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
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
|
from manimlib.imports import *
class SineVectors(GraphScene):
CONFIG = {
"x_min": 0,
"x_max": 10,
"y_min": -5,
"y_max": 5,
"graph_origin": ORIGIN+4*LEFT,
"x_axis_width": 7,
"y_axis_height": 7,
}
def construct(self):
XTD = self.x_axis_width/(self.x_max - self.x_min)
YTD = self.y_axis_height/(self.y_max - self.y_min)
self.setup_axes(animate = True)
sine = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 0, x_max = 6.3, color = GREEN)
dot1 = Dot().rotate(PI/2).set_color(RED_C)
alpha1 = ValueTracker(0)
vector1 = self.get_vector(alpha1.get_value(),sine)
dot1.add_updater(lambda m: m.move_to(vector1.get_end()))
self.play(
ShowCreation(sine),
GrowFromCenter(dot1),
GrowArrow(vector1)
)
vector1.add_updater(
lambda m: m.become(
self.get_vector(alpha1.get_value()%1,sine)
)
)
self.add(vector1,dot1)
self.play(alpha1.increment_value, 1, run_time=5, rate_func=linear)
self.play(FadeOut(vector1), FadeOut(dot1), FadeOut(sine))
self.wait()
sine1 = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 0, x_max = 1.575, color = GREEN_C)
point1 = Dot().shift(self.graph_origin+np.pi*YTD*UP + 1.575*XTD*RIGHT)
point1_lab = TextMobject(r"$t = (\frac{\pi}{2})$", color = GREY).scale(0.6).next_to(point1, 0.5*UP)
vector1 = Arrow(self.graph_origin, self.graph_origin+np.pi*YTD*UP + 1.575*XTD*RIGHT, buff=0, color = RED_C, tip_length = 0.25)
vector1_lab = TextMobject(r"$r(\frac{\pi}{2})$", color = RED).scale(0.7).move_to(self.graph_origin+1.5*XTD*RIGHT+ 1.5*YTD*UP)
self.play(GrowArrow(vector1),Write(vector1_lab))
self.play(ShowCreation(point1), Write(point1_lab))
self.play(ShowCreation(sine1))
self.wait(1)
sine2 = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 1.575, x_max = 3.15, color = GREEN_C)
point2 = Dot().shift(self.graph_origin+3.15*XTD*RIGHT)
point2_lab = TextMobject(r"$t = (\pi)$", color = GREY).scale(0.6).next_to(point2, 0.5*UP+0.5*RIGHT)
vector2 = Arrow(self.graph_origin, self.graph_origin+3.15*XTD*RIGHT, buff=0, color = BLUE, tip_length = 0.25)
vector2_lab = TextMobject(r"$r(\pi)$", color = BLUE).scale(0.7).move_to(self.graph_origin+1.5*XTD*RIGHT+ 0.4*YTD*UP)
self.play(GrowArrow(vector2),Write(vector2_lab))
self.play(ShowCreation(point2), Write(point2_lab))
self.play(ShowCreation(sine2))
self.wait(1)
sine3 = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 3.15, x_max = 4.725, color = GREEN_C)
point3 = Dot().shift(self.graph_origin+np.pi*YTD*DOWN + 4.725*XTD*RIGHT)
point3_lab = TextMobject(r"$t = (\frac{3\pi}{2})$", color = GREY).scale(0.6).next_to(point3, 0.5*DOWN)
vector3 = Arrow(self.graph_origin, self.graph_origin+np.pi*YTD*DOWN + 4.725*XTD*RIGHT, buff=0, color = YELLOW_C, tip_length = 0.25)
vector3_lab = TextMobject(r"$r(\frac{3\pi}{2})$", color = YELLOW_C).scale(0.7).move_to(self.graph_origin+2.5*XTD*RIGHT+ 1*YTD*DOWN)
self.play(GrowArrow(vector3),Write(vector3_lab))
self.play(ShowCreation(point3), Write(point3_lab))
self.play(ShowCreation(sine3))
self.wait(1)
sine4 = self.get_graph(lambda x : np.pi*np.sin(x), x_min = 4.725, x_max = 6.3, color = GREEN_C)
point4 = Dot().shift(self.graph_origin+6.3*XTD*RIGHT)
point4_lab = TextMobject(r"$t = (2\pi)$", color = GREY).scale(0.6).next_to(point4, 0.5*UP+0.5*RIGHT)
vector4 = Arrow(self.graph_origin, self.graph_origin+6.3*XTD*RIGHT, buff=0, color = PURPLE, tip_length = 0.25)
vector4_lab = TextMobject(r"$r(2\pi)$", color = PURPLE).scale(0.7).move_to(self.graph_origin+4.5*XTD*RIGHT+ 0.4*YTD*DOWN)
self.play(GrowArrow(vector4),Write(vector4_lab))
self.play(ShowCreation(point4), Write(point4_lab))
self.play(ShowCreation(sine4))
self.wait(3)
self.play(FadeOut(sine1), FadeOut(point1), FadeOut(point1_lab), FadeOut(vector1), FadeOut(vector1_lab),
FadeOut(sine2), FadeOut(point2), FadeOut(point2_lab), FadeOut(vector2), FadeOut(vector2_lab),
FadeOut(sine3), FadeOut(point3), FadeOut(point3_lab), FadeOut(vector3), FadeOut(vector3_lab),
FadeOut(sine4), FadeOut(point4), FadeOut(point4_lab), FadeOut(vector4), FadeOut(vector4_lab))
def get_vector(self, proportion, curve):
vector = Arrow(np.array([-4,0,0]), curve.point_from_proportion(proportion), color = ORANGE, buff=0, tip_length = 0.25)
return vector
|
