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
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
|
from manimlib.imports import *
class VectorFields(GraphScene):
CONFIG = {
"x_min" : -4,
"x_max" : 4,
"y_min" : -4,
"y_max" : 4,
"graph_origin": ORIGIN+2.5*LEFT,
"x_axis_width": 7,
"y_axis_height": 7,
"x_tick_frequency": 1,
"y_tick_frequency": 1,
"default_vector_field_config": {
"delta_x": .5,
"delta_y": .5,
"min_magnitude": 0,
"max_magnitude": 4,
"colors": [GREEN,GREEN,YELLOW,RED],
"length_func": lambda n: n/2.5,
"opacity": .75,
"vector_config": {
"stroke_width":6,
"max_stroke_width_to_length_ratio":4
},
},
"a":-3.5 ,"b": 4, "c": -3.5 ,"d": 4,
}
def construct(self):
X = RIGHT*self.x_axis_width/(self.x_max- self.x_min)
Y = UP*self.y_axis_height/(self.y_max- self.y_min)
self.X=X ;self.Y=Y
self.setup_axes(animate=False)
vector_function = lambda v: np.array([
(v[0]-self.graph_origin[0])*(v[1]-self.graph_origin[1]),
-(v[0]-self.graph_origin[0]),
0,
])
vector_field=self.get_vector_field(
vector_function,
colors= [GREEN]
)
self.show_points()
self.wait(.5)
self.show_func_machine()
self.wait(1)
self.produce_vectors(vector_field)
self.wait(.5)
self.scale_down_vectors(vector_function)
self.wait(2)
def show_points(self):
dn=1
x_vals=np.arange(self.a,self.b,dn)
y_vals=np.arange(self.c,self.d,dn)
dots=VGroup()
for x_val in x_vals:
for y_val in y_vals:
dot=Dot(
self.coords_to_point(x_val,y_val),
radius=.05,
color=TEAL,
)
dots.add(dot)
self.play(ShowCreation(dots, run_time=1))
self.dots=dots
def show_func_machine(self):
machine=RoundedRectangle(
height=2,
width=3.5,
color=PURPLE,
stroke_width=8
).to_edge(RIGHT, buff=.4)
machine_label=TexMobject(
r"\vec F=xy\hat i-x\hat j",
stroke_width=1.5,
).set_color_by_gradient(
*self.default_vector_field_config["colors"]
).next_to(machine,IN)
machine=VGroup(machine,machine_label)
self.add(machine)
self.func_machine=machine
def produce_vectors(self,vector_field):
count,i=3,0
self.run_time=1
non_scaled_vectors=VGroup()
for dot in self.dots:
if i==count:
self.run_time=.05
position=dot.get_center()
vect= vector_field.get_vector(position)
self.go_to_machine(dot)
self.take_vec_from_machine(vect,position)
non_scaled_vectors.add(vect)
i+=1
self.non_scaled_vectors=non_scaled_vectors
def go_to_machine(self,dot):
if self.run_time>.5:
self.play(ApplyMethod(
dot.next_to,
self.func_machine,4*UP,
),
run_time=self.run_time
)
self.dot=dot
def take_vec_from_machine(self,vect,position):
vect.next_to(self.func_machine,DOWN,buff=.1)
if self.run_time>.5:
point_coord=TexMobject(
"(x_i,y_i)"
).next_to(self.dot,RIGHT,buff= .01).scale(.75)
input_point=VGroup(point_coord, self.dot)
self.play(
ApplyMethod(
input_point.shift,DOWN,
run_time=self.run_time
)),
self.play(
FadeOut(input_point),
run_time=.2
)
self.play(
FadeIn(vect),
run_time=.4
)
else:
self.remove(self.dot)
self.add(vect)
self.wait(1.0/15)
self.play(
vect.move_to,position,
run_time=self.run_time
)
def scale_down_vectors(self,vector_function):
scale_down_text=TextMobject(
r"Vectors are rescaled\\ for clarity\\ and \\",
r"colors are used to \\ indicate magnitudes",
stroke_width=1.2
)
scale_down_text[0][:7].set_color(BLUE)
scale_down_text[1].set_color_by_gradient(
*self.default_vector_field_config["colors"]
)
scale_down_text.to_corner(UR).shift(DOWN)
scaled_vector_field= self.get_vector_field(
vector_function,
length_func= lambda norm : .75*sigmoid(norm)
)
for vector in self.non_scaled_vectors:
scaled_vect= scaled_vector_field.get_vector(vector.get_center())
vector.target= scaled_vect
self.play(FadeOut(self.func_machine))
self.play(Write(scale_down_text))
self.wait(1.2)
self.play(LaggedStartMap(
MoveToTarget, self.non_scaled_vectors,
run_time=3
))
def get_vector_field(self,func,**kwargs):
config = dict()
config.update(self.default_vector_field_config)
config.update(kwargs)
vector_field= VectorField(func,**config)
return vector_field
#uploaded by Somnath Pandit. FSF2020_Vector_fields
|
