camera(phi=0* DEGREES,theta=90*DEGREES)
alpha1 = ValueTracker(0)
self.add(vector1,dot1)
self.play(alpha1.increment_value, 1, run_time=10, rate_func=linear)
def get_vector(self, proportion, curve):
vector = Line(np.array([0,0,0]), curve.point_from_proportion(proportion), color = YELLOW_C, buff=0)
return vector
|
