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
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
|
from manimlib import *
from scipy import signal as sig
def square(t, slew_rate=.1):
t = t % 1
if t < .1:
return t * 1 / slew_rate
elif t < .5 - slew_rate / 2:
return 1
elif t < .5 + slew_rate / 2:
return 1 - (t - (.5 - slew_rate / 2)) * 1 / slew_rate
else:
return 0
class TimeDependentComplexPlane(ComplexPlane):
CONFIG = {
"dimension": 3,
"t_range": np.array([0., 5., 1.]),
"t_axis_config": {
"include_ticks": True,
},
"background_line_style": {
"stroke_color": GREY_D,
},
"depth": 8,
}
def __init__(self, **kwargs):
ComplexPlane.__init__(self, **kwargs)
t_axis = self.create_axis(self.t_range, self.t_axis_config, self.depth)
t_axis.rotate(-PI / 2, UP, about_point=ORIGIN)
t_axis.shift(self.n2p(0))
self.t_axis = t_axis
self.add(t_axis)
self.axes.add(t_axis)
def number_to_point(self, number, time=0):
return self.coords_to_point(number.real, number.imag, time)
def point_to_number(self, point, time=0):
return point[0] + 1j * point[1]
def n2p(self, number, time=0):
return self.number_to_point(number, time)
def get_t_axis(self):
return self.axes[2]
def get_graph(self, function, axis, t_range=None, **kwargs):
# sample range
s_range = np.array(self.t_range, dtype=float)
if t_range is not None:
s_range[:len(t_range)] = t_range
if t_range is None or len(t_range) < 3:
s_range[2] /= self.num_sampled_graph_points_per_tick
graph = ParametricCurve(
lambda t: self.t_axis.number_to_point(t) + axis.number_to_point(function(t)),
t_range=s_range,
**kwargs
)
graph.underlying_function = function
graph.t_range = t_range
return graph
def get_inphase_graph(self, function, **kwargs):
return self.get_graph(function, self.get_x_axis(), **kwargs)
def get_quadrature_graph(self, function, **kwargs):
return self.get_graph(function, self.get_y_axis(), **kwargs)
class QamModulation(Scene):
CONFIG = {}
def construct(self):
self.camera.frame.reorient(0, 0, 0)
# create a complex plane
cplane = TimeDependentComplexPlane()
self.play(ShowCreation(cplane))
# a complex number
dot = Dot(cplane.n2p(1 + 2j), color=GREEN)
number = DecimalNumber()
number.add_updater(lambda m: m.next_to(dot, RIGHT))
def update_nums(m):
x, y, z = dot.get_center()
num = cplane.p2n((x,y))
m.set_value(num)
number.add_updater(update_nums)
# create and move complex number around
self.play(ShowCreation(dot), ShowCreation(number))
self.play(dot.animate.move_to(cplane.n2p(-5+3j)), run_time=2)
self.play(dot.animate.move_to(cplane.n2p(-4-3j)), run_time=2)
# move the number according to a time dependend complex function
def signal_func(t):
real = -2 * np.cos(2 * t)
imag = 3 * (square(t / 2) - .5)
return real + 1j * imag
signal_func_at_zero = signal_func(0)
self.play(dot.animate.move_to(cplane.n2p(signal_func_at_zero)), run_time=2)
def dot_update_func(m, dt):
m.move_to(cplane.n2p(signal_func(m.time)))
m.time = m.time + dt / 2
dot.time = 0
dot.add_updater(dot_update_func)
self.wait(5)
# get out and show time dependence
self.play(self.camera.frame.animate.shift(2 * OUT))
# show functions
graph_y = cplane.get_inphase_graph(lambda t: signal_func(t).real, color=RED)
graph_x = cplane.get_quadrature_graph(lambda t: signal_func(t).imag, color=BLUE)
self.play(self.camera.frame.animate.reorient(-90, 90, 90))
self.play(ShowCreation(graph_x))
self.play(self.camera.frame.animate.reorient(0, 90, 90))
self.play(ShowCreation(graph_y))
self.play(self.camera.frame.animate.reorient(-100, 90, 90))
self.play(self.camera.frame.animate.rotate(40 * DEGREES, axis = UP))
# create arrow for complex value
dot.remove_updater(dot_update_func)
self.play(dot.animate.move_to(cplane.n2p(signal_func_at_zero)), run_time=2)
arr = Arrow(cplane.n2p(0), cplane.n2p(signal_func_at_zero))
self.play(ShowCreation(arr))
def arr_update_func(m, dt):
m.set_points_by_ends(
cplane.n2p(0, time=m.time),
cplane.n2p(signal_func(m.time), time=m.time)
)
m.time = m.time + dt / 2
dot.time = 0
arr.time = 0
dot.add_updater(dot_update_func)
arr.add_updater(arr_update_func)
self.wait(10)
self.play(*map(FadeOut, (arr, graph_x, graph_y)))
self.play(
self.camera.frame.animate.rotate(50 * DEGREES, axis = UP),
dot.animate.move_to(cplane.n2p(1+1j))
)
self.play(self.camera.frame.animate.shift(-2 * OUT))
dot.remove_updater(dot_update_func)
arr.remove_updater(arr_update_func)
# open an interactive IPython shell here
# self.embed()
|
